13ｨｪｨ 0002ｨｪｨ 00ｨｦ1 702ｨｮｨｰｨｨｲ071 7ｨ 06ｨｦ02, ISSN

13ｨｪｨ 0002ｨｪｨ 00ｨｦ1 702ｨｮ050702 0709ｨｰｨｨｲ071 7ｨ 06ｨｦ02, ISSN 1992-6138 1 70306070302071 70307090303 07030209020703 1 7 03000009070807 01090803010908071 7030709030503 0300060903031 709020705 ｨｦ0302090803001 7 07 091 7060302070803001 7: 03030202 01090803010908071 7030709030503 0300060903031 709020705 07 040603071 7030603020705 117419 ｨｪ0307091 709, 0900. 01030207090905, 02. 37 0400091 7020208 0603020909080306 ｨｦ010908090702 1 7.ｨｪ. ｨｰ0302090901070302020905 0903000003050705 090302020900 ｨ.ｨｦ. 010306071 703020903 ｨｮ.ｨ. (030901030708070803001 7 0500091 702030503 060302090908030609) 010900031 70701090905 06.1 7. (03081 7030807081 70302020208 07030906030809061 7) 010900031 70701090708 ｨ.1 7. 0503010906031 7 ｨｮ.ｨｦ. 05030207080902080702031 7 06.06. 0503070803020903 ｨｦ.1 7. ｨｮ0900000702 ｨ.ｨｦ. 1 7 4 (52), 2009 05. c ｰｨｪ090803010908071 70307090303 0300060903031 709020703", 07030708091 70003020703, 2009 05. 03030202 01090803010908071 7030709030503 0300060903031 709020705 07 040603071 7030603020705, ｨｪ0307091 709, 2009 05. ｰｨｪ090803010908071 70307090303 0300060903031 709020703", 040306070302071 70307090303 07030209020703. ｨｲ09060305070708060706031 7090203 1 7 ｨｰ030709030104031 7090807 ｨｰ03, 0007010302030705 1 7 015955 0308 15.04.97. 1 70302040707090203 09 04031 7090807 30.12.2009 05. 050301041 708080306020208 0209000306 07 1 7030607080909, 090301041 708080306020905 05060904070909: ｨｮ. 0509000304031 7. ｨｹ09070403020708030602: 01091 70202031 7 01.ｨ., 0206010704090702 ｨｦ.ｨ., ｨｦ070803010702 01.06. 070804031 70908090203 1 7 08070403050609040707 ｨ 09090203010707 1 7020304020308 08030605031 70007, 05.ｨｪ0307091 709, 0900. 1 70902031 709070209, 02.4. 0700SS0301 4 04.00. 0007060900 1000 050903. 00030209 071 703000302020905.

13ｨｪ09080301090807070307090303 030006090303 ﾁ09020703 020906020900 0303020209 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 6 5 4 (52), 03090805000601 { 02030909000601 2009 05. ｨｮ030203060009020703 0107090607010705 07 0907070803000501 07060302020308 0409030002 ﾂ. 09. 010603030203 ﾁ. ｨｮ030101 0503030103080607070307090706 0309020907 2 02. ﾂ. 0803080307090903 ﾁ. 07 02030300060302070103070807 090605090103020809010707 040607 06030403020707 0708030603030103080607070307090706 0309020907 11 ｨｮ0809020302080901 07 04060304030209 ﾁ090803000501 0109080301090807070307090706 0704030107090001020307080308 ﾂ. 04. ｨｪ0308090203 ﾁ. ｨｮﾁ030203020703 030902090707 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301 09 0902090003050707020308 030902090703 07 0007020308020201 040902090107030209000301 19 ｨｦ03 07070803060707 01090803010908070907 ｨｨ030209 ｨｦ. ｨｪ. 090307. 07070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 24 01070300020303 04030703000703 ﾁ 00090602090003 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ. ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 (0406030203000003020703) 36 ｨｦ020403060109010705 69

130107090607010705 07 0907070803000501 07060302020308 0409030002 ｨｮ030101 0503030103080607070307090706 0309020907 ﾂ. 09. 010603030203 ﾁﾂ 070809080103 0609070701030806030202 0203030006030207010203 07 0203070809080307020203 09070003 ﾁ0705, 040607 09030803060206 03080603030907 GH, GL, HL (G 0803070909 0403060307030703020705 010302070902 080603090503000102070909, H 0803070909 0403060307030703020705 ﾁ02070308, L 0803070909 0403060307030703020705 00070707030908060707) 0409060900000300010202 070007 040306040302020709090005060202 0302020308 0703 070803060302 080603090503000102070909. ｨｦ070700030203 ﾁ09020703 040603 ﾁ0302030203 ﾁ0309080306020201 01030803020301. ｨｮ0809080108 0103000203 0707040300010303 ﾁ090801 0209 04090909000108090807 ﾁ- 020206 0309020508070506 0403 01090803010908070903, 09 0809090003 ﾁ 04060304070001020206 040703070903-0109080301090807070307090706 09000907070906. I. 0806030202070803060705 ﾂ 00090602090003 縺0803080302010709001 7 6 5 10, 2008 05., 0304090000070903 ﾁ090209 070809080105 ｨｬ. ｨ. 090309000301070403 ﾁ0308 罟ｲ0902090709 ﾂ03 ﾁ021 7. 01070003 ﾁ0703 030902090707 08090903 ﾁ03: 010902 03070806030905030001020208 0806030905030001020709, 07 0409070801 03080603030309 MN 070303020702050308 0803070909 0403060307030703-020705 030503 ﾁ02070308 07 080307090308 0403060307030703020705 00070707030908060707. ﾂ03030103000203 0007, 070803 03080603030309 MN 0309090003080705 040906090000030001020201 0302020308 0703 070803060302 080603090503000102070909? 02070007 0209, 0803 040607 0909090706 09070003- ﾁ070506? 050909 030503 ﾁ0207070700070801? 080302060300020303 06030403020703 030902090707 02090203 000303 04060701030203020705 ﾁ030908030603 ﾁ. 0506090707 ﾁ0203 0109080301090807070307090703 030902090707 0709070803 02030406030703 ﾁ0300010203 030904030107020908080705. 01020900030701 0209080807 04030603-000908 030902090709, 0406030200090509 ﾁ0409080705 0209 04070307070307090708 040909090001080308 ｨｪ0401 ﾁ 1966 05030209: 0103090903090801, 070803 03070007 0200070202 070803060302 080603090503000102070909 0300060903090808 0906070401030807070307090908 040603-05060307070708, 0803 0103020806 03090609000203070807, ﾁ0407070902020308 ﾁ 05080308 0806030905030001020709, 07 0803070909 0403060307030703-020705 030503 010302070902 0003000908 0209 040605010308, 040906090000030001020308 07060302020308 0403 0200070203 07080306030203 0806030905030001-02070909 (04. ﾂ. 01030603040303 ﾁ, ｨｪ. 05. 080308090403 ﾁ, 06. ｨｨ. ｨｰ030303 ﾁ, 縺08030703000703 0403 01090803010908070903 020005 0403070809040908060706 ﾁﾁ0903021 7, ｨｪ.: 縺06090909091 7, 1968, 07. 368). 020708030708 ﾁ03020203 ﾁ0303020709090308 080603080105 030902090709, ﾁ 09030803060308 04070509060706090808 0803070907 0403060307030703020705 ﾁ02070308 07 010302070902 080603090503000102070909. ｨｦ 030603 080607 030902090707, 050203 ﾁ0103070803 0409060900000300010203070807 040306040302020709090005060203070801. 06090007070703 0403070807 0309020907 07 03020203080704020201 07080003080301 0309070809 ﾁ00050308 070709090801 030207020208 0103080302 0706 06030403020705. ｨ 08090903 ﾁ0201 0103000308 00020801 080300010903 0300060708 0103080302. 080307090300010909 06030701 07020308 03 0409060900000300010203070807 07 04030604030202070909-0005060203070807, 0803 ﾁ02000706090301 05040403090807 ﾁ020208 ﾁ 05080706 07000907090506 ﾁ0309080306020208 0103080302. 000301 0003000303 070803 ﾁ030908030602 090003 0209 ﾁ0203 070309070908080705 ﾁ 07060302020308 0409030003. ﾂ03 ﾁ070306 03090209070906 07070403000103090301 030207020203 0300030302090703020705: 06 030608030103020806 080603090503000102070909 (0803070909 0403060307030703020705 030503 ﾁ02070308). G 0103020806030702 080603090503000102070909 (0803070909 0403060307030703020705 030503 010302070902). L 0103020806 ﾁ0407070902020308 ﾁ 0806030905030001020709 03090609000203070807 (0803070909 0403060307030703020705 030503 00070707030908060707). 0102070407010706090301 040306010900070603 ﾁ0907 07 06030403020705 0309020907. 0809060900000300010203070801 060907070109080607 ﾁ090301 0403 030802030403020708 09 07080306030203 ｨｨｮ = b 080603090503000102070909 ABC, a 040306040302020709090005060203070801 09 07080306030203 BC = a. ﾂ0309080306020208 0103080302 06030403020705 030802080201 0203 07030009 ﾁ00050308 0308 0300070001020206 080607050302030103080607070307090706 07 09000503-00060907070307090706 ﾁ02090009020309. ｨｰ0907070109080607 ﾁ0903010203 030902090707 ﾁ 0406070201070403 09030603080903 0203 0603040908080705. 08030508030109 ﾁ02-000706090301 縺03030003080908 07030603020702091 7: 0406070201070407090001020203 01030103020802 ﾁ020707070003020708 040607 ﾁ030205080705, 09 縺08030602070703070907031 7 0307080908080705 0707080908030008 ﾁ 090907030708 ﾁ03 0403000303020206 09040609000203020708. ﾂ030201 070708090801 0109080301090807070307090908 070809080108 0209-0203 07 09090609020209040301 ﾁ 0609090906! 2

13ｨｮ030101 0503030103080607070307090706 0309020907 3 II. ﾂ0309080306020905 04030601090009 ﾂ02 ﾁ03020301 04030601090009, ﾁ0307010109 0403000303020908 040607 06030403020707 010203050706 0503030103080607070307090706 0309020907, 090909 0400090207-0103080607070307090706, 080909 07 0708030603030103080607070307090706. 0809070801 ﾁ 080603090503000102070903 ABC 0703 070803060302090107 AB = c, AC = b, BC = a 0803070909 E 020906030207080705 0209 07080306030203 BC, 0803070909 D 0209 07080306030203 AB. ｨｦ03 ﾁ0307080202 030802030403020705 CE=EB = 1 07 AD=DB = 2. 07080603030907 AE 07 CD 040306030703090908080705 ﾁ 0803070903 F (0701. 060707. 1). 0003070909 O 0406030703 ﾁ030001020905 (0103000308 00020801 ﾁ 040003070903070807 080603090503000102070909, 09 0103000308 07 020308). 0809070801 e 1, e 2, e 3 030207020707020203 ﾁ030908030602, 07030209040609 ﾁ000302020203 ﾁ03090803060901 6ﾓ1 6ﾓ1 6ﾓ1 OA, OB, OC 07030308 ﾁ03080708 ﾁ03020203. 0003050209 07040609 ﾁ03020007 ﾁ09 04030601090009: 6ﾓ1 OF = 1 OA e 1 + 1 2 OB e 2 + 2 OC e 3 1 + 2 + 1 2 : (1) ｨｰ0707. 1 010309090309080300010708 ﾁ03. 070703 ﾁ07020203, 070803 OF 6ﾓ1 = OC e3 + CF. 6ﾓ1 6ﾓ1 0608030002 ﾁ02060903070801 ﾁ0309080306 CF, 02090203 0209080807 030802030403020703 CF=F D = x. 010005 07030503 07070403000103090301 04000306090201 090909 07 ﾁ03030503 06030209 01090803010908070703-07090708 07020708060901030208. ｨｮ03030207020701 0803070907 B 07 F 07 030003030209070701 04000306090207 080603090503000102070903 ﾁ: S CEF = S 1, S EBF = S 2, S BDF = S 3, S DAF = S 4, S ACF = S 5. 000909 090909 090909 04000306090201 ﾁ03000707070209 090202070807 ﾁ- 020905 07 04000306090207 080603090503000102070903 ﾁ 07 0300060308 ﾁ020703080308 030802030705080705 090909 0706 03070203 ﾁ09020705, 0803 0102 0406070603020701 09 07070708030103 090609 ﾁ0203020708: 61 S 1 = S 1 ; 2 S 4 6462 = S 2 ; 3 S 1 + S 5 = S 2 + S 3 + S 1 ; 4 6463 S 4 + S 5 = S 1 + S 2 + S 2 : 3 S 0506030103 08030503, 1 + S 2 = x 07 S 5 = x. 070807080209 0203080609020203 0403000907070801, 070803 x = 1(1 + 2 ). 0003050209 S 3 S 4 2 CF CD = x x + 1 = 1(1 + 2 ), 09 030209070708 6ﾓ1 CF = 1 (1 + 2 ) 6ﾓ16ﾓ1 CD. 0803 07 ﾁ03080708 ﾁ09 0007070703090806070702 1 + 2 + 1 2 1 + 2 + 1 6ﾓ1 2 080603090503000102070909, AD = 2 BD, 0700030203 ﾁ09080300010203, AD = 2 6ﾓ16ﾓ1 BD. 0603 6ﾓ1 AD = OC 6ﾓ1 6ﾓ1 6ﾓ16ﾓ1 6ﾓ16ﾓ1 6ﾓ16ﾓ1 6ﾓ1 6ﾓ1 6ﾓ1 OA + CD 07 BD = 6ﾓ1CD + OB 6ﾓ1 OC: ｨｦ03 08060306 040307000302020706 040306010900 0003050903 ﾁ02060903070801 ﾁ0309080306 6ﾓ16ﾓ1 CD: 6ﾓ1 6ﾓ1 6ﾓ1 6ﾓ16ﾓ1 OA + CD = 2 OB 6ﾓ1 (1 + 2 ) OC : 1 + 2

134 ﾂ. 09. 010603030203 ﾁ 6ﾓ1 CF = 1 6ﾓ1 6ﾓ1 6ﾓ1 OA + 1 2 OB 6ﾓ1 1 (1 + 2 ) OC ; 1 + 2 + 1 2 030809090209 07 090703080301 0609 ﾁ03020708 ﾁ 6ﾓ1 6ﾓ1 OA = OA e 1, OB = OB e2, OC 6ﾓ1 = OC e3, OF 6ﾓ1 = OF e3 + CF 6ﾓ1 0406070603020701 09 04030601090003 (1). ｨｮ03 ﾁ0103070807 ﾁ 0803070907 O 07 C, 04030009070701 07090708020208 070009070908 04030601090002 (1): 6ﾓ1 CF = 1 CA e 1 + 1 2 CB e 2 1 + 2 + 1 2 : (2) 03030601090009 (2) 0009020308 040607010302030209 040607 06030403020707 02070003070003020908060706 0309020907. III. 0809060900000300010203070801 000909 090909 ﾁ 070003020908060706 02070003 03090209070906 ﾁ020707070003020705 0300060908070102, 0803 0102 ﾁ040609 ﾁ03 0503 ﾁ0306070801 03 020303000603-0207010206 07 0203070809080307020206 09070003 ﾁ070506. ｨｲ0902090709 1. 0609080807 0203030006030207010203 07 0203070809080307020203 09070003 ﾁ0705 0409060900000300010203070807 03080603030909 GL 0302020308 0703 070803060302 080603090503000102070909. ｨｰ0707. 2 ｨｰ030403020703. ｨｮ01. 060707. 2. 010005 010302070902, 040603 ﾁ03020302020206 0703 ﾁ0306040702 A 07 C, 0701030301: 1 = 2 = 1, 0803050209 ﾁ 07070009 04030601090002 (2) CG 6ﾓ1 b e = 1 + a e 2. 010005 00070707030908060707, 040603 ﾁ03020302020206 0703 ﾁ0306040702 A 07 3 C 07030308 ﾁ03080708 ﾁ03020203 0701030301: 1 = b=c, 2 = b=a. 03030601090009 (2) 02090308: 6ﾓ1 CL = ab( e 1 + e 2 ) a + b + c. 080307090300010909 6ﾓ1 GL = 6ﾓ1 CL 6ﾓ1 CG, 6ﾓ1 0803 6ﾓ1 (2a 6ﾓ1 b 6ﾓ1 c)b GL = 3(a + b + c) e (2b 6ﾓ1 a 6ﾓ1 c)a 1 + 3(a + b + c) e 2: (3) 09070203, 070803 GL ｬ AC 6ﾍ2 6ﾓ1 GL ｬ e 1, 08. 03. 2b 6ﾓ1 a 6ﾓ1 c = 0, 030809090209 b = a + c 2. ｨｦ080909, 020005 08030503, 0708030002 03080603030309 GL 000200 04090609000003000302 0302020308 0703 070803060302 080603090503000102070909, 020303000603-02070103 07 02030708090803070203, 0708030002 07080306030202 080603090503000102070909 030006090303 ﾁ02 ﾁ090007 0906070401030807070307090908 04060305060307070708. 080607 05080301 0609030203070801 04060305060307070707 020300000209 00020801 0308000707020308 0308 02090005, 0702090703 ﾁ 070009070903 0609 ﾁ020307080306030202030503 080603090503000102070909 03080603030309 GL ﾁ02060300020903080705 ﾁ 0803070909. 070703 ﾁ07020203, 070803 03080603030309 GL 0203 0103000308 00020801 0409-0609000003000302 0207 0302020308 07080306030203 0609 ﾁ020300030206030202030503, 0203 0203 0609 ﾁ020307080306030202030503 080603090503000102070909. ｨｮ01. 060707. 3. 0603 090109000505 0300060203070807, 07070708090301 09 < b < 07. 0003050209 09050300 C 02090700030001040708. 06090603020701 cos C 0703 08030306030102 0903070702090703 ﾁ: ( ) c 2 = a 2 a + c 2 ( ) a + c + 6ﾓ1 2a cos C: 2 2 5a 6ﾓ1 3c ﾂ 0708030503 04030009070701: cos C =. ｨｮ00030203 ﾁ09080300010203, 040607 5a > 3c 0806030905030001020709 0009020308 03070806030905030001-4 020201, 040607 5a = 3c 04060501030905030001020201, 040607 5a < 3c 080904030905030001020201. ｨｦﾁ03 ﾁ070306 08060306 07000907090506 0609030203070803060302020701.

13ｨｮ030101 0503030103080607070307090706 0309020907 5 ｨｰ0707. 3 ｨｲ0902090709 2. 0609080807 0203030006030207010203 07 0203070809080307020203 09070003 ﾁ0705 0409060900000300010203070807 03080603030909 GH 0302020308 0703 070803060302 080603090503000102070909. ｨｰ0707. 4 ｨｰ030403020703. ｨｮ01. 060707. 4. ﾂ0309080306 CG 6ﾓ1 b e = 1 + a e 2 3 ﾁ03020302020206 0703 ﾁ0306040702 A 07 C, 07030308 ﾁ03080708 ﾁ03020203 0701030301: 03030601090009 (2) 02090308: 1 = ctg C ctg B ; ﾁ020609000302 ﾁ 040306 ﾁ0308 030902090703. 010005 ﾁ02070308, 040603-2 = ctg A ctg B : 6ﾓ16ﾓ1 CH = b ctg B ctg C e 1 + a ctg A ctg C e 2 : 080607 05080301 0102 ﾁ0307040300010303 ﾁ0900070701 0003050903 020309090302 ﾁ0903010201 08030002030708 ﾁ0301: ctg A ctg B + ctg A ctg C + ctg B ctg C = 1; (4) 050203 A, B, C 09050002 080603090503000102070909 ABC. 080307090300010909 6ﾓ16ﾓ1 GH = 6ﾓ16ﾓ1 CH 6ﾓ1 6ﾓ1 6ﾓ16ﾓ1 GH = b ( ctg B ctg C 6ﾓ1 1 ) e 3 1 + a CG, 0803 ( ctg A ctg C 6ﾓ1 1 3 ) e 2 : (5)

136 ﾂ. 09. 010603030203 ﾁ 09070203, 070803 GH ｬ AC 6ﾍ2 6ﾓ16ﾓ1 GH ｬ e 1, 08. 03. ctg A ctg C = 1=3, 070007 tg A tg C = 3. ｨｦ080909, 020005 08030503, 0708030002 03080603030309 GH 000200 04090609000003000302 0302020308 0703 070803060302 080603090503000102070909, 0203-0300060302070103 07 02030708090803070203, 0708030002 0406030703 ﾁ030203020703 0809020503020703 ﾁ 09050003 ﾁ, 04060700030009060706 09 05080308 07080306030203, 00020003 0609 ﾁ0203 08060301. 080607 05080301 090900020208 0703 09050003 ﾁ 03080007070302 0308 60 71, 0702090703, ﾁ 070009070903 0609 ﾁ020307080306030202030503 080603090503000102070909, 03080603030309 GH ﾁ02060300020903080705 ﾁ 0803070909. 070703 ﾁ07020203, 070803 03080603030309 GH 0203 0103000308 00020801 04090609000003000302 0207 0302020308 07080306030203 0609 ﾁ020300030206030202030503, 0203 0203 0609 ﾁ020307080306030202030503 080603090503000102070909 (0701. 060707. 3). 000909 090909 tg A tg C > 0, 0803 09050002 A 07 C 030708060203. 080300030007 ﾁﾁ 04030601090003 (4) ctg A ctg C = 1=3, 020908020301, 070803 ctg B = 2 3(ctg A + ctg C) > 0: ｨｲ0209070708 07 09050300 B 030708060208. 0003050209 ABC 0609030203070803060302020708 03070806030905030001020208. ｨｲ0902090709 3. 0609080807 0203030006030207010203 07 0203070809080307020203 09070003 ﾁ0705 0409060900000300010203070807 03080603030909 LH 0302020308 0703 070803060302 080603090503000102070909. ｨｰ030403020703. 000909 090909 LH 6ﾓ1 6ﾓ1 6ﾓ16ﾓ1 = LG + GH, 0803 ﾁ 07070009 040306010900 (3) 07 (5) 0701030301: 6ﾓ1 LH = b ( ctg B ctg C 6ﾓ1 a 2p ) e 1 + a 09070203, 070803 LH ｬ AC 6ﾍ2 6ﾓ1 LH ｬ e1, 08. 03. ctg A ctg C = b=2a, 070007 ｨｦ080909, ( ctg A ctg C 6ﾓ1 b 2p ) e 2 : (6) tg A tg C = 2p b : (7) 020005 08030503, 0708030002 03080603030309 LH 000200 04090609000003000302 0302020308 0703 070803060302 080603090503000102070909, 0203-0300060302070103 07 02030708090803070203, 0708030002 0406030703 ﾁ030203020703 0809020503020703 ﾁ 09050003 ﾁ, 04060700030009060706 09 05080308 07080306030203, 00020003 0609 ﾁ0203 040306070103080609 080603090503000102070909, 020300030202030109 0209 050809 07080306030209. 080607 05080301 090900020208 0703 09050003 ﾁ 03080007070302 0308 60 71, 0702090703 ﾁ 070009070903 0609 ﾁ020307080306030202030503 080603090503000102070909 0308-0603030309 LH ﾁ02060300020903080705 ﾁ 0803070909. 0803090900070803 0709010307080305080300010203, 070803 03070007 0403000300070801 ﾁ 0609 ﾁ03020708 ﾁ03 (7) 03020702 0703 09050003 ﾁ 0609 ﾁ020201 60 71, 0803 07 020609050308 0009020308 0609 ﾁ020201 60 71. 070703 ﾁ07020203, 070803 03080603030309 LH 0203 0103000308 00020801 04090609000003000302 0207 0302020308 07080306030203 0609 ﾁ020300030206030202030503, 0203 0203 0609 ﾁ020307080306030202030503 080603090503000102070909 (0701. 060707. 3). 000909 090909 tg A tg C > 0, 0803 09050002 A 07 C 030708060203. ｨｲ0901030207 ﾁﾁ 04030601090003 (4) ctg A ctg C = b=2a, 020908020301, 070803 a + c ctg B = 2p(ctg A + ctg C) > 0: ｨｲ0209070708 07 09050300 B 030708060208. 0003050209 ABC 0609030203070803060302020708 03070806030905030001020208. 0707080900070701, 030202090903, ﾁ0307010109 0203030006030207010203 ﾁ020707070003020705. ｨｲ090609020303 0203030703 ﾁ07020203, 070803 090609 ﾁ0203020703 (7) 0701030308 06030403020705. ｨ 090609 ﾁ0203020703 tg A tg C = 3 0703 ﾁ0803060308 030902090707 0701030308 06030403020705 ﾁ0203 ﾁ070509030503 0703010203020705. 08030508030109 07 ﾁ03020301 090609 ﾁ0203020703 (7) 09 08060705030203010308060707030709030109. ｨｦ01030301: 2p b = a + b + c 2R(sin A + sin B + sin C) = = b 2R sin B 2 sin A+C = 2 cos A6ﾓ1C 2 + 2 sin A+C 2 sin A+C 2 cos A+C 2 (sin A + sin C) + sin(a + C) = sin(a + C) 2 cos A6ﾓ1C = 2 + cos A+C 2 cos A+C 2 2 cos A+C = 2 cos A 2 cos C 2 cos A 2 cos C 2 6ﾓ1 sin A 2 sin C 2 = = 2 1 6ﾓ1 tg A 2 tg C : 2

13ｨｮ030101 0503030103080607070307090706 0309020907 7 02070007 040607010302070801 04030601090002 tg A = 2 tg A 2 1 6ﾓ1 tg 2 A ; tg C = 2 tg C 2 2 1 6ﾓ1 tg 2 C 2 07 03000303020907070801 tg C 2 = x, tg A 2 = t (07070708090301 t 04090609010308060301) 0803 090609 ﾁ0203020703 (7) 040607 ﾁ030207080705 09 ﾁ070209 (3t 2 6ﾓ1 1)x 2 6ﾓ1 2tx + (1 6ﾓ1 t 2 ) = 0: (8) 000909 090909 ABC 03070806030905030001020208, 0803 0 < t < 1 07 0 < x < 1. 02070007 t = 1= ﾌ 3 6ﾍ2 A = 60 71, 0803 090609 ﾁ0203020703 (8) 0708090203 ﾁ07080705 0007020308020201, 07010308060701 090306030201 x = 1= ﾌ 3 6ﾍ2 C = 60 71. 0009090701 03000609030301 0403000907090301 0609 ﾁ0203070803060302020708 0806030905030001020709 07 ﾁ02060300020302020201 ﾁ 0803070909 0308060303090301 LH. 02070007 t ﾙ 1= ﾌ 3, 0803 020707090607010702090208 09 ﾁ090206090802030503 090609 ﾁ0203020705 (8) 0403000300070803000302 040607 0008000301 t, 070803 0500030103020809060203 040603 ﾁ03060503080705. 0503060207 090609 ﾁ0203020705 (8) 03070801: x 1 = t + ﾌ 3t 4 6ﾓ1 3t 2 + 1 3t 2 6ﾓ1 1 ; x 1 = t 6ﾓ1 ﾌ 3t 4 6ﾓ1 3t 2 + 1 3t 2 : 6ﾓ1 1 02070007 0 < t < 1= ﾌ 3, 0803 0403 08030306030103 ﾂ07030809 x 1 < 0; x 2 > 0. 06030609 ﾁ03020708 ﾁ03 x 2 < 1 040607 ﾁ030207080705 09 ﾁ070209 t(1 6ﾓ1 t)(1 6ﾓ1 3t 2 ) > 0, 070803 ﾁ03060203 040607 0008000301 0 < t < 1= ﾌ 3. 02070007 1= ﾌ 3 < t < 1, 0803 0403 08030306030103 ﾂ07030809 x 1 > 0; x 2 > 0. 06030609 ﾁ03020708 ﾁ03 x 1 < 1 040607 ﾁ030207080705 09 ﾁ070209 t(1 6ﾓ1 t)(1 6ﾓ1 3t 2 ) > 0, 070803 0203 0701030308 0103070809 0207 040607 0302020301 1= ﾌ 3 < t < 1. 06030609 ﾁ03020708 ﾁ03 x 2 < 1 040607 ﾁ030207080705 09 ﾁ070209 t(1 6ﾓ1 t)(1 6ﾓ1 3t 2 ) < 0, 070803 ﾁ03060203 040607 0008000301 1= ﾌ 3 < t < 1. ｨｮ00030203 ﾁ09080300010203, 090609 ﾁ0203020703 (8) 0701030308 06030403020703 x = t 6ﾓ1 ﾌ 3t 4 6ﾓ1 3t 2 + 1 3t 2 : 6ﾓ1 1 IV. 080306040302020709090005060203070801 000909 090909 ﾁ 0609 ﾁ0203000302060302020301 080603090503000102070903 ﾁ0207030809, 040603 ﾁ03020302020905 09 03070203 ﾁ09020708, 05 ﾁ000503080705 03020203- ﾁ06030103020203 0103020709020308 07 000707070309080607070308, 0803 0609 ﾁ02030003020603020203070801 080603090503000102070909 05 ﾁ000503080705 0203070809080307020201 09070003 ﾁ070301 040306040302020709090005060203070807 09090002030503 0703 03080603030903 ﾁ GL, GH, LH 03070203 ﾁ09020708 080603090503000102070909 (0701. 060707. 3). 08030508030109 02070003 07060301 02030609 ﾁ0203000302060302020203 080603090503000102070907, 03000009020908060703 07030308 ﾁ03080708 ﾁ090806070107 07 ﾁ03080708 ﾁ090107. ｨｲ0902090709 4. ｨｮ0906030708 ﾁ090308 0007 02030609 ﾁ0203000302060302020208 0806030905030001020709, ﾁ 09030803060301 03080603030309 GL 040306040302-020709090005060302 0302020308 0703 070803060302 080603090503000102070909?

138 ﾂ. 09. 010603030203 ﾁｨｰ0707. 5 ｨｰ030403020703. ｨｮ01. 060707. 5. 09070203, 070803 GL ﾍ BC 6ﾍ2 6ﾓ1 GL e 2 = 0. 080607010302050301 04030601090009 (3) 07 090703080301 08030503, 070803 e 1 e 2 = cos C = (a 2 + b 2 6ﾓ1 c 2 )=2ab: (b 3 6ﾓ1 c 3 ) + (3a 2 c 6ﾓ1 3a 2 b) + (2ac 2 6ﾓ1 2ab 2 ) + (b 2 c 6ﾓ1 bc 2 ) = 0; (b 6ﾓ1 c)(b 2 + bc + c 2 ) 6ﾓ1 3a 2 (b 6ﾓ1 c) 6ﾓ1 2a(b 6ﾓ1 c)(b + c) + bc(b 6ﾓ1 c) = 0; (b 6ﾓ1 c) ( (b + c) 2 6ﾓ1 2a(b + c) 6ﾓ1 3a 2) = 0; (b 6ﾓ1 c)(b + c + a)(b + c 6ﾓ1 3a) = 0: 000909 090909 b ﾙ c, 0803 b + c = 3a. ｨｦ080909, 020005 08030503, 0708030002 03080603030309 GL 000200 040306040302020709090005060302 0302020308 0703 070803060302 02030609 ﾁ0203000302060302-02030503 080603090503000102070909, 02030300060302070103 07 02030708090803070203, 0708030002 090806030302020905 07080306030209, 09 09030803-060308 040306040302020709090005060302 03080603030309 GL, 00020009 0609 ﾁ0209 0709010103 02 ﾁ0906 020609050706 070803060302. 0603 090109000505 0300060203070807, 07070708090301, 070803 b < c. 0003050209 c 02090700030001040905 07080306030209 080603090503000102070909 ABC, 070003 08090903 ﾁ0308 05 ﾁ0203 0203 0103000308 00020801 07080306030209 BC = a. 0803 08030306030103 0903070702090703 ﾁ 02090603020701 cos C = (a 2 + b 2 6ﾓ1 c 2 )=2ab, 050203 C 02090700030001040708 09050300 080603090503000102070909. 080607 a = (b + c)=3 04030009070701 cos C = (5b 6ﾓ1 4c)=3b. ｨｮ00030203 ﾁ09080300010203, 040607 5b > 4c 0806030905030001020709 0009020308 03070806030905030001020201, 040607 5b = 4c 04060501030905030001020201, 040607 5b < 4c 080904030905030001020201. ｨｦﾁ03 ﾁ070306 08060306 07000907090506 0609030203070803060302020701. ｨｲ0902090709 5. ｨｮ0906030708 ﾁ090308 0007 02030609 ﾁ0203000302060302020208 0806030905030001020709, ﾁ 09030803060301 03080603030309 GH 040306040302-020709090005060302 0302020308 0703 070803060302 080603090503000102070909? ｨｰ030403020703. 09070203, 070803 GH ﾍﾂｨｮ 6ﾍ2 6ﾓ16ﾓ1 GH e 2 = 0. 080607010302050301 04030601090009 (5) 07 090703080301 08030503, 070803 e 1 e 2 = cos C: ( b ctg B ctg C 6ﾓ1 1 ) ( cos C + a ctg A ctg C 6ﾓ1 1 ) = 0: 3 3 0803 08030306030103 070702090703 ﾁ a = 2R sin A, b = 2R sin B. 0107070802 ﾁ090301, 070803 A = 180 71 6ﾓ1 (B + C) 07 0309010302050301 09030809020503020702 0209 030802030403020705 0903070702090703 ﾁ 09 07070209070901. ﾂ 06030309000108090803 04030009070701: ( 1 sin B 3 ) ( cos B cos C 1 cos(b + C) 6ﾓ1 cos C + sin(b + C) + sin B sin C 3 sin(b + C) cos C ) = 0: sin C

13ｨｮ030101 0503030103080607070307090706 0309020907 9 080607 ﾁ03020701 09 030006030109 0302090103020908030008, 060907090602 ﾁ090301 070903000907, 0907070802 ﾁ090301, 070803 cos(b + C) = = cos B cos C 6ﾓ1 sin B sin C. ｨｦ01030301: 1 sin C(2 sin B cos C + sin C cos B) + cos C(cos B cos C 6ﾓ1 sin B sin C 6ﾓ1 cos B cos C) = 0; 3 1 sin C(sin C cos B 6ﾓ1 sin B cos C) = 0; sin C sin(c 6ﾓ1 B) = 0: 3 000909 090909 B 07 C 09050002 080603090503000102070909, 0803 B = C 6ﾍ2 b = c. ｨｦ080909, 02030609 ﾁ0203000302060302020208 0806030905030001020709, ﾁ 09030803060301 03080603030309 GH 040306040302020709090005060302 0302020308 0703 070803060302, 0203 070906030708 ﾁ090308. ｨｲ0902090709 6. ｨｮ0906030708 ﾁ090308 0007 02030609 ﾁ0203000302060302020208 0806030905030001020709, ﾁ 09030803060301 03080603030309 LH 040306040302-020709090005060302 0302020308 0703 070803060302 080603090503000102070909? ｨｰ030403020703. 09070203, 070803 LH ﾍ BC 6ﾍ2 LH 6ﾓ1 e2 = 0. 080607010302050301 04030601090009 (6) 07 090703080301 08030503, 070803 e 1 e 2 = cos C: ( ) ( ) cos B cos C b cos C sin B sin C 6ﾓ1 sin A cos A cos C + a sin A + sin B + sin C sin A sin C 6ﾓ1 sin B = 0: sin A + sin B + sin C 0803 08030306030103 070702090703 ﾁ 09 = 2R sin A, b = 2R sin B. ｨｦ0709000807090301 09050300 A = 180 71 6ﾓ1 (B + C): ( ) cos B cos C sin B sin(b + C) cos C 6ﾓ1 6ﾓ1 sin C sin(b + C) + sin B + sin C 0806030300060903090301 0300060303 020005 0300030706 070903000309 ﾁ0206090003020703: sin B sin(b + C) sin(b + C) + sin B + sin C = 08030700030203 ﾁ09080300010203 0701030301: cos C ( 6ﾓ1 2 sin B 2 cos B 2 2 sin B+C cos ( cos(b + C) cos C sin C + 2 sin B+C 2 cos B+C 2 2 + 2 sin B+C 2 cos B6ﾓ1C = 2 cos B+C 2 = 2 sin B 2 cos B 2 B+C = 2 sin B 2 cos B 2 cos B+C 2 + cos B6ﾓ1C 2 cos B cos C 6ﾓ1 2 sin B 2 sin C 2 cos B + C 2 6ﾓ1 2 sin B 2 sin C 2 cos B + C 2 6ﾓ1 4 sin B 2 sin C 2 cos B + C 2 6ﾓ1 4 sin B 2 sin C 2 cos B + C 2 4 sin B 2 sin C 2 cos C 2 sin B 2 sin C 2 cos C 2 sin B 2 sin C 2 cos C 2 ( ) 6ﾓ1 ( 6ﾓ1 ) sin B sin(b + C) = 0: sin(b + C) + sin B + sin C 2 cos B 2 cos C 2 cos B+C 2 = sin B 2 cos B+C 2 cos C : 2 cos(b + C) cos C + 2 sin B 2 sin C 2 cos B + C 2 (1 + cos C) + cos B cos 2 C 6ﾓ1 cos(b + C) cos C = 0; cos 2 C + cos C(cos B cos C 6ﾓ1 cos B cos C + sin B sin C) = 0; 2 cos 2 C cos C = 0; 2 + 4 sin B 2 cos B 2 sin C 2 cos C 2 cos B 2 cos C 6ﾓ1 cos C 2 cos B + C ) = 0; 2 ( ) ( ) B B cos 2 + C + cos 2 6ﾓ1 c 6ﾓ1 cos B ( )) B 2 6ﾓ1 cos 2 + C = 0; ( ( ( ) B cos 2 6ﾓ1 C cos B 2 ) = 0; sin B 2 cos C 2 sin2 B 6ﾓ1 C 2 000909 090909 B 07 C 09050002 080603090503000102070909, 0803 ﾂ = C 6ﾍ2 b = c. ｨｦ080909, = 0: ) = 0;

1310 ﾂ. 09. 010603030203 ﾁ 02030609 ﾁ0203000302060302020208 0806030905030001020709, ﾁ 09030803060301 03080603030309 LH 040306040302020709090005060302 0302020308 0703 070803060302, 0203 070906030708 ﾁ090308. V. 0809060900000300010203070801 07 040306040302020709090005060203070801 020708030708 ﾁ03020203 0309020908010705 ﾁ03040603070301: 09 0103000308 0007 0909090308-00070003 0703 03080603030903 ﾁ: GL, GH, LH 00020801 04090609000003000302 0302020308 07080306030203 080603090503000102070909 07 040306040302020709090005060302 020609050308? ﾂ 030802030403020707 03080603030903 ﾁ GH 07 LH 0308 ﾁ0308 03080607010908030001020208. ﾂ030201 0409060900000300010203070801 09090002030503 0703 02 ﾁ0906 040307000302020706 03080603030903 ﾁ 0302020308 0703 070803060302 080603090503000102070909 ﾁ03030103000209 080300010903 ﾁ 03070806030905030001020301 080603090503000102070903. ｨｹ0803 090708090203 ﾁ00030203 ﾁ 03090209070906 2 07 3. ｨ 07070903010208 0806030905030001020709 020300000302 00020801 04060501030905030001020201. ｨｲ0902090709 7. ｨｮ0906030708 ﾁ090308 0007 0806030905030001020709, ﾁ 09030803060301 03080603030309 GL 04090609000003000302 0302020308 030503 07080306030203 07 040306040302020709090005060302 020609050308? ｨｰ030403020703. ﾂ 040306 ﾁ0308 030902090703 090708090203 ﾁ00030203, 070803 GL ｬ b 6ﾍ2 a + c = 2b. ﾂ 070308 ﾁ0306080308 030902090703 090708090203 ﾁ00030203, 070803 GL ﾍ a 6ﾍ2 b + c = 3a. ｨｦ01030301 07070708030109 090609 ﾁ0203020708: { a + c = 2b; b + c = 3a 07 030703 ﾁ0702020201 0603040302070301: b = 4a=3, c = 5a=3. ｨｲ0209070708, a : b : c = 3 : 4 : 5 (0701. 060707. 6). ｨｦ080909, ｨｰ0707. 6 03080603030309 GL 04090609000003000302 0302020308 07080306030203 080603090503000102070909 07 040306040302020709090005060302 020609050308 030503 07080306030203 0803050209 07 080300010903 0803050209, 0903050209 0806030905030001020709 04030203000302 0305070403080709030109 0407040905030603 ﾁ09 080603090503000102070909 0703 070803060302090107 3, 4, 5. 010902020208 0806030905030001020709 000200 0703 ﾁ0307080302 020603 ﾁ020701 030507040805020901 07 ﾁ020403 07030802060306 0802070507 000308 0209030902. 0603070103-080605 0209 050803, 070308070907 09020900030701 0209080807 0203 ﾁ0303 03090103070908030001020303 07 ﾁ03080708 ﾁ03 0508030503 0309010307090803000102030503 0806030905030001-02070909! 010603030203 ﾁﾂ0709080306 090306070703 ﾁ0707, 05. ｨｰ0503090201.

1307 02030300060302070103070807 090605090103020809010707 040607 06030403020707 0708030603030103080607070307090706 0309020907 02. ﾂ. 0803080307090903 ﾁﾂ 070809080103 0300060906030203 ﾁ02070109020703 0209 02030300060302070103070801 00030507070307090308 090605090103020809010707 040607 0707040300010303 ﾁ09-020707 ﾁ 06030403020707 0708030603030103080607070307090308 030902090707 030703 ﾁ0702020206 0703 0909060807020907" 0409090803 ﾁ: 0409060900000300010203070807 070007 040306040302020709090005060203070807 020309030803060206 040605010206, 040605010308 07 040003070903070807, 02 ﾁ0906 04000307090307080308 07 08.04. 080607 ﾁ0302030202 03000609030102 0809090308 090605090103020809010707 0209 04060701030603 06050209 0309020907. 080607 06030403020707 0708030603030103080607070307090706 0309020907 0907090607030705, 03070203 ﾁ02 ﾁ09050701 0209 0209050005020203070807 07 縺030703 ﾁ07020203-0708071 7 060907070109080607 ﾁ0903010308 0503030103080607070307090308 縺09090608070209071 7, 0103050908 ﾁ020709090302 ﾁ090801 090909 07020809070807 ﾁ0203 ﾁ0306020203, 080909 07 0203 ﾁ0306020203 0908 ﾁ0306000203020705. 0603 02090003 ﾁ 080301 070009070903, 0903050209 050807 0908 ﾁ0306000203020705 ﾁ03060202, 090900020303 0703 020706 07000302090308 090306060309080203 030003070203 ﾁ090801. ｨｬ0305070703070907 0203030003070203 ﾁ0902020303 06030403020703, 02090003 040607 000303030407000307020206 ﾁ02070707000302070506 07 040300090703020707 ﾁ030602030503 0308 ﾁ030809, ﾁ0003070308 0309 0703000308 0702070003020703 03010302030702030503 0009000009. 010005 040300090703020705 ﾁ020703090308 030103020907 0309 06030403020703 0708030603030103080607070307090308 030902090707 0907090607080705 020300000302 ﾁ02-0609000308090801 090103020703 000207080603 07 040609 ﾁ0700010203 07030300060900090801 040705090602, 0309020902020203 ﾁ 09070003 ﾁ0707 030902090707, 07 090306-060309080203 030003070203 ﾁ02 ﾁ090801 090900020303 0908 ﾁ0306000203020703, 040305 ﾁ0005080603030705 040607 0303 06030403020707. ﾂ 020902020308 070809080103 040607 ﾁ030205080705 020309030803060203 010308030207070307090703 060309030103020209010707 0403 ﾁ0206090003080903 09 090709-0607060705 0209 ﾁ020903 ﾁ 090306060309080203 030003070203 ﾁ02 ﾁ090801 090909 縺040905071 7 04030708060303020705 020900020308 020005 06030403020705 030902090707 040705090602, 080909 07 0908 ﾁ0306000203020705, ﾁ03030207090908060703 040607 0303 06030403020707. 0107090607010705 02030300060302070103 04030102070801, 070803 03070007 03070203 ﾁ0902070301 020909000302020308 040607030102 070009000708 040609 ﾁ070001-020208 ｨｪｨｰ05, 09 ﾁ030604070209 ｨｪ 1 ﾁ03060602030503 03070203 ﾁ09020705 04060303090807060903080705 ﾁ 0103020806 0508030503 080603090503000102070909, 0803 07020907090009 0209000203 040307080603070801 0703030006090003020703 080603090503000102070909 ｨｪｨｰ 05 07 030503 010302080609 07. ｨｲ09080301 0209 0009-0703, 040603 ﾁ03020302020301 0703 0803070907 07 040306040302020709090005060203 040003070903070807 ｨｪｨｰ05, ﾁ020006090801 0803070909 M 1, 0403070003 07030503 0309 ﾁ030604070801 04030708060303020703 ﾁ03060602030503 03070203 ﾁ09020705 040607030102 07 040603 ﾁ03070807 0303 00030903 ﾁ0203 0603000609. 080607 05080301 0203- ﾁ070207010203 0603000609 07000302090308 040603 ﾁ03070807 040806070603 ﾁ020107 00070207050107. ｨｮ 0703030006090003020705 03070203 ﾁ09020705 07000302090308 0209070702090801 0703030006090003020703 020609050706 020909000302020206 0406070301 07090708020206 ﾁ070203 ﾁ. ｨｰ090707010308060701, 0209040607010306, 06030403020703 070003020908060308 030902090707. ｨｲ0902090709 1. 07070203 ﾁ0902070301 020909000302020308 040607030102 ｨﾂｨｮｨ 1 B 1 C 1 070009000708 040609 ﾁ070001020208 0806030905030001020709 ｨﾂｨｮ, 07080306030209 0903080306030503 0609 ﾁ0209 8. ﾂ030604070209 A 1 04060303090807060903080705 ﾁ 0103020806 02070002030503 03070203 ﾁ09020705, 040607 05080301 0603000603 A 1 ｨ 0703070809 ﾁ00050308 0703 0708030603020308 ｨﾂ 03070203 ﾁ09020705 09050300 ﾁ 45 71. 06090802070803 04000306090201 00030903 ﾁ0308 0403 ﾁ0306060203070807 07 0300080301 05080308 040607030102. ｨｰ030403020703. 0809070801 0803070909 07 0103020806 040609 ﾁ07000102030503 080603-090503000102070909 ｨﾂｨｮ (060707. 1), 030209070708, 03080603030907 ｨｨｪ, ﾂ05 07 ｨｮ06 05 ﾁ000508080705 030503 ﾁ02070308090107. 0003050209 0403 08030306030103 03 08060306 04030604030202070909-0005060906 03080603030907 A 1 06 07 A 1 05 040306040302020709090005060202 07030308 ﾁ03080708 ﾁ03020203 ｨﾂ 07 ｨｨｮ, 04030508030109 030207 05 ﾁ000508080705 ﾁ02070308090107 050609020308 07030308 ﾁ0308-0708 ﾁ03020203 ｨ A 1 B 1 B 07 ｨ A 1 ｨｮ 1 ｨｮ. 080607070301, A 1 06 = A 1 05 (090909 0209-09000302020203, 07010308060703 0609 ﾁ020203 0406030309010707 0706 07 0705). ｨｹ0803 03030209-07090308, 070803 04060501030905030001020203 080603090503000102070907 A 1 ｨ 06 07 A 1 ｨ 05 0609 ﾁ- 0202, 030809090209 07000302090308: ﾏA 1 ｨ 05 = ﾏA 1 ｨ 06 = 45 71. ｨｮ00030203 ﾁ09080300010203, 050807 080603090503000102070907 0609 ﾁ0203000302060302020203 04060501030905030001020203, 0403050803-0109 A 1 06 = A 1 05 = 0;5ｨﾂ = 0;5 8 = 4. ｨｲ0209070708, S AA1 C 1 C = ｨｨｮ A 1 05 = 8 4 = 32. ｨ 020900030507070203, S AA1 B 1 B = ｨﾂ A 1 06 = 32. 01030909000301, 070803 0506090201 ﾂﾂ 1 ｨｮ 1 ｨｮ 04060501030905030001020709 07 020908020301 0303 04000306090201 S BB1 C 1 C. ﾂ 0709010301 02030003, 0701030301: A 1 07 ﾍ (ｨﾂｨｮ) 6ﾍ0 A 1 07 ﾍﾂｨｮ (0403 ｨｰ0707. 1. 0304060302030003020708 040605010308, 04030604030202070909000506020308 040003070903070807); ｨｨｪﾍﾂｨｮ. ｨｲ0209070708, ﾂｨｮﾍ (A 1 ｨｨｪ) (0403 11

1312 02. ﾂ. 0803080307090903 ﾁ 0406070302090909 040605010308 07 040003070903070807) 6ﾍ0 ﾂｨｮﾍ A 1 ｨ (0403 0304060302030003020708 040605010308, 04030604030202070909000506020308 04000307-0903070807). 0109000303, 080909 090909 A 1 ｨｬ ( ﾂ 1 ｨｮ 1 ｨｮ), 0803 040605010905 ｨｰｨｪ = ( ﾂ 1 ｨｮ 1 ｨｮ) ﾉ (A 1 ｨｨｪ) 0409060900000300010209 A 1 ｨ (0403 08030306030103 03 0007020707 0403060307030703020707 02 ﾁ0906 04000307090307080308, 03020209 0703 09030803060206 0406030603020708 0703060303 040605010908, 0409060900-00030001020908 020609050308). 0803000907090301: ﾂｨｮﾍ A 1 ｨ, A 1 ｨｬｨｮ 1 ｨｮ 6ﾍ0 ﾂｨｮﾍｨｮ 1 ｨｮ, 030209070708, 070308020603060905030001020709 ﾂﾂ 1 ｨｮ 1 ｨｮ 04060501030905030001020709, 07 S BB1 C 1 C = ﾂｨｮｨｮ 1 ｨｮ. 060908020301 0200070209 0603000609 A 1 ｨ. ﾂ 0609 ﾁ0203000302060302020301 04060501030905030001020301 A 1 ｨ 06 07 09090803080301 ｨ 06 = 4 0403000907090301: A 1 ｨ = 4 ﾌ 2. 000909 090909 ｨｮ 1 ｨｮ = A 1 ｨ = 4 ﾌ 2, 0803 S BB1 C 1 C = 8 4 ﾌ 2 = 32 ﾌ 2. 0009090701 03000609030301, S 000309. = 2S AA1 C 1 C + S BB1 C 1 C = 2 32 + 32 ﾌ 2 = 32(2 + ﾌ 2) (09 ﾁ. 0302.): 060908020301 0300080301 V 020902020308 040607030102. ﾂ 04060501030905030001020301 A 1 ｨ 07: A 1 07 = ﾌｨ 1 ｨ 2 6ﾓ1 07ｨ 2 = ﾌﾌ ( 4 ﾌ 2 ) 2 6ﾓ1 ( 8 ﾌ 3 3 ) 2 = 4 ﾌ 6 3 : 0003050209 0300080301 V = S ABC A 1 07 = 82 ﾌ 3 4 0708 ﾁ0308: 32(2 + ﾌ 2) 09 ﾁ.0302.; 64 ﾌ 2 090900.0302. 4 ﾌ 6 3 = 64 ﾌ 2 (090900. 0302.): 01070708030001 0103000308 060907040706070801 0403060307030201 07090708020206 ﾁ070203 ﾁ 0406070301 07 040906090000030003040704030203 ﾁ. 000909, 0209040607010306, 0103000203 06090707090903090801 0907090607010705 03 020909000302020301 040906090000030003040704030203, 00030903 ﾁ0303 0603000603 0903-080306030503 0300060903090308 0609 ﾁ020203 09050002 07 040306030703090908060701070705 07 020701 0603-0006090107 03070203 ﾁ09020705: ﾁ 05080301 070009070903 0903020301 02090202030503 0603000609, 05 ﾁ000508-0607080705 ﾁ03060407020308 ﾁ03060602030503 03070203 ﾁ09020705 040906090000030003040704030209, 03060803-0503020900010203 04060303090807060903080705 0209 0007070703090806070709 09050009, 030006090303 ﾁ090202030503 0508070107 06030006090107 03070203 ﾁ09020705. ｨｰ090707010308060701, 09 04060701030609, 070003020908060908 030902090709. ｨｲ0902090709 2. 07070203 ﾁ0902070301 02090900030202030503 040906090000030003040704030209 070009ｨｰ0707. 2. 000708 06030100 0703 0708030603020308, 0609 ﾁ020308 6, 07 030708060201 0905000301 ﾁ 60 71. 060908-02070803 0300080301 040906090000030003040704030209, 03070007 030503 00030903 ﾁ0203 0506090207 060301-0002 07 030708060201 0905000301 ﾁ 45 71. ｨｰ030403020703. 0809070801 020902 0409060900000300030407040302 ｨﾂｨｮDA 1 ﾂ 1 ｨｮ 1 D 1 (060707. 2), ﾁ 09030803060301 ﾏﾂｨ D = = 60 71, ﾏC 1 C ﾂ = ﾏC 1 CD = 45 71 ; C 1 ｨｪ 07 C 1 05 ﾁ0207030802 00030903 ﾁ0206 050609020308 040906090000030003040704030209, C 1 06 030503 ﾁ0207030809. 000909 090909 00030903 ﾁ0203 0506090207 0603010002, 0803 C 1 C = ﾂｨｮ = 6. 080607070301 ﾁ 0609 ﾁ0203000302060302020206 04060501030905030001-020206 08060309050300010207090906 C 1 Cｨｪ 07 C 1 C05 0701030301: Cｨｪ = C05 = 6 ﾌ 2 2 = 3 ﾌ 2. 0803 08030306030103 03 08060306 040306040302020709090005060906 06ｨｪﾍﾂｨｮ, 0605 ﾍ CD, 040607070301 06ｨｪ = 0605 (090909 040603-0309010707 0609 ﾁ020206 020909000302020206 ｨｮ 1 ｨｪ 07 ｨｮ 1 05). ｨｹ0803 0303020907090308, 070803 0803070909 06 03070203 ﾁ09020703 ﾁ0207030802 C 1 06 040906090000030003040704030209 0406070209020003000708 0007070703090806070703 09050009 ﾂｨｮD, 08. 03. 020709050302090007 ｨｨｮ 0603010009 ｨﾂｨｮD. ﾂ 04060501030905030001020301 ｨｮｨｪ06 (Cｨｪﾍ 06ｨｪ) 02090603020701: ｨｮ06 = CM cos 30 71 = 3 ﾌ 2 : ﾌ 3 2 = 2 ﾌ 6; 0803050209 ﾁ 04060501030905030001020301 ｨｮ 1 ｨｮ06 (C 1 06 ﾍ 06ｨｮ) 0403000907090301: ｨｮ 1 06 = ﾌﾌ C 1 C 2 6ﾓ1 CH 2 = 6 2 ( ﾌ ) 2 ﾌ 6ﾓ1 2 6 = 2 3:

1307 02030300060302070103070807 090605090103020809010707 040607 06030403020707 0708030603030103080607070307090706 0309020907 13 0009090701 03000609030301, 0708 ﾁ0308: 108 090900.0302. V = ｨﾂ 2 sin 60 71 ｨｮ 1 06 = 36 ﾌ 3 2 2 ﾌ 3 = 108 (090900. 0302.): ｨｮ0003020908060701 ﾁ07020301 01020305030506090202070903 ﾁ 05 ﾁ000503080705 0407060901070209. 06030300060302070103 04030102070801, 070803 02 ﾁ0905060902-020201 0905000301 040607 0603000603 0407060901070202 02090302 ﾁ090808 07030203060009060708 050809 0407060901070209 02 ﾁ0905060902020208 09050300, 030006090303- ﾁ0902020208 0400030709030708050107 080306 050609020308, ﾁ 09030803060206 0609070403000300030203 020902020303 0603000603. ｨｦ0309070905 0407060901070209, 0708030708 0307030003 030708090203 ﾁ0708010705 0209 0806030905030001020206 040706090107020906 08030806090502060906. ｨｮ0003-02090308 0609070701030806030801 0803080609050206, ﾁ0703 ﾁ0207030802 0903080306030503 040306030703090908080705 ﾁ 0302020308 0803070903 (030608030103020806070703-07090708 0803080609050206), 07 0803080609050206, ﾁ0703 0506090207 0903080306030503 0609 ﾁ020203 080603090503000102070907 (0609 ﾁ020305060902020208 0803-080609050206). 080609 ﾁ070001020208 0803080609050206 05 ﾁ000503080705 0609 ﾁ020305060902020201 07 03060803010302080607070307090701. 06030300060302070103 0609070701030806030801 07 07030300060903070801 020309030803060203 07090708020203 ﾁ070202 04070609010702: 09) 0407060901070209, ﾁ0703 00030903 ﾁ0203 0603000609 09030803060308 0300060903090808 0609 ﾁ020203 09050002 07 04000307090307080108 0303 03070203 ﾁ09020705; ﾁ030604070209 0809090308 0407-060901070202 04060303090807060903080705 ﾁ 0103020806 03090609000203070807, 030407070902020308 0309030003 0303 03070203 ﾁ09020705; 00) 0407060901070209, ﾁ0703 02 ﾁ0905060902020203 09050002 09030803060308 040607 060300060906 03070203 ﾁ09020705 0609 ﾁ0202 0103000209 0703000308; 03060803050302090001020308 040603030901070308 ﾁ030604070202 0809090308 0407060901070202 0209 0303 03070203 ﾁ09020703 05 ﾁ000503080705 0103020806 03090609000203070807, ﾁ0407070902020308 ﾁ 050803 03070203 ﾁ09-020703; ﾁ) 0407060901070209, 07010308060908 00030903 ﾁ0203 0506090207, 04030604030202070909000506020203 040003070903070807 0303 03070203 ﾁ09020705. 01070708030001 070901 0103000308 060907040706050801 0403060307030201 07090708020206 ﾁ070203 ﾁ 04070609010702 07 06090707090903090801: 09) 03 0407060901070203, 00030903 ﾁ0303 0603000603 09030803060308 0300060903090308 0609 ﾁ020203 09050002 07 040306030703090908060701070705 07 020701 06030006090107 03070203 ﾁ09020705; 03060803050302090001020905 0406030309010705 ﾁ030604070202 0809090308 0407060901070202 0209 0303 03070203 ﾁ09020703 0406070209020003000708 0007070703090806070703 09050009, 030006090303 ﾁ090202030503 0508070107 06030006090107 03070203 ﾁ09020705; 00) 03 0407060901070203, 02 ﾁ09 00030903 ﾁ0206 0603000609 09030803060308 0609 ﾁ0202 0103000209 0703000308; ﾁ030604070209 0809090308 0407060901070202 04060303090807060903080705 0209 07030603020702020208 04030604030202070909000506 03080603030909, 070303020702050806030503 03070203 ﾁ09020705 0609 ﾁ020206 00030903 ﾁ0206 0603000306. ｨｮ000302090308 ﾁ02060900090802 ﾁ090801 09 0907090607060705 040607 ﾁ02070909 0209070702090801 0703030006090003020705 07090708020206 ﾁ070203 ﾁ 040706090107-0202 07 0703030006090003020705 0706 03070203 ﾁ09020708. 02070007 040607 05080301 ﾁ0703 00030903 ﾁ0203 0603000609 ( ﾁ0703 00030903 ﾁ0203 0506090207) 040706090107-0202 03020702090903 ﾁ03 020909000302030202 09 040003070903070807 03070203 ﾁ09020705, 0803 07020907090009 02030300060302070103 040307080603070801 0703030006090003020703 010302080609 03090609000203070807, 030407070902020308 0309030003 03070203 ﾁ09020705 ( ﾁ0407070902020308 070007 ﾁ0203 ﾁ0407070902020308 ﾁ 02030503), 07 08030001-0903 0403070003 0508030503 0703 040307080603030202030503 010302080609 040603 ﾁ03070807 04030604030202070909000506 09 040003070903070807 0102030503090503000102070909 07 ﾁ020006090801 0209 05080301 0403060403020207090900050603 ﾁ 090907030708 ﾁ03 ﾁ030604070202 0407060901070202 0008000908 0803070909, 0308000707020908 0308 010302080609 0102030503090503000102070909. ｨｰ090707010308060701 06030403020703 030902090707 03 0407060901070203 030202030503 0703 04030603070707000302020206 ﾁ070203 ﾁ. ｨｲ0902090709 3. 01 ﾁ09 00030903 ﾁ0206 0603000609 0806030905030001020308 0407060901070202 07 0309-090008070302020905 0103000209 02070107 07080306030209 03070203 ﾁ09020705 0609 ﾁ0202 07030308 ﾁ03080708 ﾁ0302-0203 12 0201, 18 0201 07 18 0201. 06090802070803 0300080301 0407060901070202, 03070007 ﾁ0703 0303 00030903 ﾁ0203 0506090207 0300060903090808 0609 ﾁ020203 02 ﾁ0905060902020203 09050002 07 04000307090307080108 03070203 ﾁ09020705, 09 ﾁ0207030809 0407060901070202 0609 ﾁ0209 6 ﾌ 3 0201. ｨｰ030403020703. 0809070801 ｨｨｰ = ｨﾂ = 18, ﾂｨｰ = 12, ｨｰ 07 = = 6 ﾌ 3 ﾁ0207030809 0407060901070202 ｨｰｨﾂｨｮ (060707. 3). 080603 ﾁ03020301 ﾁ0207030802 ｨｰ 05, ｨｰｨｪ 07 ｨｰ 06 050609020308 07030308 ﾁ03080708 ﾁ03020203 ｨｰｨﾂ, ｨｰﾂｨｮ 07 ｨｰｨｨｮ. ｨｦ03 ｨｰ05 ﾍｨﾂ, ｨｰｨｪﾍﾂｨｮ, ｨｰ06 ﾍｨｨｮ 0403 08030306030103 03 08060306 040306040302020709090005060906 07000302090308: 0705 ﾍｨﾂ, 07ｨｪﾍﾂｨｮ, 0706 ﾍｨｨｮ. 0003050209 ﾏ0705ｨｰ = ﾏ07ｨｪｨｰ = ﾏ0706ｨｰ (090909 0007020308020203 09050002 0609 ﾁ020206 02 ﾁ0905060902020206 09050003 ﾁ 040607 060300060906 ｨﾂ, ﾂｨｮ 07 ｨｨｮ). ｨｹ0803 0303020907090308, 070803 04060501030905030001020203 080603090503000102070907 0705ｨｰ, 07ｨｪｨｰ 07 0706ｨｰ 0609 ﾁ0202, 030809090209: 0705 = = 07ｨｪ = 0706; ｨｰ05 = ｨｰｨｪ = ｨｰ06. 0803000907070007: 03070203 ﾁ09020703 07 ﾁ0207030802 ｨｰ 07 0407060901070202 0609 ﾁ020309020900030203 0308 ﾁ070306 070803060302 080603090503000102070909 ｨﾂｨｮ, ｨｰ0707. 3. 04030508030109 0803070909 07 0103020806 03090609000203070807, ﾁ0407070902020308 ﾁ 0806030905030001020709 ｨﾂｨｮ 07 0705 = R, 050203 R 060902070907 05080308 03090609000203070807.

1314 02. ﾂ. 0803080307090903 ﾁ 000909 090909 0803070907 05, ｨｪ 07 06 05 ﾁ000508080705 08030709090107 09090709020705 ﾁ0407070902020308 ﾁｨﾂｨｮ 03090609000203070807, 0803 ｨ 05 = ｨ 06, ﾂ05 = ﾂｨｪ, ｨｮ06 = ｨｮｨｪ (0403 07 ﾁ03080708 ﾁ09 03080603030903 ﾁ 0909070908030001020206 09 03090609000203070807). 060908020301 0200070202 070803060302 ｨｨｮ 07 ﾂｨｮ. ﾂ 080603090503000102070903 ｨﾂｨｰ 02090603020701: ｨｰ05 = 2S ABP 18 = 8 ﾌ 2. 0003050209 ﾁ 04060501030905030001020301 AB = 2 ﾌ 24 12 6 6 ﾌｨｨｰ05 0403 08030306030103 0807040905030609: AK = ﾌ AP 2 6ﾓ1 PK 2 = 18 2 6ﾓ1 (8 ﾌ 2) 2 = 14. ｨｲ0209070708, ｨ 06 = ｨ 05 = 14 07 ﾂ05 = ｨﾂ 6ﾓ1 ｨ 05 = 4 = ﾂｨｪ. 0506030103 08030503, ﾁ 04060501030905030001020301 07ｨｰ05 0403 08030306030103 0807040905030609: 07K = ﾌ P05 2 6ﾓ1 07P 2 = ﾌ 128 6ﾓ1 108 = 2 ﾌ 5 = R. 02070007 ｨｮｨｪ = ｨｮ06 = 06, 0803 0403060701030806 080603090503000102070909 ｨﾂｨｮ 0609 ﾁ0302: ｨｰｨﾂｨｮ = 18 + (14 + 06) + (4 + 06) = 2 (18 + 06); S ｨﾂｨｮ = ﾌ (06 + 18)(06 + 18 6ﾓ1 18)(06 + 18 6ﾓ1 (06 + 14))(06 + 18 6ﾓ1 (06 + 4)) = = ﾌ (06 + 18) 06 4 14 = 2 ﾌ 1406(06 + 18): 0003050209 070007 R = 2S ABC P = 2 2 ﾌ 14x(x + 18) ABC 2 (18 + x) = 2 ﾌ 14x(x + 18) 18 + x = 2 ﾌ 5 ﾌﾌﾌ 1406(06 + 18) 1406 5 = = ﾌ 06 + 18 06 + 18 6ﾍ0 5(06 + 18) = 1406 6ﾍ0 06 = 10: 0003050209 ﾂｨｮ = 14, ｨｨｮ = 24. 000304030601 02090603020701 0300080301 V 0407060901070202: 0708 ﾁ0308: 112 ﾌ 15 0201 3. V 040706. = 1 3 S ABC ｨｰ07 = 1 3 2 ﾌ 14 10 (10 + 18) 6 ﾌ 3 = 112 ﾌ 15 (0201 3 ): 06030300060302070103 ﾁ 0707070003 0603040903010206 ﾁ09000807090801 030902090707 03 070308020603060905030001020206 040706090107020906, ﾁ 03070203 ﾁ09020707 0903-0803060206 0003000908 0203 080300010903 040906090000030003050609010102, 0406050103090503000102070907, 09 ﾁ090206090802, 0203 07 0806090403010707. ｨｲ0902090709 4. 07070203 ﾁ0902070301 0407060901070202 ｨｰｨﾂｨｮD 05 ﾁ000503080705 0609 ﾁ0203000302060302020905 0806090403010705 ｨﾂｨｮD (ｨﾂｬｨｮD); ﾁ0703 02 ﾁ0905060902020203 09050002 040607 060300060906 0303 03070203 ﾁ09020705 0609 ﾁ0202. 06090802070803 04000306090201 00030903 ﾁ0308 0403 ﾁ030606-0203070807 0407060901070202, 03070007 0303 0300080301 0609 ﾁ0302 3200 0701 3, ｨﾂ = 32 0701, ｨｮD = 18 0701. ｨｰ030403020703. 000909 090909 ﾁ0703 02 ﾁ0905060902020203 09050002 040607 0603-00060906 03070203 ﾁ09020705 0407060901070202 ｨｰｨﾂｨｮD 0609 ﾁ0202, 0803 03070203- ﾁ09020703 ﾁ0207030802 ｨｰ07 0407060901070202 0703 ﾁ040902090308 07 01030208060301 07 03090609000203070807, ﾁ0407070902020308 ﾁ 0806090403010708 ｨﾂｨｮD; 0803070909 07 05 ﾁ000503080705 070306030207020308 03080603030909 06ｨｪ, 070303020702050806030503 07030603-02070202 03070203 ﾁ09020708 0806090403010707. 070003030209070701: ' = ﾏ0705ｨｰ = ﾏ07ｨｪｨｰ = ﾏ0706ｨｰ 0007020308020203 09050002 02 ﾁ0905060902020206 09050003 ﾁ 040607 060300060906 03070203 ﾁ09020705 0407060901070202, 050203 ｨｪ06 ﾍｨﾂ, 0705 ﾍ AD (060707. 4). ｨｰ07 ﾍ (ｨﾂｨｮ), 030209070708, 040605010905 ｨｰ07 040306040302020709090005060209 0008000308 040605010308 040003070903070807 03070203 ﾁ09020705 0407060901070202. 000909 090909 06, ｨｪ 07 05 0803070907 09090709020705 ﾁ0407070902-020308 ﾁ 0806090403010708 ｨﾂｨｮD 03090609000203070807, 0803: ｨ 05 = = ｨ 06 = ｨｰ0707. 4. 1 2 ｨﾂ = 16; 05D = DM = 2 1 ｨｮD = 9. ｨｲ0209070708, AD = ｨ 05 + 05D = 16 + 9 = 25. ﾂ 04060501030905030001020301 080603090503000102070903 ｨ OD 02090603020701: 0705 = ﾌｨ 05 05D = ﾌ 16 9 = 12: ｨｲ0209070708, ﾁ0207030809 ｨｪ06 0806090403010707 0609 ﾁ0209 20705 = 24, 09 0303 040003-06090201 0609 ﾁ0209 CD + AB 18 + 32 MH = 24 = 600: 2 2

1307 02030300060302070103070807 090605090103020809010707 040607 06030403020707 0708030603030103080607070307090706 0309020907 15 ｨｦ0704030001030905 04030601090009 030008030109 0407060901070202 V = 1 3 S 030702: ｨｰ07, 0701030301: 3200 = 1 3 600 ｨｰ07, 030809090209 ｨｰ07 = 16. ﾂ 04060501030905030001020301 07ｨｪｨｰ: tg ' = 07ｨｪ 07ｨｰ = 16 12 = 4 3 6ﾍ0 cos ' = 0;6. 000909 090909 00030903 ﾁ0203 0506090207 0407060901070202 04060303090807060908080705 ﾁ 080603090503000102070907 AOB, BOC, COD 07 DOA, 0703070809 ﾁ000508060703 050803 03070203 ﾁ09020703, 0803 S 030702: = S 000309: cos ' 6ﾍ0 S 000309: = S 030702: cos ' = 600 0;6 = 1000 (07012 ): 0708 ﾁ0308: 1000 0701 2. 010005 06030403020705 010203050706 0309020907 080603000903080705 07030300060903070801 010203050305060902020709, 09030803060208 05 ﾁ020201 03000609030301 0309020902 09070003 ﾁ070301 030902090707. ｨｹ080701 0102030503050609020207090301 0103000308 00020801: 04060501030905030001020208 (020909000302020208) 0409060900000300030407-040302, 020909000302020905 (040605010905) 040607030109, 040609 ﾁ070001020905 0407060901070209 07 020609050703 0706 ﾁ070202. 070202090903, 020005 060903 ﾁ07080705 04060307080609020708 ﾁ030202030503 ﾁ03030006090003020705 040607 06030403020707 0309020907 02030300060302070103 04060302000905090801 0907090607010705 0809090703 030902090707, 020005 06030403020705 09030803060206 030207 020300000202 0709010307080305080300010203 縺0102070003020203 0709030207080609070603 ﾁ0908011 7, 04060302-070809 ﾁ070801, 09 0309080301 07030300060903070801 0703 ﾁ07030107 030003070203 ﾁ090207050107 010203050305060902020709, 090203 ﾁ000308 ﾁ03060508060708 09070003 ﾁ070501 030902090707. ﾂ 090907030708 ﾁ03 04060701030609 06090707010308060701 070003020908060908 030902090709. ｨｲ0902090709 5. 07070203 ﾁ090207050107 0806030905030001020308 090703070302020308 0407060901070202 ｨﾂｨｮA 1 ﾂ 1 ｨｮ 1 05 ﾁ000508080705 040609 ﾁ070001-020203 080603090503000102070907 ｨﾂｨｮ 07 A 1 ﾂ 1 ｨｮ 1, 07080306030202 09030803060206 0609 ﾁ0202 07030308 ﾁ03080708 ﾁ03020203 12 07 4. 06090802070803 0200070202 00030903 ﾁ0206 0603000306 05080308 090703070302020308 0407060901070202, 03070007 ﾁ030604070209 ｨ 1 09020900030209 0209 06090707080305020703 8 0308 090900020308 0703 ﾁ0306040702 03070203 ﾁ09020705 ｨﾂｨｮ. ｨｰ030403020703. ｨｮ020907090009 07000302090308 040603090209000703070603 ﾁ090801 縺0907080603080708 ﾁ031 7 020902020308 090703070302020308 0407060901070202. 0809070801 0803070909 07 0103020806 03070203 ﾁ09020705 ｨﾂｨｮ, ｨｪ 0703060302070209 ﾂｨｮ, M 1 0703060302070209 ﾂ 1 C 1. ﾂ030604070209 ｨ 1 0609 ﾁ020309020900030209 0308 090900020308 0703 ﾁ0306040702 03070203 ﾁ09020705 ｨﾂｨｮ, 030209070708, A 1 07 ﾍﾍ (ｨﾂｨｮ) (060707. 5), 030809090209 A 1 O ﾍﾂｨｮ. 0506030103 08030503, ｨｨｪﾍﾂｨｮ (090909 01030207090209 040609 ﾁ07000102030503 080603-090503000102070909 ｨﾂｨｮ). ｨｮ00030203 ﾁ09080300010203, 0403 0406070302090909 040306040302020709090005060203070807 040605010308 07 040003070903070807 (A 1 ｨｨｪ) ﾍﾂｨｮ. 0003050209 ﾁ 07070009 ﾂｨｮｬ B 1 C 1 0403000907090301: (A 1 ｨｨｪ) ﾍ B 1 C 1, 040607 05080301 040003070903070801 A 1 07ｨｪ 0406030603020708 0703060303 0703060302070209 ｨｪ 1 03080603030909 ﾂ 1 C 1, 080909 090909 ｨ 1 ﾊ (A 1 ｨｨｪ) 07 A 1 M 1 ﾍ B 1 C 1. 0109000303, 080909 090909 A 1 M 1 = 2 ﾌ 3 07 07ｨｪ = 2 ﾌ 3, 0803 A 1 M 1 = 07ｨｪ, 030209070708, 070308020603060905030001020709 A 1 M 1 ｨｪ07 0409060900000300030506090101. ｨ 080909 090909 A 1 O ﾍ (ｨﾂｨｮ), 0803 A 1 M 1 ｨｪ07 04060501030905030001020709, 04030508030109 M 1 M ﾍ (ｨﾂｨｮ), 030809090209 040003070903070801 0506090207 ﾂﾂ 1 C 1 ｨｮ 04030604030202070909-0005060209 040003070903070807 ｨﾂｨｮ 07 040003070903070807 A 1 ｨｨｪ (0403 0406070302090909 040306040302-020709090005060203070807 02 ﾁ0906 04000307090307080308). 000304030601 020908020301 0200070202 00030903 ﾁ0206 0603000306 ﾂ 1 ﾂ 07 ｨｮ 1 ｨｮ. ﾂ 04060501030905030001020301 A 1 ｨ 07: M 1 ｨｪ = A 1 07 = ﾌｨ 1 ｨ 2 6ﾓ1 07ｨ 2 = ﾌ 8 2 6ﾓ1 (4 ﾌ 3) 2 = 4: 000909 090909 ﾂ 1 ｨｮ 1 = 3 1 ﾂｨｮ, 0803 ﾂ 1M 1 = 1 3 ﾂｨｪ, 07 03070007 MD = ﾂﾂ 1 M 1 = 2, 0803 BD = ﾂｨｪ 6ﾓ1 MD = 6 6ﾓ1 2 = 4. 0003050209 ﾁ 0406050103-0905030001020301 ﾂﾂ 1 D 02090603020701: ﾂ 1 ﾂ = ﾌ B 1 D 2 + BD 2 = 4 ﾌ 2. ｨ 080909 ｨｰ0707. 5. 090909 ﾂﾂ 1 ｨｮ 1 ｨｮ 0609 ﾁ0203000302060302020905 0806090403010705, 0803 ｨｮｨｮ 1 = ﾂ 1 ﾂ = 4 ﾌ 2. 0009090701 03000609030301, 00030903 ﾁ0203 0603000609 020902020308 090703070302020308 0407060901070202 0609 ﾁ0202 8, 4 ﾌ 2, 4 ﾌ 2. 0708 ﾁ0308: 8, 4 ﾌ 2, 4 ﾌ 2. ｨｮ000302090308 030703000303 ﾁ02070109020703 09020300070801 06030403020708 0309020907, ﾁ 09030803060206 02030300060302070103 07080603070801 07030703020703 01020305030506090202070909 07 040300020201 0906050901030208070603 ﾁ0902020201 030003070203 ﾁ0902070301 09090002030503 縺040905091 7 04030708060303020705, 0403070003 07030503 0209080807 04000306090201 0508030503 07030703020705. 010603 ﾁ030201 070003000203070807 0309020907 0209 04030708060303020703 07030703020708 01020305030506090202070903 ﾁ 07000302090308 0403 ﾁ0204090801 090909 縺0209-060302050701 ﾁ0209080607 030202030503 ﾁ070209 01020305030506090202070903 ﾁ1 7, 080909 07 040607 0403060306030203 0308 030202030503 0706 ﾁ070209 09 02060905030109 (0308 0406070301 07 040906090000030003040704030203 ﾁ 09 040706090107020901).

1316 02. ﾂ. 0803080307090903 ﾁﾂ 04060304070001020206 09000907070906 (07 040607 020704040306030201070603 ﾁ0902020301 010308030203 0300090703020705 ﾁ 03000603030006090303 ﾁ0908030001020206 09000907070906) 04030003030203 060304090801 07020803060307020203 07 0906090707 ﾁ0203 030902090707, 0403020300020203 070003020908060308. ｨｲ0902090709 6. 080307080603080803 07030703020703 09090009 04000307090307080108, 04060306030205060308 0703060303 030503 0103020806 07 04030604030202070909-000506020308 020709050302090007 09090009. 06090802070803 04000306090201 0508030503 07030703020705, 03070007 0603000603 09090009 0609 ﾁ0203 6. ｨｰ030403020703. 0809070801 ｨﾂCDA 1 ﾂ 1 C 1 D 1 020902020208 090900, 0803070909 ｨｪ 0703060302070209 030503 020709050302090007 A 1 ｨｮ, 040003070903070801, 04060306030205060905 0703060303 ｨｪ 040306040302020709090005060203 A 1 ｨｮ (060707. 6). ｨｰ0707. 6 07060803050302090001020308 040603030901070308 020709050302090007 A 1 ｨｮ 0209 040003070903070801 ｨﾂｨｮ 05 ﾁ000503080705 020709050302090001 ｨｨｮ 03070203- ﾁ09020705 ｨﾂCD, 04030604030202070909000506020905 ﾂD. ｨｲ0209070708, A 1 ｨｮﾍﾂD (0403 08030306030103 03 08060306 040306040302020709090005-060906). ｨ 020900030507070203, A 1 ｨｮﾍｨｮ 1 ﾂ. 0003050209 0403 0406070302090909 040306040302020709090005060203070807 040605010308 07 040003070903070807 A 1 ｨｮﾍ ( ﾂC 1 D), 030809090209 A 1 ｨｮﾍ C 1 07. 070003030209070701: L = A 1 ｨｮﾉ ( ﾂｨｮ 1 D) = A 1 ｨｮﾉ C 1 07. ｨｲ090103080701, 070803 A 1 ｨｮ = 6 ﾌ 3, ｨｪｨｮ = 0;5A 1 ｨｮ = 3 ﾌ 3, ｨｨｮ = 6 ﾌ 2, 07ｨｮ = 3 ﾌ 2. ｨｦ03 04030203000705 0406050103-0905030001020206 080603090503000102070903 ﾁ 07ｨｮL 07 A 1 Cｨ 0701030301: 07ｨｮ : A 1 ｨｮ = ｨｮL : Cｨ 6ﾍ0 ｨｮL = 07ｨｮｨｮｨｨ 1 ｨｮ = 3 ﾌ 2 6 ﾌ 2 6 ﾌ = 2 ﾌ 3: 3 0003050209 ML = ｨｪｨｮ 6ﾓ1 ｨｮL = 3 ﾌ 3 6ﾓ1 2 ﾌ 3 = ﾌ 3. ｨｲ0209070708, ｨｪL : LC = 1 : 2. 000909 090909 ﾍ A 1 ｨｮ 07 ( ﾂｨｮ 1 D) ﾍ A 1 ｨｮ, 0803 ｬ ( ﾂｨｮ 1 D), 030209070708, 040605010905 m = ﾉ (ｨﾂｨｮ) 0409-060900000300010209 BD (0403 08030306030103 03 0403060307030703020707 02 ﾁ0906 040906090000030001020206 04000307090307080308 08060308010308 04000307090307080108), 040607070301 04030603070309090308 ｨｨｮﾁ 0809090308 0803070903 00, 070803 0007 : 07ｨｮ = ｨｪL : LC = 1 : 2. 0107070802 ﾁ0905 040607 05080301, 070803 07ｨ = 07ｨｮ, 0406070603020701 09 ﾁ02 ﾁ030209: 0803070909 00 = ﾉｨｨｮ 05 ﾁ000503080705 070306030207020308 03080603030909 07ｨ. 0009090701 03000609030301: 00 ﾊ m, 00 0703060302070209 07ｨ 07 m ｬ BD 6ﾍ0 0803070907 P = m ﾉｨﾂ = ﾉｨﾂ 07 Q = m ﾉｨ D = ﾉｨ D 05 ﾁ000508080705 07030603020702090107 0603000306 ｨﾂ 07 ｨ D (0403 08030306030103 030900030709). 0003070907 ｨｰ 07 Q ﾁ030604070202 0707090301030503 07030703020705. 01090001020308040303 04030708060303020703 07030703020705 0103000203 03070906030708 ﾁ00050801, 070704030001030905 0409060900000300010203070801 04000307090307080308 ｬ ( ﾂｨｮ 1 D), 09 0809090003 0409060900000300010203070801 0406030807 ﾁ030403000300020206 050609020308 09090009 07 08030306030109 03 0403060307030703020707 02 ﾁ0906 040906090000030001020206 04000307090307080308 08060308010308 04000307090307080108. 0103080708 ﾁ07080300010203, 080909 090909 ｬ ( ﾂｨｮ 1 D), 09 0809090003 0506090201 ｨﾂﾂ 1 A 1 0409060900000300010209 0506090207 ｨｮDD 1 C 1 07 0803070909 ｨｰ 0703060302070209 ｨﾂ, 0803 040306030703070302070301 040003070903070807 07 0506090207 ｨﾂﾂ 1 A 1 05 ﾁ000503080705 03080603030309 ｨｰ05 ｬ DC 1 ｬ AB 1, 050203 05 0703060302070209 0603000609 ﾂﾂ 1 ; 0803070909 05 ﾁ030604070209 07030703020705. ｨ 020900030507070203, 040306030703070302070301 040003070903070807 07 0506090207 ｨ DD 1 A 1 05 ﾁ000503080705 03080603030309 QR ｬｬ BC 1 ｬｨ D 1, 050203 R 0703060302070209 0603000609 DD 1 ; 0803070909 R ﾁ030604070209 07030703020705. 0109000303 040603 ﾁ03020701 03080603030907 R06 ｬ DC 1 (06 0703060302070209 ｨｮ 1 D 1 ) 07 05N ｬﾂｨｮ 1 (N 0703060302070209 ﾂ 1 C 1 ). 0003070907 H 07 N ﾁ030604070202 07030703020705.

1307 02030300060302070103070807 090605090103020809010707 040607 06030403020707 0708030603030103080607070307090706 0309020907 17 0009090701 03000609030301, 07070903010201 0703070302070301 09090009 05 ﾁ000503080705 040609 ﾁ070001020208 04030708070905030001020709 P QRHNK, 0708030603-0209 0903080306030503 0609 ﾁ0209 04030003 ﾁ070203 020709050302090007 0506090207 09090009, 08. 03. ｨｰ05 = 3 ﾌ 2. 08000306090201 0508030503 07030703020705 0609 ﾁ0209 6 (3 ﾌ 2) 2 ﾌ 3 4 = 27 ﾌ 3 (09 ﾁ. 0302.). 0708 ﾁ0308: 27 ﾌ 3 09 ﾁ. 0302. ｨｲ0902090709 7. 0603060303 07080306030209 03070203 ﾁ09020705 040609 ﾁ070001020308 0703-08020603060905030001020308 0407060901070202 040603 ﾁ0302030209 040003070903070801, 040306-04030202070909000506020905 0406030807 ﾁ030403000300020308 0506090207 07 040306030703090908060905 0303. 06090802070803 04000306090201 07030703020705, 03070007 07030909060905 040003070903070801 0300060903090308 07 04000307090307080108 03070203 ﾁ09020705 09050300, 09 ﾁ0207030809 0407-060901070202 0609 ﾁ0209 h. ｨｰ030403020703. 0809070801 ｨｰｨﾂｨｮD 040609 ﾁ070001020905 0407060901070209 (060707. 7); ｨｰ07 = h ﾁ0207030809 0407060901070202; 0803070907 E 07 F 0703060302070202 0603000306 ﾂｨｮ 07 ｨ D. 0803070806030701 07030703020703 020902020308 0407060901070202 04000307090307080108, 040603 ﾁ03020302020308 0703060303 0603000603 ｨ D 040306040302020709090005060203 0506090207 ﾂｨｮｨｰ. 000909 090909 ｨ D ｬﾂｨｮ, 0803 0403 0406070302090909 0409060900000300010203070807 040605010308 07 040003070903070807 ｨ D ｬ ( ﾂｨｮｨｰ). ｨｲ0209070708, 03080603030309 ｨｪ05, 0403 0903080306030109 040003070903070801 04030603070309090308 0506090201 ﾂｨｮｨｰ, 0409060900-0003000302 ｨ D (0403 08030306030103 03 040605010308 0403060307030703020705 02 ﾁ0906 04000307-090307080308, 03020209 0703 09030803060206 0406030603020708 0703060303 040605010908, 0409060900- ｨｰ0707. 7. 00030001020908 020609050308). 0009090701 03000609030301, 0703070302070301 020902020308 0407060901070202 04000307090307080108 05 ﾁ000503080705 0806090403010705 ADKM. ｨｦ01030301: EF ﾍﾂｨｮ; P02 ﾍﾂｨｮ (090909 01030207090209 0609 ﾁ020300030206030202030503 ﾂｨｰｨｮ) 6ﾍ0 ﾂｨｮﾍ (EFP) (0403 0406070302090909 040306040302020709090005060203070807 040605010308 07 040003070903070807) 6ﾍ0 ( ﾂｨｮｨｰ) ﾍ (EFP) (0403 0406070302090909 0403060403020207-09090005060203070807 04000307090307080308). 070003030209070701: FL = ﾉ (EFP), ｨｪ05 = ﾉ ( ﾂｨｮｨｰ). 000909 090909 ｨ D ｬﾂｨｮ, ﾂｨｮﾍ (EFP), 0803 ｨ D ﾍ (EFP), 030809090209 ｨ D ﾍ FL, ｨ D ﾍ F02. ｨｲ0209070708, ﾏEFL = 0007020308020208 09050300 02 ﾁ090506090202030503 09050009, 030006090303 ﾁ090202030503 04000307090307080108 07 04000307090307080108 03070203 ﾁ09020705 0407060901070202. 000909 090909 ﾍ ( ﾂｨｮｨｰ), (EFP) ﾍ ( ﾂｨｮｨｰ), 0803 FL ﾍ ( ﾂｨｮｨｰ). 0003050209 0403 0304060302030003020708 040605010308, 04030604030202070909000506020308 040003070903070807, FL ﾍｨｰ02 07 FL ﾍｨｪ05, 040607 05080301 L = ｨｰ02 ﾉｨｪ05 07 MK ｬ AD (080909 090909 040003070903070807 BCP 07 0406030603020508 0703060303 040906090000030001020203 040605010203 BC 07 AD). ｨｲ0209070708, 07030703020703 ADKM 0609 ﾁ0203000302060302020905 0806090403010705, 09 09030803060308 FL ﾁ0207030809 (L 0703060302070209 ｨｪ05). 060908020301 S ADKM. 0809070801 ｨｪ 1, 05 1, L 1 03060803050302090001020203 0406030309010707 0209 040003070903070801 03070203 ﾁ09020705 07030308 ﾁ03080708 ﾁ03020203 0803070309 ｨｪ, 05, L, 040607 05080301 L 1 0703060302070209 M 1 05 1. 0706080305030209000102020107 04060303090107050107 040605010206 ｨｰｨｮ, ｨｰﾂ 07 ｨｰ02 0209 050809 040003070903070801 05 ﾁ000508080705 07030308 ﾁ03080708 ﾁ03020203 040605010203 ｨｨｮ, ﾂD 07 EF. ｨｮ00030203 ﾁ09080300010203, ｨｪ 1 ﾊ BD, K 1 ﾊ AC, L 1 ﾊ EF. 0009090701 03000609030301, 0609 ﾁ0203000302060302020905 0806090403010705 ADK 1 M 1, 020709050302090007 ｨ 05 1 07 DM 1 09030803060308 ﾁ030907010203 040306040302020709090005060202, 05 ﾁ000503080705 03060803050302090001020308 040603030901070308 07030703020705 ADKM 0209 040003070903070801 03070203 ﾁ09020705. ｨｹ0803 0303020907090308, 070803 S ADKM = S ADK 1 M 1 cos. 060908020301 S ADK1 M 1. 000909 090909 020709050302090007 0806090403010707 ﾁ030907010203 040306040302020709090005060202, 0803 04060501030905030001020203 080603090503000102070907 0705 1 L 1 07 07FD 0609 ﾁ0203000302060302020203, 030209070708, 07L 1 = L 1 K 1, OF = FD. 08030508030109 S ADK1 M 1 = AD + K 1M 1 2 L 1 F = 2OF + 2OL 1 2 FL 1 = FL 2 1: 0003050209 S ADKM = FL2 1 cos. 060908020301 L 1F. ﾂ 04060501030905030001020301 L 1 FL: L 1 F = LF cos. 000909 090909 FL ﾍｨｰ02, EF ﾍ 07ｨｰ, 0803 ﾏ07P02 = = ﾏ02FL = (090909 09050002 07 07030308 ﾁ03080708 ﾁ03020203 0403060403020207090900050602020107 070803060302090107). 0003050209 ﾁ 07ｨｰ02: 0702 = 07ｨｰ tg = h tg. ｨｲ0209070708, 02F = 20702 = 2h tg. 08030508030109 ﾁ 04060501030905030001020301 02FL: FL = 02F cos = 2h tg cos = 2h sin :

1318 02. ﾂ. 0803080307090903 ﾁｨｮ00030203 ﾁ09080300010203, L 1 F = LF cos = 2h sin cos. 0009090701 03000609030301, 0403000907090301: S ADKM = FL2 1 cos = 4h2 sin 2 cos 2 = 4h cos 2 sin 2 cos : ｨｲ0901030709020703. 08000306090201 07030703020705 0103000203 0209080807 0702090703: S 070307 = AD+MK 2 F L. 07080603030309 ｨｪ05 0103000203 0209080807 070003020908060701 03000609030301. ｨｮ03070302070301 020902020308 0407060901070202 04000307090307080108, 04060306030205060308 0703060303 040605010908 ｨｪK 0409060900000300010203 03070203 ﾁ09020708 0407060901070202, 05 ﾁ000503080705 09 ﾁ0902060908 MKD 1 A 1 (060707. 7); F 1 = A 1 D 1 ﾉ PF. 01 0508030503 09 ﾁ090206090809 LF 1 = MK. 060908020301 F 1 L. ﾂ 080603090503000102070903 LFF 1 0701030301 ﾏFLF 1 = (LF 1 ｬ EF); ﾏFF 1 L = 90 71 +, 090909 07010300020208 07 ﾏLF 1 ｨｰ = 90 71 6ﾓ1 ; ﾏF 1 FL = ﾏOFP 6ﾓ1 ﾏOFL = (90 71 6ﾓ1 ) 6ﾓ1 = 90 71 6ﾓ1 2: 0003050209 ﾁ LF 1 F 0403 08030306030103 070702090703 ﾁ 0701030301: LF 1 sin (90 71 6ﾓ1 2) = LF sin (90 71 + ) 6ﾍ0 LF 1 = LF cos 2 cos = 2h sin cos 2 : cos ｨｲ0209070708, ｨｪ05 = LF 1 = 2h tg cos 2. 0107070802 ﾁ0905, 070803 ｨ D = 02F = 2h tg, 0403000907090301: S 070307 = AD + MK 2 0708 ﾁ0308: 4h 2 sin 2 cos 09 ﾁ.0302. 2h tg + 2h tg cos 2 FL = 2h sin = 2 2h tg (1 + cos 2) 2h sin = = 4h 2 2 sin 2 cos (09 ﾁ. 0302.): ｨｲ0902090707, 0902090003050707020203 0609030300060902020201 ﾁ 080309070803 020902020308 070809080107, 0103000203 0209080807 ﾁ 030902090702070903 [2]. ｨｹ0803, 0209040607010306, 030902090707: 2.006-2.019, 2.021-2.030, 2.035-2.039, 2.043-2.057, 2.062-2.068, 2.073-2.089, 2.190-2.200, 2.205-2.225, 2.231-2.248, 2.253-2.273, 2.295-2.317, 2.320-2.330, 2.350-2.359, 2.384-2.389, 2.395-2.403. ｨｬ070803060908090609 [1] 0803080307090903 ﾁ 02. ﾂ., ｨｲﾁ09 ﾁ0707 ｨｬ. ｨｦ. 040303010308060705. 11 0900.: 01070300020709 020005 03000603030006090303 ﾁ0908030001020206 09070603-000203020708 07 0905000900000302020201 07 04060304070001020201 070309070302070301 01090803010908070907. ｨｪ.: 0106030409, 2003{2009. [2] 0803080307090903 ﾁ 02. ﾂ., ｨｲﾁ09 ﾁ0707 ｨｬ. ｨｦ. 040303010308060705. 11 0900.: ｨｲ09020907020709 020005 03000603030006090303 ﾁ0908030001020206 09070603-000203020708 07 0905000900000302020201 07 04060304070001020201 070309070302070301 01090803010908070907. ｨｪ.: 0106030409, 2003{2009. 0803080307090903 ﾁ 02 ﾁ0503020708 ﾂ070908030603 ﾁ0707, 040603040307070306 09090403020602 09000503000602 07 050303010308060707 0003000105080807020709030503 050307090209060708 ﾁ030202030503 090207 ﾁ0306070708030809, 0909020207020908 040703.-010908. 02090909, 0803070308020208 0609000308020709 030006030503 030006090303 ﾁ09020705 ｨｰ03. Email: potoskuev@pisem.net

13ｨｮ0809020302080901 07 04060304030209 ﾁ090803000501 0109080301090807070307090706 0704030107090001020307080308 ｨｮﾁ030203020703 030902090707 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301 09 0902090003050707020308 030902090703 07 0007020308020201 040902090107030209000301 ﾂ. 04. ｨｪ0308090203 ﾁｨｲ0902090703 0304080701070309010707 020603000203-0007020308020308 04090209010707 07 000702030802020107 03050609020707030207050107 040307 ﾁ0506030209 030209070708030001020905 00070803060908090609, 0701., 0209040607010306, [1]. 070202090903, 080300010903 ﾁ [2] 00020003 0309010307030203, 070803 0003000303 0300-060905 030902090709 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301 07 000800020107 03050609020707030207050107, 07 080307-0907 030603020705 04060303090807 ﾁ020308 050303010308060707, 04090908070703070907 0609 ﾁ0203070700010209 030902090703 0304080701070309010707 07 0007020308020201 040902090107030209000301. ﾂ 03080007070703 0308 [2], ﾁ 020907080305060308 070809080103 030902090709 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301 0009020308 04030603 ﾁ0302030209 ﾁ 030902090709 07 0007020308020201 040902090107030209000301 0809090701 04060303090807 ﾁ020201 040603030006090303 ﾁ0902070301, 09030803060303 070306060902050308 09070003 ﾁ0703 0203030806070109080300010203070807 04030603010302020206, 030002070203 02090009-050903010303 0209 01020300030708 ﾁ03 0305060902070703020708. ｨｰ090707010308060701 070003020908060908 030902090709: 0109090707010703070603 ﾁ090801 040607 030506090207070302070506 n ﾆ j=1 a jy j + a n+1 n ﾆ j=1 b jy j + b n+1 (1) f k (y 1 ; y 2 ; :::; y n ) ﾜ B k ; (k = 1; 2; :::; m); (2) y j ﾝ 0; (j = 1; 2; :::; n): (3) 070003030209070701 01020300030708 ﾁ03 06030403020708 02030609 ﾁ03020708 ﾁ (2),(3) 0703060303 M. 02070007 0302090103020908030001 04090209010707 (1) ﾁ 080307090906 01020300030708 ﾁ09 ｨｪ 03000609060903080705 ﾁ 0, 0803 04090209010705 (1) 0203 03050609020707030209 0209 01020300030708 ﾁ03 ｨｪ 0207 07 ﾁ03060609, 0207 0702070309. ﾂ 05080301 070009070903 030902090709 (1), (2), (3) 080607 ﾁ070900010209. 08030508030109 0406030204030003000701, 070803 03020901030209-08030001 ﾁ 080307090906 01020300030708 ﾁ09 ｨｪ 0203 03000609060903080705 ﾁ 0. ｨｲ0902090709 (1), (2), (3) 040607 05080301 04060302040300030003020707 0009020301 02090302 ﾁ090801 03090209070308 D. 0709090302 ﾁ0903080705, 070803 07 0803070907 030603020705 04060303090807 ﾁ020308 050303010308060707 030902090709 D 0509 ﾁ07 ﾁ09000302080209 030902090703 0304080701070309010707 07 0007020308020201 040902090107030209000301, 09030803060908 0009020301 02090302 ﾁ090801 03090209070308 L. 000307020303, ﾁ0703050209 0209080203080705 020309030803060303 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703 04060307080609020708 ﾁ09 {y 1 ; y 2 ; :::; y n }, 04030603 ﾁ030205060303 030902090709 D ﾁ 030902090709 L, 040607070301 050803 040603030006090303 ﾁ09020703 0203 0609030602 ﾁ090308 01020300030708 ﾁ03 ｨｪ, 080909 090909 0507040306040003070903070801, 0403060306030205060905 ﾁ 00030709030203070203 090209000302020908 0507040306040003070903070801, 0203 0406030603020708 0703060303 ﾁ020908060302020703 0803070907 01020300030708 ﾁ09 ｨｪ. ﾂ 070907080203070807, 03070007 0305060902070703020705 (2) 00070203080202, 0803 030902090709 D 0009020308 03090209070308 020603000203-000702030802030503 0406030506090101070603 ﾁ09020705, 09030803060908 020005 090609080903070807 0009020301 02090302 ﾁ090801 030902090709 DL. ﾂ 05080301 070009070903 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703 04030603 ﾁ03020708 010203050305060902020303 01020300030708 ﾁ03 ｨｪ 070203 ﾁ09 ﾁ 010203050305060902020303 01020300030708 ﾁ03, 040307090300010909 0507040306040003070903070801, 0403060306030205060905 ﾁ 00030709030203070203 090209000302020908 0507-040306040003070903070801, 0203 0406030603020708 0703060303 ﾁ020908060302020703 0803070907 01020300030708 ﾁ09 ｨｪ. ﾂ 05080301 070009070903 030902090709 DL 0509 ﾁ07 ﾁ09000302080209 030902090703 000702030802030503 0406030506090101070603 ﾁ09020705, 09030803060908 020005 090609080903070807 0009020301 02090302 ﾁ090801 0309-0209070308 LL. 0803 080308 0003 04060707070203, 03070007 0305060902070703020705 (2) ﾁ020409090002, 0803 030902090709 D ﾁ 05080301 070009070903 0009020308 0509 ﾁ07 ﾁ09000302080209 030902090703 ﾁ0204090900030503 0406030506090101070603 ﾁ09020705 07 0007020308020301 040902090107030209000301. 08030909000301, 070803 07 0803070907 030603020705 04060303090807 ﾁ020308 050303010308060707 030902090709 D 0509 ﾁ07 ﾁ09000302080209 030902090703 L. 010005 0508030503 07020907090009 04030909000301, 070803 0008000303 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703, 04030603 ﾁ030205060303 0507040306040003070903070801 n ﾆ j=1 b j y j + b n+1 = 0 (4) 19

1320 ﾂ. 04. ｨｪ0308090203 ﾁﾁ 00030709030203070203 090209000302020908 0507040306040003070903070801, ﾁ020406050100050308" 020603000203-0007020308020908 04090209010708 (1), 08.03. 0403-0603 ﾁ03020708 020603000203-0007020308020908 04090209010708 (1) ﾁ 0007020308020908 04090209010708. 08030203080708 ﾁ090301 04060303090807 ﾁ020201 040603030006090303 ﾁ0902070301 y j = 0209 0507040306040003070903070801 (4). 08030009070701 ( n ﾆﾆ n b j j=1 i=1 070007, 0103020505 04030605020309 07090101070603 ﾁ09020705, 69 n ﾆ n ﾆ 61 i=1 j=1 n ﾆ j=1 d ijy i + d j;n+1 n ﾆ i=1 d iy i + d n+1 (j = 1; 2; :::; n) (5) ) ( n ) ﾆ d ij y i + d j;n+1 + b n+1 d i y i + d n+1 = 0 62 b j d ij + b n+1 d i 64 y i+ n ﾆ j=1 i=1 b j d j;n+1 + b n+1 d n+1 = 0: 08060303090807 ﾁ020201 040603030006090303 ﾁ0902070301 (5) 0507040306040003070903070801 (4) 04030603 ﾁ030207080705 ﾁ 00030709030203070203 090209000302020908 0507040306040003070903070801 0803050209 07 080300010903 0803050209, 0903050209 n ﾆ j=1 b j d ij + b n+1 d i = 0; (i = 1; 2; :::; n): ﾆ 0603 ﾁ 05080301 070009070903, 03070007 n b jd j;n+1 + b n+1 d n+1 ﾙ 0; 0803 030703 ﾁ07020203, 070803 020603000203-0007020308020905 04090209010705 j=1 (1) 040306030603020708 ﾁ 0007020308020908, 08.03. 030902090709 D 040306030603020708 ﾁ 030902090709 L. 010909030902020206 04060303090807 ﾁ020206 040603-030006090303 ﾁ09020708 070906030708 ﾁ090308 00030709030203070203 0102030503. ﾂ0303020709090308 030902090709 02090603000203020705 0209070003000303 0406030708030503 080909030503 040603030006090303 ﾁ09020705. 0506070803060707 0406030708030802 040607 05080301 ﾁ03030103000202 060903000707020203. ﾂ0900020201 0906070803-06070301 0406030708030802 05 ﾁ000503080705 07030606090203020703 070806090908090602 0305060902070703020708 (2), (3), 08.03. 07030606090203020703 090909 0707-070009 0305060902070703020708 ﾁ070209 (2), 080909 07 0707070009 0305060902070703020708 ﾁ070209 (3). 0909020301 070709090801 0809090303 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703 (5), 09030803060303 0305060902070703020705 (3) 04030603 ﾁ03020708 ﾁ 0305060902070703020705 080909030503 0003 ﾁ070209, 08.03. ﾁ 0305060902070703020705 y j ﾝ 0; (j = 1; 2; :::; n): (6) ｨｮ020907090009 04030909000301, 070803 0508030503 ﾁ0703050209 0103000203 0203000708010705, 03070007 b n+1 ﾙ 0: 0103080708 ﾁ07080300010203, 060907070103-08060701 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703 ﾁ070209: y j y j = n ﾆ d iy i + d ; (j = 1; 2; :::; n): (7) n+1 i=1 08030203080708 ﾁ090301 05080701 040603030006090303 ﾁ0902070301 0209 0507040306040003070903070801 (4). 08030009070701 69 n ﾆ 60 61 b j n ﾆ j=1 y j 62 63 d iy i + d 64 + b n+1 = 0; (j = 1; 2; :::; n): (8) n+1 i=1 080603030006090303 ﾁ09020703 (7) 04030603 ﾁ03020708 00030709030203070203 090209000302020908 0507040306040003070903070801 ﾁ 0507040306040003070903070801 n ﾆ i=1 d i y i + d n+1 = 0 (9)

13ｨｮﾁ030203020703 030902090707 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301... 21 0609 ﾁ020908060302020706 080307090906 01020300030708 ﾁ09 M ( ﾁ 09030803060303 04030603 ﾁ030207080705 01020300030708 ﾁ03 ｨｪ 040603030006090303 ﾁ0902070301 (7)) 0003 ﾁ0905 0709070801 (9) 03080007070209 0308 02090005. 08030508030109 0209 ﾁ020908060302020706 080307090906 01020300030708 ﾁ09 M 090609 ﾁ0203020703 (8) 0103000203 04030603040707090801 ﾁﾁ070203: 070007 n ﾆ j=1 ( n ) ﾆ b j y j + b n+1 d i y i + d n+1 = 0 i=1 n ﾆ j=1 (b j + b n+1 d j )y j + b n+1 d n+1 = 0: 000304030601 ﾁ020003060301 d j ; (j = 1; 2; :::; n + 1) 080909070107, 0708030002 0507040306040003070903070801 (4) 04030603 ﾁ03020700090701 040603-030006090303 ﾁ0902070301 (7) ﾁ 00030709030203070203 090209000302020908 0507040306040003070903070801. 08030009050905 d j = 6ﾓ1 b j b n+1 ; (j = 1; 2; :::; n); d n+1 = 1 (10) 0203000103010705 0508030503. 0506030103 08030503, 0003050903 040603 ﾁ03060503080705, 070803 04060303090807 ﾁ020303 040603030006090303 ﾁ09020703 y j = y j ﾆ 1 6ﾓ1 n b i bn+1 i=1 y i 04030603 ﾁ03020708 020603000203-0007020308020908 04090209010708 (1) ﾁ 0007020308020908 04090209010708 ; (j = 1; 2; :::; n) (11) 050203 n ﾆ j=1 j y j + n+1 ; (12) j = b n+1a j 6ﾓ1 a n+1 b j b 2 ; (j = 1; 2; :::; n); n+1 = a n+1 : n+1 b n+1 06070003 0009020308 0403090903090203, 070803 0209 01020300030708 ﾁ03 ｨｪ 04090209010705 n ﾆ 1 6ﾓ1 i=1 b i b n+1 y i 0701030308 03020702 07 080308 0003 03020909. 070807080209 07000302090308, 070803 0305060902070703020705 (3) 040607 040603030006090303 ﾁ09020707 (11) 030703- ﾁ07020203 040306030603020508 070007 ﾁ 0305060902070703020705 (6), 070007 ﾁ 0305060902070703020705 y j ﾜ 0; j = 1; 2; :::; n; 09030803060203 03090103020308 y j 0209 6ﾓ1y j 0403060308020908 ﾁ 0305060902070703020705 ﾁ070209 (6). 0809070801 0305060902070703020705 (2), (3) 040603030006090303 ﾁ0902070301 (11) 04030603 ﾁ030205080705 ﾁ 070003020908060703 0305060902070703020705 ' k (y 1; y 2; :::; y n) ﾜ k ; (k = 1; 2; :::; m) (13) y j ﾝ 0; (j = 1; 2; :::; n): (3 ) 070703 ﾁ07020203, 070803 010909070701090102 (0107020701090102) 04090209010707 (1) 0209 01020300030708 ﾁ03 ｨｪ 07 04090209010707 (12) 0209 01020300030708 ﾁ03 ｨｪ 03020702090903 ﾁ02. 0009090701 03000609030301, ﾁ 070009070903 b n+1 ﾙ 0, 030902090709 D 04060303090807 ﾁ020201 04060303000609-0303 ﾁ0902070301 090303060207020908 (11) 04030603 ﾁ030207080705 ﾁ 070003020908060908 0509 ﾁ07 ﾁ0900030208020908 030902090709 L: 0109090707010703070603 ﾁ090801 0007020308020908 04090209010708 (12) 0209 01020300030708 ﾁ03 ｨｪ, 030406030203000503010301 02030609 ﾁ03020708 ﾁ090107 (13), (3 ). 080607 05080301 0709-06030708 ﾁ03020203, 070803 0309 07070308 070403010709000102030503 ﾁ0200030609 04060303090807 ﾁ02030503 040603030006090303 ﾁ09020705 0305060902070703020705 (2), (3) (6ﾓ5)

1322 ﾂ. 04. ｨｪ0308090203 ﾁ 040306030603020508 ﾁ 0305060902070703020705 080909030503 0003 08070409 (13), (3 ). ﾂ 070907080203070807, 03070007 0305060902070703020705 (2) 00070203080202, 0803 0305060902070703020705 (13) 0809090003 0009020908 000702030802020107. ﾂ 05080301 070009070903 030902090709 (1), (2), (3) 05 ﾁ000503080705 03090209070308 020603000203-000702030802030503 0406030506090101070603 ﾁ09020705 07 04060303090807 ﾁ020201 040603030006090303 ﾁ0902070301 (11) 030209 04030603 ﾁ030207080705 ﾁ 030902090709 000702030802030503 0406030506090101070603 ﾁ09020705 (12), (13), (3 ) 07 0703060609020302070301 070806090908090602 0305060902070703020708 (2), (3). 0803070003 0304060302030003020705 030408070109000102030503 06030403020705 04030009070302020308 030902090707 (12), (13), (3 ) ﾁ 040806070603 ﾁ0902020206 0903030602070209080906 07 04030103060108 040306010900 (11) ﾁ020609030701 050803 06030403020703 ﾁ 0707060302020206 0903030602070209080906. 07070809000705 02030603040302020201 ﾁ0304060307 0300 0304060302030003020707 0302090909 04090209010707 (*) 0209 080307090906 01020300030708 ﾁ09 M. 08030909000301, 070803 05080308 03020909 03020203030209070203 030406030203000503080705 030209090301 0302090103020908030005 04090209010707 (1) 0209 080307090906 01020300030708 ﾁ09 ｨｪ 07 030209090301 0707070009 b n+1. 010005 0508030503 02030300060302070103 ﾁ0307040300010303 ﾁ0908010705 040603030006090303 ﾁ0902070301, 0300060908020201 09 040603030006090303 ﾁ09020708 (11). 060908020301 050803 040603030006090303 ﾁ09020703. ｨｦ03 (11) ﾁ02080309090308, 070803 020005 0008000206 i, j = 1; 2; :::; n. 070807080209 y j y j = y i y i = 1 6ﾓ1 n ﾆ i=1 b i b n+1 y i: y jy i = y j y i; (i; j = 1; 2; :::; n) : (15) 0109000303, 0703 (11) 0701030301 b n+1 y j = y j (b n+1 6ﾓ1 070807080209, ﾁ 07070009 (15) n ﾆ i=1 b i y i ) = b n+1 y j 6ﾓ1 n ﾆ i=1 b i y j y i; (j = 1; 2; :::; n) : 070007 ｨｮ00030203 ﾁ09080300010203, b n+1 y j = b n+1 y j 6ﾓ1 (b n+1 + n ﾆ i=1 n ﾆ i=1 b i y j y i; (j = 1; 2; :::; n) b i y i )y j = b n+1 y j ; (j = 1; 2; :::; n) : b y j = n+1 y j ﾆ b n+1 + n b ; (j = 1; 2; :::; n): (16) iy i i=1 080302070809 ﾁ000505 (16) ﾁ (*), 0403070003 020307000300020206 040603030006090303 ﾁ09020708 04030009070701 n ﾆ 1 6ﾓ1 i=1 b i b n+1 y i = 08.03. 03020909 04090209010707(*) 0703 ﾁ040902090308 0703 030209090301 ﾁ0206090003020705 b n+1 b n+1 b n+1 + n ﾆ j=1 b jy j ; n ﾆ j=1 b jy j + b n+1 : ｨｮ00030203 ﾁ09080300010203, 03070007 0302090907 0302090103020908030005 04090209010707 (1) 0209 01020300030708 ﾁ03 ｨｪ 07 0707070009 b n+1 0703 ﾁ040902090808, 0803 04090209010705 (*) 040300030007080300010209 0209 01020300030708 ﾁ03 M. ﾂ 0406030807 ﾁ020301 070009070903 04090209010705 (*) 0209 01020300030708 ﾁ03 M 030806070109080300010209.

13ｨｮﾁ030203020703 030902090707 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301... 23 ｨｮ0009070908 b n+1 =0 07 ﾁ030207080705 09 0609070701030806030202030109 070009070908, 0209040607010306, 07 04030103060108 000702030802030503 040603-030006090303 ﾁ09020705 ﾁ070209: y i = y i + ij ; (i = 1; 2; :::; n) ; 050203 j; (1 ﾜ j ﾜ n) 0809090303; 070803 b j ﾙ 0; 09 ij = ｨｮ 0103000108 0700000807080609010707 07030003000302020308 080303060707 06090707010308060701 050003010302080906020208 040607010306. 0809070801 080603000903080705 0109090707010703070603 ﾁ090801 020603000203-0007020308020908 04090209010708 0209 01020300030708 ﾁ03 ｨｪ f (y 1 ; y 2 ) = y 1 6ﾓ1 y 2 y 1 + y 2 + 1 61 62 63 2y 1 + y 2 6ﾓ1 2 ﾜ 0 y 1 ﾝ 0 y 2 ﾝ 0 { 0; 03070007 i ﾙ j 1; 03070007 i = j : ｨｮ03050009070203 0300060308 080303060707, 050809 030902090709 020603000203-000702030802030503 0406030506090101070603 ﾁ09020705 04060303090807 ﾁ020201 040603-030006090303 ﾁ0902070301 y 1 = y 1 1 6ﾓ1 y 1 6ﾓ1 y 2 (17) y y 2 = 2 1 6ﾓ1 y 1 6ﾓ1 : (18) y 2 04030603 ﾁ030207080705 ﾁ 070003020908060908 030902090709 000702030802030503 0406030506090101070603 ﾁ09020705: 0109090707010703070603 ﾁ090801 0007020308020908 04090209010708 '(y 1; y 2) = y 1 6ﾓ1 y 2 0209 01020300030708 ﾁ03 M 4y 1 + 3y 2 6ﾓ1 2 ﾜ 0; y 1 ﾝ 0; y 2 ﾝ 0: ｨｬ03050903 090003020708010705, 070803 010909070701090001020303 06030403020703 040307000302020308 030902090707 0203070807050903080705 ﾁ 0803070903 y 1 = 1 2 ; y 2 = 0 07 ' ( 1 2 ; 0 ) = 1 2. ｨｹ08030109 06030403020708 07030308 ﾁ03080708 ﾁ090308 070003020908060303 010909070701090001020303 06030403020703 0707060302020308 030902090707 020603000203-000702030802030503 0406030506090101070603 ﾁ09020705 y 1 = 1; y 2 = 0; f (1; 0) = 1 2, 09030803060303 ﾁ02070707000503080705 0403 0403060109000901 (17), (18). ｨｬ070803060908090609 1. ｨｪ. 090903090609, 05. 0403080807. 06030007020308020303 0406030506090101070603 ﾁ09020703, ｨｪ030709 ﾁ09: ｨｪ0706", 1982 05. 2. ｨｪ0308090203 ﾁﾂ.04. 07 03090209070906 0304080701070309010707 07 020603000203-0007020308020201 040902090107030209000301 // ｨｹ0903020301070909 07 0109080301090807070307090703 010308030202, 6 54, 1971 05. ｨｪ0308090203 ﾁﾂ090003060708 0406070503060103 ﾁ0707, 020301030208 09090403020602 ﾁ0207040308 01090803010908070907 ｨｪ03070903 ﾁ0709030503 050307090209060708 ﾁ030202030503 090207 ﾁ0306070708030809 0406070603020303000907080603080708 ﾁ09, 0909020207020908 0803060207070307090706 02090909.

13ｨｦ03 07070803060707 01090803010908070907 07070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 1 ｨｨ030209 ｨｦ. ｨｪ. 090307 080603020009050903010905 ﾁ02070109020708 0707080908030005 070809080105 04060302070809 ﾁ00050308 0703000308 020309000902 0209 07070104030307090103 300-0003080703 060900030802 04. ﾂ. ｨｬ03080002070109 `Nova Methodus' (1684{1984)1 7, 0701. 070203070909 09 030905030003 ﾁ0909. ﾂ 020308 0403090903090203, 070803 0403070806030302020303 ｨｬ0308000207010301 07070707070003020703 02070404030603020107090003 ﾁ, 03070203 ﾁ0902020303 0209 0403020508070506 04030603010302020308 07 04060305060307070707 04030603010302020308 ( ﾁ 03080007070703 0308 04030205080705 04090209010707, 0003000906030503 ﾁ 03070203 ﾁ03 0703- ﾁ060301030202030503 010908030109080707030709030503 09020900070309) 05 ﾁ000500030701 000305070703070907 0708060308020308, 0406090908070703070907 0302090707010308 07 0507080308070703070907 0703 ﾁ0306040302020308 08030306070308. ｨｰ09020303 070809080105 02090403070908090209 ﾁ 00090602090003 ｨｪ090803010908070909 ﾁﾁ0207-040301 030006090303 ﾁ09020707", 6 52, 2004 05. 060907080305060905 04090000070909010705 03070906030708 ﾁ00030209 07 06090306030403020705 0603020909010707 09090903090202030503 00090602090009. ﾂﾁ030203020703 ｨｪ02 040609030202090301 300-0003080703 040305 ﾁ0003020705 040306 ﾁ0308 070809080107 0300 07070707070003020707 00030709030203070203 0109000206 2. ﾂ 020308 030605 0703020306000900030701 0102030503 02030507020206 ﾁ020709090302 ﾁ09020708 07 02090003 0309000009000203020708 3. 070202090903 09 1684 05. 09 ｨｬ0308000207-0109 090003 070003000700030701 070508090303 04060302070809 ﾁ0003020703 0300 05080301 07070707070003020707. ｨｹ0803 04060302070809 ﾁ0003020703 05 07 030003030209070908 ﾁ020609000302070301 縺0003080002070103 ﾁ03 070707070700030207031 7. 罟ｦ030300060308030207031 7 070007 縺03080906020807031 7 ｨｬ0308000207010301 07070707070003020705 000307-09030203070203 0109000206 030002070203 02090807060903080705 1675 05. 4, 0203 03070203 ﾁ020203 04030205080705 07 07020307, 07040306010900070603 ﾁ0902020203 0701 0403020907090009, 00020007 070906030708 ﾁ03020203 040306030609000308090202 0309 0203 ﾁ050801 000308, 040603040302040706 07 01030103020809 0308090602080705 0203 040306 ﾁ0308 04090000070909010707. 0903000303 04030302020703 070809080107 070901030503 ｨｬ03080002070109, 09 0809090003 000609080103 ﾁ 0903060209000007, ｨｬ030407-08090005 07 020609050706 07020300090007 050803 07070707070003020703 0703 ﾁ030708020201; 030203 000207080603 06090704060307080609020700030701 07 0708090003 0406070103-020508010705 020005 06030403020705 0709010206 06090302030300060903020206 0309020907. ｨｮ 1684 05. 0203 1720 05. 03070203 ﾁ0304030009050908060703 04030205-080705 0003080002070103 ﾁ09 07070707070003020705 04060308030604030007 00070401 0203030209070708030001020303 070301030203020703 5. ﾂ 05080308 070809080103 05 00090209 1 010309000902 000200 04060302070809 ﾁ000302 0209 07070104030307090103 300-0003080703 060900030802 04. ﾂ. ｨｬ03080002070109 `Nova Methodus' (1684{1984)1 7, 04060306030207 ﾁ040301 ﾁ 05. 06030602 ﾁ07090306060908 (06070203060009020202) ﾁ 09 ﾁ0509070803 1984. 0704090000070903 ﾁ0902 ﾁ Studia Leibnitiana, Sonderheft 14 (Wiesbaden (Steiner Verlag), 1986), pp. 103{118. 2 G.W. Leibniz, 絲ova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratur, et singulare pro illis calculi genus1 7, Acta Eruditorum. 03090805000601 1684, pp. 467{473; 0809090003 ﾁ G. W. Leibniz Mathematische Schriften (7 vols., ed. C. I. Gerhardt), Berlin and Halle, 1849{1853 (040306030403070908090203 Hildesheim 1961{1962), vol. 5, pp. 220-226. 3 ｨｮ06. H.-J. Hess 綮ur Vorgeschichte der `Nova Methodus1 7', Studi09 Leibnitiana, Sonderheft 14 (Wiesbaden (Steiner), 1986), pp. 64{102. ｨｮ01. 0809090003 ﾁ0703070803060302020703 07 07060303 ﾁ020709080203 0403000303020203 04060701030709020705 ﾁ 040307000302020301 0708090001050207090301 07030209020707 ｨｪ0308030209 P. Dupont'0301 07 C. S. Roero: Leibniz 1684, Torino (Fac. Sci. Mat. Fis. Nat., Univ. Torino; Series Quaderni di Mathematica 56), 1984. 4 ｨｮ01. Hofmann, J. E., Die Entwicklungsgeschichte der Leibnizschen Mathematik wahrend des Aufenthaltes in Paris (1672{1676), Munchen, 1949, pp. 118-130; Hofmann, J. E., Leibniz in Paris 1672{1676 (04030603 ﾁ0302 0406030202020906030503 07030209020705), Cambridge, 1974, pp. 187{201; Baron, M. and Bos, H. J. M., Newton and Leibniz (Unit C3 of the Open University course AM 289 History of Mathematics origins and development of the calculus), Milton Keynes (Open University Press), 197, pp. 35{46 07 Bos, H. J. M. Newton, Leibniz and the Leibnizian tradition, (040009 ﾁ09 II 0304090000070903 ﾁ090209 ﾁ: From calculus to set theory, and introductory history (ed. I. Grattan Guinness), London, 1980), pp. 49{93, 0307030003020203 pp. 60{70. 5 0609070003000303 ﾁ0900020303 040902020901030208090001020303 070301030203020703 0003080002070103 ﾁ09 07070707070003020705 ﾁ 060902020708 040306070302 0703070803050003 ﾁ 0403060302030703 010308030203 ﾁ, 060903 ﾁ07080206 020005 06030403020705 03020203010306020206 0309020907 ( ﾁ 03070203 ﾁ020301 060900030809 07 090607 ﾁ020107) 0209 02 ﾁ09010306020203 (07030103080708 ﾁ09 090607 ﾁ0206, 04030603010302020203 07 02 ﾁ090105 070803040302050107 07 ﾁ0300030202, 0403 ﾁ0306060203070807); 0701. S.B. Engelsman 絨rthogonaltrajektorien im Prioritatsstreit zwischen Leibniz und Newton1 7 Studia Leibnitiana, Sonderheft 14 (Wiesbaden (Steiner) 1986), pp. 144{156, 09 0809090003 Engelsman, S.B. Families of curves and the origins of partial dierentiation, Amsterdam a. o. (North-Holland Publ.), 1984. 24

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 25 0701030801 02030003 07 0508070107 03070203 ﾁ030403000905090806070107 040302050807050107 6. ｨｪ030308 0103000108 0009020308 0403090903090801 0609060909080306020203 0307030003020203070807 0003080002070103 ﾁ09 07070707070003020705. 09 040304020809080701 07020300090801 050803, 0707070003020905, ﾁ 070501 030203 03080007070903080705 0308 0703 ﾁ060301030202030503 010908030109080707030709030503 09020900070309. 09 070300070609080701 030007090002090801 ﾁ030406030702 040302070109020705 07 08030602070907 ﾁ 00030001040308 01030603, 020300030007 ﾁ030406030702 03070203- ﾁ09020708. 01060905070107 070003 ﾁ090107, 01030205 0009020308 0702080306030703 ﾁ090801 0203 0803, 070803 0809090303 0003080002070103 ﾁ02 02070404030603020107090002 070007 0709010102, 09 0803, 090909 0706 04060302070809 ﾁ00050007 07030003 07 0707040300010303 ﾁ090007 ｨｬ030800020701 07 030503 040306 ﾁ0203 04030700030203 ﾁ0908030007. 09 04030009050908, 070803 0809090308 040302060302 070103000308 040603050702070801 020309030803060203 040300030003020705 0003080002070103 ﾁ09 07070707070003020705, 0709070803 09040907090903010203 0703 ﾁ070209. ｨｬ030109020905 07 0003070903020307020201 070707000301 ﾁ0306040702 ｨｬ030800020701 020303020203090609080203 03080103070900, 070803 090008070301 09 040302070109020708 030503 07070707070003020705 070009000708 04060302070809- ﾁ0003020703 03 090607 ﾁ0308 090909 03 00030109020308 07 0003070903020307020201 070707000301 ﾁ0306040702. 05 04060701030609, ﾁ 1684 05. 0302 0407070900 03 07 ﾁ030706 0503030103080607070307090706 01030803020906: ﾁ0703 030207 0103050908 00020801 ﾁ02 ﾁ0302030202 0703 030006030503 0406070201070409, 09030803060201 05 040300010309080701 040607 0703-01030603020707 090607 ﾁ030007020308020206 0407050906: 0302 07030708030708 ﾁ 080301, 070803 090607 ﾁ0905 0007020705 0103000308 00020801 04060302070809 ﾁ00030209 090909 00030109020905 07 0003070903020307020201 070707000301 070803060302. 7 0608030002 0403050702070801 090302010304010708 090607 ﾁ0308 090909 00030109020308 07 0003070903020307020201 070707000301 ﾁ0306040702, 05 060907070103080608 07020907090009 080308 070009070908 (060707. 1), 0903050209 090607 ﾁ0905 040607000007000903080705 0903020307020308 0003-0109020308 OABC. 0806030204030003000701, 070803 ﾁ030604070202 00030109020308 0003-000908 0209 090607 ﾁ0308. 010005 090900020308 0703 05080706 ﾁ0306040702 06090707010308060701 0306020702090809 y, 0900070107070709 x, 0200070209 02090507 s, 07030103060503010908 0308 0209-07090009 090607 ﾁ0308, 04000306090201 Q 0103000209 090607 ﾁ0308, 03070108 09000701070707 07 030602070209080308 (02090302 ﾁ0903010908 0809090003 縺09 ﾁ0902060908090603081 7 090607 ﾁ0308), 07 ﾁ0303000603 0008000908 04030603010302020908, 09030803060905 0103000308 00020801 03040603-020300030209 ﾁ 07 ﾁ050307 07 05080308 090607 ﾁ0308. 080607000007000908060905 00030109020905 040306030002090308 0809090701 03000609030301 04030700030203 ﾁ09080300010203070807 04030603010302-020206. 010003 ﾁ 07 ﾁ030706 060902020706 07070700030203 ﾁ0902070506 ｨｬ030800020701 0704030107-0900010203 0702080306030703 ﾁ09000705 080308 0603000108, 09030803060908 050807 04030700030203 ﾁ09- ｨｰ0707. 1. 080300010203070807 070506090808 ﾁ 02 ﾁ0906 03070203 ﾁ020206 03090209070906, 07 ﾁ05030902020206 07 090607 ﾁ020107: 030902090703 03 09 ﾁ090206090809060906 07 030902090703 03 0909070908030001020206. 0702 030703030209 ﾁ0900, 070803 09 ﾁ0902060908090602 07 ﾁ050309-0202 07 07090101090107 0403060300020903010206 04030700030203 ﾁ0908030001020307080308, 09 0909070908030001020203 07 0706 06090302030708050107. ｨ 070103020203: 03070007 00030109020905 ﾁ020006090209 0809090701 03000609030301, 0708030002 0609030203070801 0103000209 04030700030203 ﾁ090803000102020107 03020907030207050107 x 00020009 040307080305020203 0609 ﾁ0209 1, 0803 0803050209 0709010109 03060207020908 02090508 0406070000070003020703 020005 09 ﾁ0902060908090602, 09 0609030203-070807 0103000209 04030700030203 ﾁ090803000102020107 03060207020908090107 0009020908 0406070000070005020203 03090209 ﾁ090801 020909000302 0909070908030001020206 ﾁ 07030308 ﾁ03080708 ﾁ0908060706 080307090906 090607 ﾁ0308. ﾂ 070009070903 0406030703 ﾁ030001020206 040607000007000908060706 00030109020206 030802030403020703 07090101 07 060903020307080308 09 09 ﾁ090206090809060901 07 0909070908030001020201 0009020308 020307090300010903 0003000303 080302090701, 0203 0403-0406030002030109 09020300020201. ﾂ 060902020706 07070700030203 ﾁ0902070506 0707070003 ﾁ0206 04030700030203 ﾁ0908030001020307080308 ｨｬ030800020701 060907070109080607 ﾁ0900 07090101070603 ﾁ09020703 07 040300090703020703 060903020307080308 090909 0304030609010707, 07030308 ﾁ03080708 ﾁ03020203 0309020908060703 020005 020902020308 04030700030203 ﾁ09080300010203070807 0203 ﾁ0203 04030700030203 ﾁ09080300010203070807 07090101 07 060903020307080308, 090909 050803 0403090903090203 ﾁ 08090000. 1. 0702 03080103070900 0809090003, 070803 050807 0304030609010707 ﾁ030907010303000609080202: 04030708060307 ﾁ 04030700030203 ﾁ09080300010203070801 060903020307080308 020005 04030700030203 ﾁ09080300010203070807 07090101, 0102 ﾁ03070708090203 ﾁ0701 0707060302020908 04030700030203 ﾁ09080300010203070801, 07 0803070203 080909 0003, ﾁ0305 ﾁ 04030700030203 ﾁ09080300010203070801 6 09 0300070900020900 050807 ﾁ030406030702 0003000303 0403020603000203 ﾁ 01030308 070809080103 絅ierentials, higher-order dierentials and the derivative in the Leibnizian calculus1 7, Archive for History of Exact Sciences, 14, 1974, pp. 1{90; 020907080305060905 070809080105 040302 ﾁ03020708 07080305 020309030803060201 070907080501 05080308 060900030802, 0307030003020203 050009 ﾁ03 II, pp. 12{35. 7... omnes deduci posse ex generali quodam meo dimentiendorum curvilineo-rum principio, quod gura curvilinea censenda sit aequipollere Polygono innitorum laterum1 7. (Leibniz, Mathematische Schriften (04060701. 1) vol. 5, p. 126). 000708090809 0703 070809080107, 0304090000070903 ﾁ0902020308 ﾁ Acta Eruditorum ﾁ 02030909000603 1684 05.; ｨｬ030800020701 03080709070807 070702000903080705 0209 070204070207-0803030701090001020208 0103080302, 0304090000070903 ﾁ0902020208 ｨｦ. ｨｨ. 04080906010301 ﾁ 0109060803 ﾁ07090301 020301030603 0508030503 0003 00090602090009 0309 1684 05.

1326 ｨｨ030209 ｨｦ. ｨｪ. 090307 07090101 020005 04030700030203 ﾁ09080300010203070807 060903020307080308, 0102 0304050801 04030009070701 0700030202 0707060302020308 04030700030203 ﾁ09080300010203070807 (0309 0707090008070302070301 a 1, 03070007 00020801 0003000303 080307020201). 00090000070109 1 08030700030203 ﾁ09080300010203070801: a 1, a 2, a 3, a 4,..., 04030700030203 ﾁ09080300010203070801 07090101: 04030700030203 ﾁ09080300010203070801 060903020307080308: s 1, s 2, s 3, s 4,... d 1, d 2, d 3, d 4,... 050203 050203 s 1 = a 1, d 1 = a 2 6ﾓ1 a 1, s 2 = a 1 + a 2, d 2 = a 3 6ﾓ1 a 2, s 3 = a 1 + a 2 + a 3, d 3 = a 4 6ﾓ1 a 3, s 3 = a 1 + a 2 + a 3 + a 4, d 4 = a 5 6ﾓ1 a 4, 07 08. 02. 07 08. 02. 080603050609010109 ｨｦ0706030205 0703 07030308 ﾁ03080708 ﾁ0705 0103000209 07 ﾁ03080708 ﾁ090107 090607 ﾁ0206 07 04030700030203 ﾁ0908030001020307080308, ｨｬ030800020701 070203000900 02 ﾁ09 ﾁ0900020206 07020809070807 ﾁ020206 ﾁ02 ﾁ030209: 6ｦ1 ｨｦ03090703020703 0909070908030001020206 07 09 ﾁ09020609080906 090607 ﾁ0206 040607 ﾁ03020708 09 060907070103080603020708 04030700030203 ﾁ09080300010203-07080308 09000701070707, 03060207020908 07 08. 02.; 0909070908030001020203 07030308 ﾁ03080708 ﾁ090808 060903020307080501, 09 ﾁ0902060908090602 070901-010901. 080307090300010909 0304030609010707 ﾁ0305080705 04030700030203 ﾁ0908030001020307080308 07090101 07 04030700030203 ﾁ0908030001020307080308 0609030203-07080308 ﾁ030907010303000609080202, 030902090707 03 0909070908030001020206 07 09 ﾁ090206090809060906 0809090003 05 ﾁ000508080705 ﾁ03090701030300060908-02020107. 6ｦ1 02070007 090607 ﾁ0905 040607000007000903080705 0903020307020308 00030109020308, 0403060300020903010203 04030700030203 ﾁ09080300010203070807 0203070809 ﾁ0005-0808 0406070000070003020705 020005 09 ﾁ09020609080906 07 0909070908030001020206. ｨｹ0807 0406070000070003020705 0009020908 080301 0009070403, 070301 0103020104070107 0009020908 ﾁ03050802 0609030203070807 0703070302020706 0700030203 ﾁ. ｨｦ 030207 070809020908 08030702020107, 0903050209 0609030203070807 0009020908 ﾁ03050802 00030709030203070203 010900020107 (09 0703070302020703 0700030202 070809020908 00030709030203070203 0000070309070107), 0803 03070801 0903050209 090607 ﾁ0905 0009020308 060907070109080607 ﾁ0908010705 090909 00030109020905 07 0003070903020307020201 070707000301 ﾁ0306040702. ｨｹ0807 0702080907010707, 0709030001 0002 0203050702020107 030207 0207 00020007, 00020007 03000803020702030202 ﾁ 040603050609010109, 09030803060908 ｨｬ030800020701 030703030209020203 07040306010900070603 ﾁ0900 ﾁ 1765 05. 07 09030803060908 0302 09070403040203 03070906030708 ﾁ000500 ﾁ 0403070003020908060703 05030202. 05030208090602 05080308 040603050609010102 08090903 ﾁ02: 6ｦ1 0205 01030001 07030708030708 ﾁ 0703030209020707 07070707070003020705 09 ﾁ09020609080906, 0909070908030001020206 07 0603020708 ﾁ0302020206 0309020907, 07 ﾁ05-030902020206 07 090607 ﾁ020107, 09030803060303 04060302070809 ﾁ00050003 0002 0703000308 0103080302, 03070203 ﾁ02 ﾁ09080607080705 0209 0403060109000906 07 040609 ﾁ07000906 ﾁ020707070003020708. 6ｦ1 ｨｹ0803 07070707070003020703 0909070903080705 04030700030203 ﾁ0908030001020307080308 (03060207020908, 09000701070707 07 020609050706 04030603010302020206) 07 00030709030203070203 010900020107 06090302030708050107. 6ｦ1 ｨｹ0803 07070707070003020703 0703020306000708 0809090003 0304030609010707 020902 0508070107 04030700030203 ﾁ090803000102030708050107, 09 070103020203 0304030609-010708 (07 070701 ﾁ03000301 d), 070809 ﾁ05060908 ﾁ 07030308 ﾁ03080708 ﾁ0703 020902020308 04030700030203 ﾁ09080300010203070807 0305 06090302030708020908 04030700030203 ﾁ09080300010203070801, 07 0304030609010708 (07 070701 ﾁ03000301 ﾆ ), 070809 ﾁ05060908 ﾁ 07030308 ﾁ03080708 ﾁ0703 020902020308 0403070003-0203 ﾁ09080300010203070807 04030700030203 ﾁ09080300010203070801 0305 07090101. 080306 ﾁ0905 0304030609010705 070704030001030903080705 020005 0304060302030003020705 0909070908030001020206, ﾁ0803060905 020005 0304060302030003020705 09 ﾁ09020609080906. 6ｦ1 0704030609010707 d 07 ﾆﾁ030907010303000609080202. 080603070000080708060706090301 0203070903000109070107 0107080908090107, 090909 ｨｬ030800020701 040306010900070603 ﾁ0900 050807 060902020703 0406030506090101-020203 07020307. ﾂ 1697 05. 0302 0407070900 ﾂ090000070709:

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 27 ｨｰ0907070103080603020703 060903020307080308 07 07090101 0707070003 ﾁ0206 04030700030203 ﾁ0908030001020307080308 040607 ﾁ030003 01030205 09 01030308 040306 ﾁ0308 02030509020903, 0903050209 05 03070303020900, 070803 0609030203070807 030802030705080705 09 0909070908030001020201 07 0709010102 09 09 ﾁ090206090809060901 8. ﾂ 020609050301 0103070803 ｨｬ030800020701 0407070900: 07070203 ﾁ09020703 09020900070309: ｨｰ09030203070807 07 0709010102 03000609080202 02060905 0206090509, 080909 070803 0709010109 060903-02030708020308 04030700030203 ﾁ09080300010203070807 03070801 07000302 04030700030203 ﾁ09080300010203070807, 07 0609030203070801 070901010906020308 04030700030203 ﾁ09080300010203070807 0809090003 03070801 07000302 04030700030203 ﾁ09080300010203070807. 080306 ﾁ0303 05 030003030209070908 080909: ﾆ dx = x; ﾁ0803060303 080909: d ﾆ x = x. 9 ｨｹ090708060904030005010705 0903020307020308 00030109020308 070407070902020905 ﾁ020403 040603050609010109 00020009 06030900070303 ﾁ090209 ﾁ 0003080002070103 ﾁ0301 07070707070003020707. 09 06030709 060903080507-02070801 050803 07070707070003020703, 0300070900020905 ﾁ030406030702 040302070109020705 07 08030602070907, 07 0903080306020107 ｨｬ030800020701 07080300090209000705 ﾁ 060900030803 020902 07 ﾁ030308 04060305060901010308. 08060302070809 ﾁ0701 07030003 ( ﾁ0103070803 07 ｨｬ0308000207010301), 070803 04060307030308020508, 0903-050209 0903020307020905 00030109020905, 040607000007000908060905 090607 ﾁ0908, 0703 ﾁ0409020508 07 090607 ﾁ0308. 02070007 0102 ﾁ070309090007030706090301 05080308 04060302030001020208 04060301030707 (060707. 2), 050803 020901 0203 010203050701 04030103000308: 0609030203070807 0103000209 07000302090107 04030700030203 ﾁ09-080300010203070807 03060207020908 07 08. 04. 070809020908 0609 ﾁ0202 02090008, 0306020702090802 0309040300020508 ﾁ0708 04000306090201 0103000209 090607 ﾁ0308 07 03070108 09000701070707, 09 0308 00030109020308 020707030503 0203 030708090203080705. 07020702 0703 07040307030003 ﾁ 07040609 ﾁ0708010705 07 05080308 040603000003010308 07030708030708 ﾁ 080301, 0708030002 04060302070809 ﾁ070801 04060302030001020208 04060301030707 0003090900010203 (060707. 3). ﾂ 0909-00020308 0803070903 090607 ﾁ0308 07030909060905 (0406030203000003020703 07080306030202 00030109020308) 070809-0203 ﾁ07080705 0909070908030001020308, 07 ﾁ0207030809 04000307090308 04030003070907, 030506090207070302020308 0302-020701 0703 03 ﾁ03020103 ﾁ 00030109020308, 0708090203 ﾁ07080705 0609 ﾁ020308 0306020702090803. ｨｹ080308 000309090001-020208 04060302030001020208 04060301030707 0003050903 ﾁ07030909000703070603 ﾁ090801 07 0707040300010303 ﾁ090801; ﾁ 0203080708 ﾁ07080300010203070807 0302 05 ﾁ000503080705 03070203 ﾁ020201 ﾁ 0703 ﾁ0603010302020301 010908030109- ｨｰ0707. 2. 0807070307090301 09020900070303, 050203 0406030703 ﾁ0302020905 030406030203000503080705 070103020203 040307060302-0708 ﾁ0301 0508030503 0406030103070709. 070202090903 ｨｬ030800020701 0203 040300010303 ﾁ09000705 000309090001020201 040607000007000302070301, 0406030204030707080905 030109 05000300090001020303. 0702 0203 04060302070809 ﾁ000500 07030003 04030603060302 0308 0903020307020308 00030109020308 09 00030109020308 07 0003070903020307020201 070707000301 ﾁ0306040702 090909 04060302030001020208 04060301030707. ﾂ 05080301 070009070903 03 ﾁ03020105 07 09050002 00030109020308 07070703030007 0002, 07 04060302030001020208 04060301030707, 090909 050803 030008050702030203 ﾁ020403, 010305 0002 00020801 070208030604060308070603 ﾁ0902 00070401 0003090900010203. ｨｬ030800020701 07010308060300 0209 05080308 04030603060302 070903060303 090909 0209 040605010908 05090708060904030005010708 090302030702030503 070009070905 0209 0003070903020307020208. 080607 05080301 0703060609020508080705 0809090703 0500030103020802 ｨｰ0707. 3. 00030109020308, 090909 07080306030202 07 09050002, 09 0809090003 0403060300020903010203 04030700030203 ﾁ09080300010203070807. 04000300090001020303 0703090703020703 090607 ﾁ0308 0403-0406030002030109 ﾁ03030103000203; 00070401 0700030202 04030700030203 ﾁ0908030001020307080308 0708090203 ﾁ05080705 00030709030203070203 00000703-09070107. 05030203070203, 080609020203 ﾁ07030909000703070603 ﾁ090801 00030109020908 07 0003070903020307020201 070707000301 ﾁ0306040702 07 0403060300020903010203 04030700030203 ﾁ09080300010203070807; 0406030000030109 0903000009040709, 070303000609000502020905 0209 060707. 2, ﾁ0705 030605 0703060609020503080705. ｨｬ030800020701 0609030603040700, 070007 070903060303 030003040500 050809 0903020103040809090001020908 0406030000030109 040603000203 ﾁ07030503 03080909030301 0308 060907070103-080603020705 08030503, 070803 04060307070603020708 07 06090302030708050107 07 07090101090107 070901070107 0403 07030003. 070207 0708090203 ﾁ05080705 07020407-0207080303070109000102020107, 030202090903 ｨｬ030800020701 0708090609000705 0703000305090801 03000709000203020705 04060706030202 0702040702070803030701090001020206 8 絎ihi considerationern dierentiarum et summarum in seriebus numerorum primam lucern auderat, cum animadverterem dierentias tangentibus, et summas quadraturis respondere1 7. (040707010103 ｨｬ03080002070109 ﾂ090000070709 28.05.1697, Leibniz, Mathematische Schriften (04060701. 1) vol. 4, p. 25). 9 紮undamentum calculi: Dierentiae et summae sibi reciprocae sunt, hoc est summa dierentiarum seriei est seriei terminus, et dierentia summarum seriei est ipse seriei terminus, quorum illud ita enuntio: P dx aequ. x; hoc ita; d P x aeq. x1 7 (0703 0609090304070707 ｨｬ03080002070109 Elementa calculi novi pro dierentiis el summis, tangentibus et quadraturis, 0304090000070903 ﾁ0902020308 C.I. Gerhardt'0301 ﾁ Die Geschichte der h01heren Analysis, erste Ableilung, die Entdeckung der hoheren Analysis, Halle 1855, pp. 149-155; 010708090809 p. 153).

1328 ｨｨ030209 ｨｦ. ｨｪ. 090307 ﾁ030007070702 ﾁ 07 ﾁ030501 07070707070003020707. ｨｮ0903060303 0302 070309070900, 070803 04060307070603020708 07 03040306090107050107 ﾁ0305080705 070901010906020206 07 06090302030708020206 04030700030203 ﾁ0908030001020307080308 0403070003 0403060306030209 09 000307090302030702030109 070009070908. ｨｹ0803 070103000208 040302060302, 07 05 070707080908, 070803 0302 06090609090803060703090308 0109080301090807070307090708 0708070001 ｨｬ03080002070109, ﾁ 070907080203070807 07070009 030503 09000708060909010707. ｨｦ07070003020905 04060301030707 040605010308 05090708060904030005010707, 030902090207010705 ﾁ03040603070301, 090909 04060303000609030908080705 0403070003-0203 ﾁ09080300010203070807, 0403060300020903010203 0903020307020308 00030109020308. 08060302070809 ﾁ000505 0809090908 00030109020908, 0102 04090908070703070907 ﾁ02020300050301 0903020307020303 0707070003 0302090703020708 04030603010302020206, 09 070103020203 080306, 09030803060203 07 ﾁ0503090202 07 ﾁ0306040702090107 00030109020308. 0009090701 03000609030301 0102 04060302070809 ﾁ00050301 090900020908 04030603010302020908 0406030003050908060308 0903020307020908 0403070003-0203 ﾁ09080300010203070801 0302090703020708. 080607 0403060306030203 09 00030109020308 07 0003070903020307020201 070707000301 ﾁ0306040702 080301 0709010201 040302060903090103 ﾁ0903080705, 070803 04030603010302020905 040603000305090308 0003070903020307020908 04030700030203 ﾁ09080300010203070801 00030709030203070203 00000703-090706 0302090703020708. ｨｦ 040307090300010909 00030109020905 07 0003070903020307020201 070707000301 ﾁ0306040702 080304030601 0703 ﾁ040902090308 07 090607 ﾁ0308, 0203 0406070207010908080705 ﾁ03 ﾁ02070109020703 02070909090703 0302090703020705 04030603010302020308, 0906030103 0302090703020708 04030700030203 ﾁ09080300010203070807. 08030205080705 04030700030203 ﾁ09080300010203070807 07 04030603010302020308 080304030601 0703 ﾁ040902090808; 04030603010302020905 07 03070801 0406030003050903010905 0308 04030700030203 ﾁ09080300010203070801. 000304030601 06090707010308060701 0304030609010707, 09030803060203 ﾁ 0903020307020301 070009070903 07030403070809 ﾁ00050808 04030700030203 ﾁ09080300010203-07080501 0302090703020708 04030603010302020308 04030700030203 ﾁ09080300010203070807 0706 060903020307080308 070007 0706 07090101. 080607 0403060306030203 09 000307-090302030702030109 070009070908 050807 0304030609010707, 07030308 ﾁ03080708 ﾁ03020203 030003030209070903010203 070701 ﾁ0300090107 d 07 ﾆ, 07030403070809 ﾁ00050808 0003070903020307020201 04030700030203 ﾁ0908030001020307080501 0003070903020307020203 04030700030203 ﾁ09080300010203070807. 0603 040307090300010909 050807 0403070003-0203 ﾁ09080300010203070807 0703 ﾁ040902090808 080304030601 07 0403060301030202020107 090909 08090903 ﾁ020107, d 07 ﾆ 0708090203 ﾁ05080705 03040306090107050107, 0203080708 ﾁ090806070107 020902 0403060301030202020107 07 040306030002090806070107 0203 ﾁ0203 04030603010302020203. 0704030609010705 d 07030403070809 ﾁ00050308 04030603010302020201 x, y, s, Q 07 08. 02. 0203 ﾁ0203 04030603010302020203, 02090302 ﾁ0903010203 0706 020704040306030201070900090107 07 0300030302090709-03010203 dx, dy, ds, dq 07 08. 02. ｨｹ0807 02070404030603020107090002 07090801 04030603010302020203, 030207 00030709030203070203 01090002, 07 030207 040603000305090808 0302090703020705 04030700030203 ﾁ09080300010203070807 00030709030203070203 0109000206 060903020307080308 020005 07030308 ﾁ03080708 ﾁ0908060308 0403-0700030203 ﾁ09080300010203070807 x, y, s 07 Q. ｨ 020900030507070203, 0304030609010705 ﾆ 070809 ﾁ0708 ﾁ 07030308 ﾁ03080708 ﾁ0703 04030603010302020201 x, y, s, Q 07 08. 02., 0203 ﾁ0203 04030603010302020203 ﾆ x, ﾆ y, ﾆ s, ﾆ Q, 05 ﾁ0005080607030705 00030709030203070203 0003000104070107. 050302010304010705 04030603010302020206, 0406030003050908060706 0003070903020307020203 04030700030203 ﾁ09080300010203070807 00030709030203070203 00000703090706 0302090703020708, 07 07030308 ﾁ03080708 ﾁ0908060905 090302010304010705 02070404030603020107090003 ﾁ 07 07090101 090909 0203 ﾁ0206 04030603010302020206, 05 ﾁ0005-03080705 0900080703 ﾁ0308 020005 040302070109020705 0003080002070103 ﾁ09 07070707070003020705. 070209 03090103080203 03080007070903080705 0308 02010808030203 ﾁ09 07070707070003020705 04000809070708, 03070203 ﾁ02 ﾁ0908060305030705 0209 04060702010704070900010203 07020308 090302010304010707 04030603010302020206, 070903060303 0406030803090908060706 0403 09030208070209090109 0302090703020708, 020300030007 0406030003050908060706 0403 04030700030203 ﾁ09080300010203070807. 080307090300010909 02070404030603020107090002 05 ﾁ000508080705 0403060301030202020107 07 040307090300010909 030403-0609010705 d 0203080708 ﾁ090308 020902 0403060301030202020107, 030209 0103000308 00020801 040607000300030209 07 09 0207040403060302010709000901. ｨｹ0803 040607 ﾁ03020708 09 0207040403060302010709000901 ﾁ0207040706 04030605020903 ﾁ: ｨｰ0707. 4. dx d 6ﾓ1 ddx ds d 6ﾓ1 dds 07 08. 02. ｨｹ0807 02070404030603020107090002 ﾁ0207040706 04030605020903 ﾁ 030406030203000508080705 090909 06090302030708020203 04030700030203 ﾁ09080300010203070807 020005 06090302030708020206 04030700030203 ﾁ0908030001020307080308 040306 ﾁ030503 0403-0605020909: ddx = dx I 6ﾓ1 dx; (060707. 4), 050203 dx I 07 dx 07090801 04030700030203 ﾁ0908030001020203 0700030202 04030700030203 ﾁ09080300010203070807 dx. 01070404030603020107090002 ﾁ080306030503 04030605020909 ﾁ0203 ﾁ01 05 ﾁ000508080705 0403060301030202020107; 030207 00030709030203070203 01090002 0403 070609 ﾁ0203020708 07 0207040403060302-01070900090107 040306 ﾁ030503 04030605020909. ｨ 020900030507070203, 0304030609010705 ﾆ 0103000308 00020801 0403 ﾁ080306030209 020307090300010903 060903, 070803 040607 ﾁ03020508 09 070901010901 ﾁ0207-04030503 04030605020909 ﾆﾆ x, ﾆﾆ y, 07 08. 02. ﾂ 0406090908070903 0003080002070103 ﾁ09 07070707070003020705 050807 00030709030203070203 00030001040703 0709010102 07 0403 ﾁ080306020203 0709010102 ﾁ07080603070908080705 02030708090803070203 0603020903, 040308030109 070803 0304030609010705 ﾆ 0406070009050903080705 ﾁ 03070203 ﾁ020301 09 04030603010302020201, 09030803060203 07090107 05 ﾁ000508080705 00030709030203070203 010900020107.

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 29 縺08060305060307070705 040306030103020202061 7 09 0203 00090209 030007090002090801 0302030701 040609 ﾁ070009 020005 0304030609010707 d, 0809090703 090909 d(x + y) = dx + dy, 07 08. 04. ｨｮ 00030001040701 0003000902070301 05 ﾁ030602090701 09 07090708020308 0406030000030103, 0308020307050603080705 09 09030201030401070501 04030603010302020206, 02070404030603020107090003 ﾁ 07 00030109020206 07 0003070903020307020201 070707000301 ﾁ0306040702, 03 09030803060206 040009 06030701 ﾁ020403. ｨｰ0903060900090802 ﾁ0905 07 ﾁ0308 040603050609010109, ｨｬ030800020701 07080300090209000705 07 030703000302020308 08060902020307080108, 09 070103020203 07 0203030406030203000502020307080108 02070404030603020107090003 ﾁ. 09 0701030509 0009070403 ﾁ07030503 0403050702070801 050809 080609020203070801, 03090209 ﾁ 070003-020908060708 ﾁ0304060307: ｨｦ01030308 0007 00030109020905 07 0003070903020307020201 070707000301 ﾁ0306040702 0609 ﾁ020203 03 ﾁ03020105? 070703 ﾁ07020203, 070803 0102 0203 0103000301 0209080807 0308 ﾁ0308, 0609030500050202 ﾁ0905 050809 00030109020908, 09 0708090003 00020801 090607 ﾁ0908. ｨｪ02 020300000202 (060707. 5) 04060302070809 ﾁ070801 0903020307020908 00030109020908, 09 0309080301 0703 ﾁ030604070801 04030603060302. 0503050209 0102 020300090301 050803, 0708090203 ﾁ07080705 05070203, 070803 0209 ﾁ0304060307 0203 ﾁ03030103000203 0308 ﾁ0308070801. ｨｬ030109020203, 040607000007000908060703 090607 ﾁ0908, 0103050908 0701030801 0609 ﾁ020203 03 ﾁ03020105 (060707. 5, 09), 0203 050803 0203 0300050309080300010203; 020609050703 ﾁ03030103000203070807, 09 04060701030609, 08090903 ﾁ02, 070803 0009020908 0609 ﾁ02020107 0406030309010707 03 ﾁ03020103 ﾁ 0209 030707 X 070007 Y (060707. 5, 00 07 ﾁ), 07 030703 ﾁ07020203, 070803 07010303080705 0102030503 020609050706 ﾁ0303010300020307080308 020005 04030708060303020705 040607000007000908060706 00030109020206 07 02030609 ﾁ02020107 070803060302090107. ｨｹ0803 0303020907090308, 070803 04030205080703 縺00030109020308 07 0003070903020307020201 070707000301 ﾁ03060407021 7 040607 ﾁ03020708 09 02030304060302030005020203070807; 0102 0203 0302090301 a priori, 0308 0909090308 0903020307020308 00030109020308 000200 0703 ﾁ0306040502 04060302030001020208 04030603060302 09 000307090302030702030905030001020308 00030109020308; 04030508030109 0102 0203 0302090301, 090909 02070404030603020107090002 0103020508080705 ﾁ02030001 090607 ﾁ0308. ﾂ03030103000203, 070803 ﾁ0703 ds 0609 ﾁ0202 0103000209 0703000308, 07 0803050209 ﾁ0703 dds 0009020908 0609 ﾁ0202 02090008, 09 dx 07 dy 0009020908 07030103020508010705, 07 080301 0709010201 ddx 07 ddy 0203 0009020908 0609 ﾁ0202 02090008 ( ﾁ 04060302040300030003020707 070803 090607 ﾁ0905 0203 05 ﾁ000503080705 040605010308 000702070308). 0603 0103000308 00020801 07 080909, 070803 ﾁ0703 dx 0609 ﾁ0202 0103000209 0703000308, 07 0803050209 dds ﾙ 0 07 ddx = 0, 07 08. 02. 000301 0709010201 ﾁ 0003080002070103 ﾁ0301 07070707070003020707 0403 ﾁ030203020703 02070404030603020107090003 ﾁ 090909 01030205080607060705 ﾁ02030001 090607 ﾁ0308 04030603010302020206 0309 ﾁ07070708 0308 02 ﾁ0906 ﾁ03-060308: 6ｦ1 0308 04060706030202 090607 ﾁ0308, 07 6ｦ1 0308 04060706030202 000307090302030702030905030001020308 00030109-020308. 08030909 04060706030209 000307090302030702030905030001020308 00030109-020308 0203 0908030702030209 02030403000207080300010203, 0403 ﾁ030203020703 02070404030603020107090003 ﾁ 0307080905080705 0203030406030203000502020201. 090307090302030702030905030001020905 00030109020905 0309 ﾁ07070708 0308 0803-0503, 070803 ｨｬ030800020701 02090302 ﾁ0900 縺0406030506030707070308 04030603-0103020202061 7. ｨｹ0803 ﾁ0206090003020703 090209070203 ﾁ020006090203, 0403-07090300010909, 09 04060701030609, 03070007 dx 04070907070603 ﾁ090203, 0403-0603010302020203 0309 ﾁ07070508 070007 040603000305090808 07 ﾁ0307 0403070003- ｨｰ0707. 5. 0203 ﾁ09080300010203070807 0302090703020708 020609050701 03000609030301, 070301 03070007 0002 04030708030502020201 00020003 ds. 05030203070203, 01030001 0003080002070103 ﾁ09 07070707070003020705 0703-0708030708 ﾁ 0304060302030003020707 02070404030603020107090003 ﾁ 090909 07030308020307050607060705 07 0406070603020308 090607 ﾁ0308. 0603 050803 0103000203 07020300090801 00070401 ﾁ 080301 070009070903, 03070007 02 ﾁ09 ﾁ070209 0403 ﾁ030203020705 0103050908 00020801 090909-020700090201 060903020300030202. ｨｪ02 06090707010308060701 070308070907, 090909 050803 00020003 07020300090203. 06030304060302030005020203070801 02070404030603020107090003 ﾁ 07020702 0703 07040307030003 ﾁ 07040609 ﾁ0708010705 07 040603000003010308 02030304060302030005020203070807 02070404030603020107090003 ﾁ 07030708030708 ﾁ 080301, 0708030002 060903 07 0209 ﾁ0703050209 02030503 ﾁ03060708010705 03 080301, 070803 02070404030603020107090002 0302020308 ﾁ0200060902020308 04030603010302020308, 09

1330 ｨｨ030209 ｨｦ. ｨｪ. 090307 04060701030609 02070404030603020107090002 dx 0900070107070702 x, ﾁ0703050209 0009020908 070707080908010705 0403070803050202020107. 0003050209 040607000007-000908060905 00030109020905 ﾁ0703050209 0009020308 0701030801 0403060109, 04030909030902020908 0209 060707. 5, 00. 010005 040302070109020705 0003080002070103 ﾁ09 07070707070003020705 ﾁ09000203 0307030302090801, 070803 ｨｬ030800020701 0203 070707080900 05080308 ﾁ02060302 04060703010003010201. 0702 0603080300 0703060609-02070801 07 ﾁ0300030209 ﾁ0200030609 040607000007000908060706 00030109020206, 09 030605 080307020303 04060305060307070708 04030603010302020206. ﾂ02000306 0302020308 04030603010302020308 ﾁ 090907030708 ﾁ03 07010308060308 04030708030502020203 02070404030603020107090002 05 ﾁ000503080705 0703 ﾁ03060403020203 040603-0703 ﾁ030001020201; 0203 ﾁ 0503030103080607070307090706 04070509060906 020308 020707030503 080909030503, 070803 ﾁ0202090002090003 0002 030802090801 050809 040607 ﾁ07000305070603 ﾁ0902020908 06030001 04030603010302020308 x, 09 0203 04030603010302020308 y 070007 0008000308 020609050308. ｨｬ030800020701 0609070709-00020900 03 ﾁ03030103000203070807 ﾁ0200030609 060903000707020206 04060305060307070708 04030603010302020206 080909: 080607 ﾁ0305080707 07090101 ﾁ03 ﾁ0703 0203 0300050309080300010203, 0708030002 dx 070007 dy 00020007 0903020708090208090107 07 ddx = 0, 0203 0103000203 ﾁ020006090801 04060305060307070708 x 070007 y (03070007 090803-00070003 03090603070308 04060702050801 y 0309 0900070107070709) 0809090308, 090909 030906030703080705 10. 08030508030109 ｨｬ030800020701 0203 0603080300 07070603020203 0406070209 ﾁ090801 0302020308 0703 04030603010302020206 0704030107090001020908 06030001; 0302 0203 0603080300 060907070109080607 ﾁ090801 030708090001020203 04030603010302020203 ﾁ0703050209 ﾁ 0706 030802030403020707 09 0302020308 070300060902020308 0403-0603010302020308. 01060905070107 070003 ﾁ090107, 0302 0203 060907070109080607 ﾁ0900 04030603010302020203 090909 04090209010707 0302020308 02030309 ﾁ070707010308 04030603010302020308. 09 070203 ﾁ09 040302070306090209 080308 04090908, 070803 04030603010302020203 0003080002070103 ﾁ09 07070707070003020705 0203 05 ﾁ000508080705 04090209010705-0107; 050803 03020209 0703 050009 ﾁ020206 030703000302020307080308, 03080007070908060706 050803 07070707070003020703 0308 060903 ﾁ07080206 ﾁ0403070003020708 ﾁ0707 04030601 010908030109080707030709030503 09020900070309. ﾂ 0709010301 02030003, 0903050209 090302010304010705 04090209010707 030902050009 0103020806090001020908 06030001 ﾁ 04030302020308040301 09020900070303, 0406030000030109 02030309 ﾁ0707070103070807 02070404030603020107090003 ﾁ 030804090009 11. ｨｬ030800020701 0603040700 0406030000030109 02030309 ﾁ0707070103070807 02070404030603020107090003 ﾁ 0702090703. 0702 0103080302070703070907 060903 ﾁ0700 040607050102 07 0300030302090703020705, 040303 ﾁ03000508060703 070306060902050801 02030309 ﾁ0707070103070801 07 060903000707090801 02 ﾁ09 06030209 07030103020503-0103070807 02070404030603020107090003 ﾁ, 03020702 07040301070900010203 020005 090607 ﾁ0206, 020609050308 0403060300020903010208 0406030506030707070308 04030603010302020206. ｨｹ0807 040607050102, 0300030302090703020705 07 07080305060905 0309 02070107 0707060302020905 07020305 000307090302030702030905030001020905 00030109020905 00020007 ﾁ030704060702050802 07 0707040300010303 ﾁ0900070701 040306 ﾁ020107 04030700030203 ﾁ09080300050107 ｨｬ03080002070109. 08030302020303 030207 00020007 030900020802; 0103000203 07090903090801, 070803 090209000703 03090103020700 040607050102, 04030603070208030604060308070603 ﾁ0900 0300030302090703020705 07 09080609080700 0707060302020908 07020308. 0603 050807 09070403090802 070906030708 ﾁ03020202 020005 040302070109020705 0003080002070103 ﾁ09 07070707070003020705; 05 06030709 0403050702070801 0706 0302030701 07 04030103060108 02030709030001090706 04060701030603 ﾁ. 080607010306 1. 0809060900030009 ｨｰ090707010308060701 0409060900030009, 0309020902020908 090609 ﾁ020302070301 ay = x 2 : ｨｮ03030802030403020705 0103000209 020704040306030201070900090107 040306 ﾁ030503 07 ﾁ0207040706 04030605020903 ﾁ 020005 04030603010302020206 x 07 y ﾁ02030001 090607 ﾁ0308 0304070702 ﾁ0908080705 0207040403060302010709000102020107 090609 ﾁ02030207050107. ｨｹ0807 090609 ﾁ0203020705 040607020701090808 060903000707020203 0403060102 ﾁ 0309 ﾁ0707070103070807 0308 04060305060307070707 04030603010302020206. 05 04060701030609, 03070007 dx 0406030204030009050903080705 04030708030502-020201, 02070404030603020107090001020203 090609 ﾁ0203020705 0009020908 0701030801 ﾁ0702: ady = 2xdx addy = 2(dx) 2 ad 3 y = 0 ad 4 y = 0 07 08. 02. 10 絋s ist ganz nicht notig dass die dx oder dy constantes und die ddx = 0 seyen, sondern man assumiert die progression der x oder y (welches man pro abscissa halten will) wie man es gut ndet1 7. (040707010103 ｨｬ03080002070109 040302 090302030206090903030209, Leibniz, Mathematische Schriften (04060701. 1), vol. 7, p. 387). 11 絅ierentials1 7 (0701. 04060701. 6) pp. 5{6 07 66{77.

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 31 070202090903 03070007 04030708030502020201 0406030204030009050903080705 dy, 090609 ﾁ0203020705 0009020908 02060905070107: ady = 2xdx 0 = 2(dx) 2 + 2xddx 0 = 6dxddx + 2xd 3 x 0 = 6(ddx) 2 + 8dxd 3 x + 2xd 4 x 07 08. 02. 010005 020609050706 ﾁ09060709020803 ﾁ 04060305060307070707 04030603010302020206 (0209040607010306, 04030708030502020308 ds 070007 04030708030502020308 ydx) 0009020908 030006090303 ﾁ02 ﾁ0908010705 020609050703 020900030602 02070404030603020107090001020206 090609 ﾁ0203020708. 070202090903 ﾁ0403000203 ﾁ03030103000203 090708090203 ﾁ070801 0703030802030403020705 0103000209 020704040306030201070900090107 04060701030207080300010203 0903 ﾁ070301 0406030506030707070501 04030603-010302020206. ﾂ 070009070903 090303060207020908 0409060900030002 x 07 y 050807 0703030802030403020705 08090903 ﾁ02: ady = 2xdx addy = 2(dx) 2 + 2xddx ad 3 y = 6dxddx + 2xd 3 x ad 4 y = 6(ddx) 2 + 8dxd 3 x + 2xd 4 x 07 08. 02. 07080103080701, 070803 090609 ﾁ0203020705 020005 02070404030603020107090003 ﾁ 040306 ﾁ030503 04030605020909 0203 0309 ﾁ07070508 0308 04060305060307070707 04030603-010302020206, 09 020005 ﾁ0207040706 0309 ﾁ07070508. 080607010306 040309090302 ﾁ090308, 070803 040607 04030206030205060301 ﾁ0200030603 04060305060307070707 0103000203 0302090707080300010203 090406030708070801 090609 ﾁ0203020705 ﾁ0207040706 04030605020903 ﾁ. ｨｹ0803 0203070301020302020303 04060307010906030708 ﾁ03 07 ﾁ0300030202030503 ﾁ0200030609 04060305060307070707 04030603010302020206, 07 040306 ﾁ0203 04030700030203 ﾁ0908030007 ｨｬ03080002070109 010907080306070907 0707-040300010303 ﾁ090007 050809 ﾁ03030103000203070801 090406030603020705 040306010900. 080607010306 2. ｨｰ0902070907 090607 ﾁ07030202 ｨｪ0308 ﾁ0803060308 040607010306 12 0909070903080705 06090207090709 090607 ﾁ07030202. ｨｰ090707010308060701 (060707. 6) 090607 ﾁ0908 ｨｮ 07 02 ﾁ03 0803070907 P 07 P, 06090704030003000302020203 02030708090803070203 00000703-0903 02060905 0308 0206090509. 0809070801 R 0803070909 0403060307030703020705 0203060109000308 09 090607 ﾁ0308, ﾁ03070708090203 ﾁ000302020206 ﾁ 080307090906 P 07 P. ｨｰ0902070907 090607 ﾁ07030202 ﾁ 0803070903 P 03070801 040603020300 0200070202 03080603030909 PR 040607 P P. (ｨｦ0007, 090909 0300 05080301 070909030900 0002 070901 ｨｬ030800020701: ﾁ030301010501 PP 00030709030203070203 0109000201 07 06090707010308060701 0803070909 R 04030603-07030703020705 0203060109000308, ﾁ03070708090203 ﾁ000302020206 ﾁ 080307090906 P 07 P; RP 03070801 060902070907 090607 ﾁ07030202.) ｨｬ03080002070103 ﾁ03 07070707070003020703 02090508 04030601090002 020005 ﾁ020707070003020705 06090207090709 090607- ﾁ07030202. ｨｹ0807 04030601090002 0703020306000908 02070404030603020107090002 ﾁ0207040706 04030605020903 ﾁ; 080301 0709010201 030207 0309 ﾁ07070508 0308 04060305060307070707 04030603010302020206. ﾂ0308 050807 04030601090002 (020005 03000207020206 04060305060307070708): r = ds3 020005 dx = const; dxddy r = ds3 020005 dy = const; dyddx r = dxds 020005 ds = const: ddy ｨｰ0707. 6. ﾂ 05080301 070009070903 0304050801 07010303080705 04030601090009, 07040609 ﾁ03020007 ﾁ0905 020005 0008000206 04060305060307070708, 09 070103020203: 12 絅ierentials1 7, pp. 35{42. r = dyds 2 dsddx 6ﾓ1 dxdds :

1332 ｨｨ030209 ｨｦ. ｨｪ. 090307 ｨｹ0807 04030601090002 07030503020205 0203 09040308060300000508080705; 030207 0103050908 04030909030908010705 020307090300010903 070806090202020107 020005 01090803-010908070903 ﾁ, 040300010309080607060705 0703 ﾁ0603010302020201 0902090007030301. 070202090903 030207 0300000902090808 0703000708 ﾁ0302020308 050003050902080203-07080108, 0307030003020203 ﾁ 070609 ﾁ0203020707 07 0703 ﾁ0603010302020308 0403060109000308 020005 06090207090709 090607 ﾁ07030202 r 05060904070909 04090209010707 y = f(x) ﾁ 0803070903 (x; y): r = [1 + (f (x)) 2 ] 3=2 : f 茖 (x) 080607010306 3. 03030601090009 d2 x dx 2. 03030601090009 d2 x dx 2 0703 ﾁ0307080209 ﾁ 0703 ﾁ0603010302020301 09020900070303 090909 04030601090009 020005 ﾁ0803060308 0406030703 ﾁ0302020308; 03070007 y = f(x), 0803 0803050209 0406030703 ﾁ0302020203 030003030209070908080705 090909 f (x) = dy dx ; f 茖 (x) = d2 y dx 2; : : : f (n) (x) = dn y dx n: 03030601090002 020005 0406030703 ﾁ0302020206 ﾁ080306030503 07 ﾁ0207040706 04030605020903 ﾁ 05 ﾁ000508080705 07030503020205 030207020708 ﾁ030202020107, ﾁ 09030803060206 0703060609020700030701 070809060303 0003080002070103 ﾁ03 0300030302090703020703 d 2, d 3, 07 08. 02. 020005 02070404030603020107090003 ﾁﾁ0207040706 04030605020903 ﾁ. 070202090903 ﾁ 0003080002070103 ﾁ0301 07070707070003020707 050807 04030601090002 ﾁ 080301 ﾁ070203, 090909 0102 0904030806030000050301 0706 07030503020205, 05 ﾁ000508080705 020303040603020300050202020107; 0706 07020803060406030809010705 0309 ﾁ07070708 0308 04060305060307070707 04030603010302020206. ｨｦ020803060406030809010705 05080706 040306010900 ﾁ 0003080002070103 ﾁ0301 07070707070003020707 0703 ﾁ040902090308 07 0703 ﾁ0603010302020308 080300010903 ﾁ 080301 070009070903, 03070007 dx 00030605080705 04030708030502020201; 020005 ﾁ070306 020609050706 04060305060307070708 04030603010302020206 010908030109080709 0409030002 ｨｬ03080002070109 0009020308 070708090801 050807 04030601090002 0702090703, 020300030007 030503 0703 ﾁ0603010302020208 09030000030509. 05 04060701030609, 020005 0409060900030002 y = f(x) = x2 a 0102 0009020301 0701030801 d 2 y dx 2 = 2 a = f 茖 (x) 020005 dx = const; d 2 y dx2 = 0 020005 dy = const; d 2 y dx 2 = 2a a 2 + 4x2 020005 ds = const (05 03040907090908 ﾁ020707070003020705). ｨｹ0809 0309 ﾁ0707070103070801 040306010900 0308 04060305060307070707 04030603010302020206 090003 0203 ﾁ0603020708 07030503020205 ﾁ 070809020209060802 010908030109080707030709030503 030209020705, 070803 ﾁ07020203 0703 08030503, 070803 0102 090003 0203 0308010307090301 040603-05060307070708 04030603010302020206 (04030708030502020303 dx), 0903050209 030904070702 ﾁ090301 04030601090009 d2 x dx 2 020005 ﾁ0803060308 0406030703 ﾁ0302020308. ｨｪ02 070306060902070007 04030601090009, 0203 0908060908070007 0707060302020908 0003080002070103 ﾁ09 07020803060406030809010708. 080607010306 4. 01070404030603020107090001020905 040603040306010703020900010203070801 ﾂ 07 ﾁ050307 07 040306010900090107 04060701030609 2 05 03080103070900, 070803 02070404030603020107090001020203 090609 ﾁ0203020705 040306 ﾁ030503 0403060502-0909 03020702090903 ﾁ02 020005 ﾁ070306 04060305060307070708 04030603010302020206. ｨｹ0803 0300060905 0703060809 0003080002070103 ﾁ09 07070707070003020705: 090609 ﾁ0203-020705, ﾁ0703 02070404030603020107090002 09030803060206 0701030808 040306 ﾁ0208 04030605020309, 0203 0309 ﾁ07070508 0308 04060305060307070707 04030603010302020206. 070202090903 03070007 030802030403020705 0103000209 020704040306030201070900090107 040306 ﾁ030503 04030605020909 ﾁ020609000908080705 02060905070107 0704030703-00090107, 020300030007 07 04030103060108 090609 ﾁ0203020708, 030207 0809090003 0103050908 0309 ﾁ0707030801 0308 04060305060307070707 04030603010302020206. ｨｹ0803 04060307070603020708, 0209040607010306, ﾁ 070009070903 02070404030603020107090001020308 040603040306010703020900010203070807. 13 05 04060701030609, 0409070801 13 絅ierentials1 7, pp. 47{53. dv :: v:

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 33 ｨｹ0809 04030601090009 0304070702 ﾁ090308 02 ﾁ070003020703 ﾁ 07030406030807 ﾁ0005080603080705 0706030203, 07 030209 0503 ﾁ03060708 03 080301, 070803 09010302010403-020703 0709030603070807 dv 040603040306010703020900010203 0709010308 0709030603070807. ｨｹ0809 04030601090009 0103000308 00020801 070208030604060308070603 ﾁ090209 00070401 0403070003 08030503, 090909 0102 090909000301, 0909090701 03000609030301 07000302090308 060907070109080607 ﾁ090801 050803 09010302010403020703 070903-0603070807: 04060307070603020708 0007 030203 0309 0609 ﾁ020203 (00030709030203070203 0109000203) 04060301030009080907 ﾁ060301030207, 070007 0209 0609 ﾁ020206 04060306030207010206 0609070708030502070506, 070007 090909-020700090201 0702090703. ｨｹ0807 090803070203020705 030802030705080705 09 08030109, 070803 ｨｬ030800-020701 02090302 ﾁ0900 0406030506030707070308 04030603010302020206; 07 07020803060406030809010705 04030601090002 0203080708 ﾁ07080300010203 070906030708 ﾁ03020203 0309 ﾁ07070708 0308 060907070109080607 ﾁ0903010308 04060305060307070707. 05 04060701030609, 03070007 ﾁ03050801 04030708030502020201 dv, 0903050209 0009020908 040603040306010703020900010202 0709030603070801 07 070301030203020705 dv 0309 0609 ﾁ020203 00030709030203070203 0109000203 04060301030009080907 ﾁ060301030207, 0803 0803050209 02 ﾁ070003020703 0009020308 0304070702 ﾁ0908010705 0403060109000308 v = ce 6ﾓ1t ; 050203 c 020309030803060905 04030708030502020905. 0603 03070007 070301030203020705 dv 0308020307030202 09 0609 ﾁ020201 04060306030207010201 060907070803-0502070501, 0803 03070801 03070007 0102 060907070109080607 ﾁ090301 04060305060307070708 04030603010302020206, ﾁ 09030803060308 ds 040307080305020203 (070007, 070803 0803 0003 0709010303, vdt 040307080305020203, 040307090300010909 ds = vdt), 050803 02 ﾁ070003020703 0304070702 ﾁ0903080705 0403060109000308 v = c t : ｨｲ09 ﾁ0707070103070801 040603040306010703020900010203070807 02070404030603020107090003 ﾁ 0308 04060305060307070707 04030603010302020206 070506090009 ﾁ0900020908 06030001 ﾁ 020707090907070707 0103000209 040808050302070301 07 ｨｬ0308000207010301, 040603070303040302040308 0309030003 1690 05. 080603020103080301 05080308 020707090907070707 00020003 02 ﾁ070003020703 ﾁ 07030406030807 ﾁ0005080603080705 0706030203, 07 030209 00020009 ﾁ0203 ﾁ090209 ﾁ03090701020201 020304030207-010902070301 02 ﾁ0906 090705020206, ﾁ0303020709040301 0703-0309 02030909090309020203070807 04060305060307070707 04030603010302020206, 0403 030802030403020708 09 09030803060308 030904070702 ﾁ0900070701 02070404030603020107090001020203 090609 ﾁ0203020705 020005 060903000707020206 07030406030807 ﾁ0005080607060705 07060302. 01090001020308040303 060903 ﾁ07080703 0803070003 05080706 04060701030603 ﾁ 0103000308 04030909030908010705, 070803 0309 ﾁ0707070103070801 040306010900 0308 04060305060307070708 04030603010302020206 00020009 0403040603070809 0203020900020308 04030103060308. 0603 ﾁ 0203080708 ﾁ07080300010203070807 030209 0209 ﾁ090009 00030001040303 04060307010906030708 ﾁ03. 080306 ﾁ0203 04030700030203 ﾁ0908030007 0003080002070103 ﾁ09 07070707070003020705 00020007 02090708030506070107 ﾁ070608090303090107 ﾁ 0703 ﾁ00030703020707 ﾁ020503-0202 0703 05080308 0309 ﾁ0707070103070807 0308 04060305060307070707 04030603010302020206. 05 04060701030609, 07010305 02030003 07 0207040403060302010709000102020107 090609 ﾁ02030207050107 ﾁ0207040706 04030605020903 ﾁ, 030207 07080603010700070701 ﾁ020006090801 04060305060307070708 04030603010302020206 0809090701 03000609-030301, 0708030002 090406030708070801 04030601090002 (0701. 040607010306 1). ﾂ02070707000505 02070404030603020107090002 ﾁ0207040706 04030605020903 ﾁ 040607 06030403020707 010306090207070307090706 0309020907 (0809090706, 090909 030902090709 03 0403060103 0209050609000302020206 09040609050706 0009000309 070007 03 02 ﾁ070003020707 080300 ﾁ 07030406030807 ﾁ0005080603080705 0706030203), 030207 0809090003 040300010303 ﾁ0900070701 0203030406030203000502020307080108 020704-04030603020107090003 ﾁ. 010005 080909030503 020704040306030201070603 ﾁ09020705 0707040300010303 ﾁ0900070701 07030608030007, 0209 09030803060206 03080103070900070701 02070404030603020107090002 040306 ﾁ030503 07 ﾁ080306030503 04030605020903 ﾁ, 07 050807 07030608030007 0709070803 0103000203 00020003 090406030708070801 ﾁ02-0003060301 09020300020308 04060305060307070707 04030603010302020206. 070407070902020203 01020308 0300030302090703020705, 07020307 07 040607050102 07030503020205 0203 09040308060300000508080705; 030207 0908060907030202 ﾁ 08030703020703 ﾁ03070301020902010908030503 07 0203 ﾁ0508020902010908030503 0708030003080708. 09 0203 00090209 030007090002090801 0302030701 04060707070202 0706 07070703030203 ﾁ03020705; 030801030709 00070401, 070803 07010300090701 020309030803060905 0203090203 ﾁ000308 ﾁ030605020203070801 ﾁ 07 ﾁ050307 07 0203030406030203-000502020307080108 02070404030603020107090003 ﾁ 0307030003020203 ﾁ 070009070903 ｨｹ0800030609 07 ﾁ 07 ﾁ050307 07 040305 ﾁ000302070301 04030205080705 04090209010707 14. 0400050205 0209030902 0209 050803 060903 ﾁ07080703, 020300010305 07090903090801, 070803 030203 0406030707060302070003 0409080501 03080006090702 ﾁ09020705 0203-040609 ﾁ070001020206 07 090603020007 ﾁ0206 070907080308 080303060707. ｨｰ090003070703 040607050102 ﾁ 03070203 ﾁ020301 0203 00020007 0203040609 ﾁ07000102020107; 05 070707080908, 070803 030207 0203 00020007 07 090603020007 ﾁ020107. 0603 030207 0203 ﾁ0407070900070701 ﾁ 02090001020308040303 0903020103040809090001020303 060903 ﾁ07080703 0406030201030809 07 040308030109 00020007 030800060304030202. ﾂ 06030203 0209000102030804030503 060903 ﾁ07080705 09020900070309 07070703030007 0203 080300010903 040607050102 07 07020307, 07 ﾁ05030902020203 07 0203-030406030203000502020307080108 02070404030603020107090003 ﾁ; 040603070703 0903020103040809090001020203 090708090203 ﾁ0907 0003080002070103 ﾁ09 07070707070003020705 0809090003 0403 00030001040308 0709070807 07070703030007 070007 04060308030604030007 030209070708030001020203 070301030203020705, ﾁ 03070203 ﾁ020301 0703-0309 080308 050009 ﾁ03020708 ﾁ0908060308 06030007, 09030803060908 0708090003 070506090801 ﾁ 09020900070303 04030205080703 04090209010707. 14 絅ierentials1 7, pp. 66{77.

1334 ｨｨ030209 ｨｦ. ｨｪ. 090307 ｨｰ09030007070705 0103000209 0003080002070103 ﾁ0201 0707070707000302070301 07 0703 ﾁ0603010302020201 0902090007030301 09 060907070109080607 ﾁ0900 02030304060302030005020203070801 02070404030603020107090003 ﾁ 090909 07070001020308040908 0700000807080609010708 0302090707-08030001020308 06090302070102 0103000209 0003080002070103 ﾁ0201 0707070707000302070301 07 0703 ﾁ0603010302020201 0902090007030301. ｨｰ030309000108090802 070609 ﾁ- 0203020705 02 ﾁ0906 080303060708 15 05 04060302070809 ﾁ0008 ﾁ 08090000. 2. 080603000203 ﾁ07030503, 02 ﾁ03 080303060707 0609030007070908080705 0403 07 ﾁ030701 00090303 ﾁ0201 0403020508070501; 07 03000803090802, 07 0903080306020107 030207 0701030808 02030003, 0809090003 0609030007070202. ｨｬ03080002070103 ﾁ03 07070707070003020703 060907070109080607 ﾁ090308 04030603010302020203, 04060300030509-08060703 0003070903020307020908 04030700030203 ﾁ09080300010203070801 00030709030203070203 00000703090706 0302090703020708. ｨｹ0807 04030603010302020203, 090909 050803 00020003 0403090903090203 ﾁ020403, 0203 05 ﾁ000508080705 040902090107050107, 040308030109 070803 02070909090905 04030603010302020905 07030209070900010203 0203 00030605080705 ﾁ 090907030708 ﾁ03 02030309 ﾁ070707010308. ｨｮ03 ﾁ0603010302020208 090209000703, 02090406030807 ﾁ, 0701030308 02030003 07 040902090107050107. ﾂ03- ﾁ0803060206, 07010303080705 0609030007070703 0103000209 03070203 ﾁ02020107 03040306090107050107. ｨｬ03080002070103 ﾁ03 020704040306030201070603 ﾁ09-020703 070809 ﾁ0708 ﾁ 07030308 ﾁ03080708 ﾁ0703 04030603010302020308 0203 ﾁ0908, 00030709030203070203 0109000908 04030603010302020908, 02090302 ﾁ0903010908 0305 0207040403060302010709000301. ｨｮ03 ﾁ0603010302020208 090209000703 070809 ﾁ0708 ﾁ 07030308 ﾁ03080708 ﾁ0703 04090209010707 0203 ﾁ0908 04090209010708, 02090302 ﾁ09-03010908 0305 0406030703 ﾁ0302020308; 050809 04090209010705 030406030203000503080705 07 04030103060108 0406030203000102030503 0403060306030209. ｨｬ03080002070103 ﾁ09 0304030609010705 ﾆ (020005 09030803060308 05 070704030001030908 0003080002070103 ﾁ 080306010702 縺07090101070603 ﾁ090207031 7, 06030805 05080308 080306010702 0709070803 030901030205000705 0803060107020301 縺070208030506070603 ﾁ090207031 7, ﾁﾁ03020502020201 0006090801050107 0903060209000007) 070809 ﾁ0708 ﾁ 07030308- ﾁ03080708 ﾁ0703 04030603010302020308 0203 ﾁ0908, 00030709030203070203 00030001040908 04030603010302020908. ｨｮ03 ﾁ0603010302020208 090209000703 070809 ﾁ0708 ﾁ 07030308 ﾁ03080708 ﾁ0703 04090209010707 0203 ﾁ0908 04090209010708, 02090302 ﾁ0903010908 0305 07020803050609000301. 06090903020301, 090302010304010705 04030603010302020206 ﾁ 0003080002070103 ﾁ0301 07070707070003020707 0703020306000708 02030304060302030005020203070801 020704-04030603020107090003 ﾁ, 09030803060905 0203000903080705 030406030203000502020308 07 ﾁ020003060301 04060305060307070707 04030603010302020206. 0806030000030102 0203-0304060302030005020203070807 02070404030603020107090003 ﾁﾁ 0703 ﾁ0603010302020301 09020900070303 0203 070906030708 ﾁ090308, 080909 090909 ﾁ 020501 060907070109-080607 ﾁ0908080705 04090209010707 05 ﾁ0203 030406030203000502020206 02030309 ﾁ070707010206 04030603010302020206. ｨｬ02ｨｺ0906ｨｦ0002 ﾂ07 ｨｦｨｮ06ｨｦｨｮｨｬ0206ｨｦ02 08030603010302020905 06090603000203020703 02070404030603020107090003 ﾁ: 04030603010302020905 00030709030203070203 0109000905 04030603010302020905 00090000070109 2 09090303 ﾁ0303 04030205080703 0704030609010707 ｨｮ07 ﾂｨｰ02ｨｪ020606ｨｴｨｺｨ 06ｨｨｬｨｦｨｲ 03090209010705 ﾂ0305080703 0406030703 ﾁ0302020308: 04090209010705 04090209010705 x dx f f dy ddy ｨｮ090101070603 ﾁ09020703: 04030603010302020905 00030709030203070203 00030001040905 04030603010302020905 x ﾆ x ydx ﾆ ydx 06030304060302030005020203070801 02070404030603020107090003 ﾁ, 090203060007 ﾁ0903010905 030406030203000302070301 04060305060307070707 04030603010302020206 06030304060302030005020203070801 ｨｦ0208030506070603 ﾁ09020703: 04090209010705 04090209010705 f F (050203 F(x) = ﾒ x a f(t)dt) 06070909090308 02030304060302030005020203070807 ﾁ 07030308 ﾁ03080708 ﾁ0707 07 0403020508070301 04090209010707 ｨｹ0803 07030403070809 ﾁ0003020703 040309090302 ﾁ090308, 070803 ﾁ 030406030203000502020301 070102070003 0703 ﾁ0603010302020208 090209000703 07030009 ﾁ07000705 0308 010203050706 07000300020307080308, 0406070709060706 0003080002070103 ﾁ09 07070707070003020708. ﾂ 020501 000300010403 020308 00030709030203070203 0109000206 15 010005 0003000303 02030809000102030503 070609 ﾁ0203020705 0701. (04060701. 4) Baron and Bos 絲ewton and Leibniz1 7 pp. 54{57, 09 0809090003 010307 060900030802 絅ierentials1 7 pp. 34{35, 絲ewton, Leibniz and the Leibnizian tradition1 7, pp. 92{93.

1307070203 ﾁ0304030009050908060703 04030205080705 0003080002070103 ﾁ09 07070707070003020705 35 07 00030709030203070203 00030001040706 0903000707030708 ﾁ; ﾁ0703 04090209010707 09030203070202. 010708060902030209 02030304060302030005020203070801 0207040403-0603020107090003 ﾁ 07 0309 ﾁ0707070103070801 040306010900 0308 04060305060307070707 04030603010302020206. 0603 05 06030709 0403020703060902090801 030605 060903, 070803 0803 040300030003020705 0003080002070103 ﾁ09 07070707070003020705, 09030803060203 00020007 090708060902030202 0703 01090803010908070907 0209 04090807 0305 060903 ﾁ07080705, 0203 00020007 0203040609 ﾁ07000102020107 070007 090603020007 ﾁ020107. 09 0403070708070203 02090203080701, 070803 07010305 0403090903090801, 070803 030207 0406070209 ﾁ090007 0003080002070103 ﾁ09 07070707070003020708 00030509080708 ﾁ03 04030708060303020705 07 02090003 030406030203000502020908 09060907030809. ｨｲ090900080703020703 ﾂ 05080301 0903060308090301 070300030003020707 010203 0406070400030701 0304090708070801 010203050703 020308090007, 030708090209 ﾁ0007 ﾁ09050701 ﾁ 03070203 ﾁ- 020301 0209 0803060207070307090706 04060705010906. 09 02090203080701, 070803 050809 07080306030209 02030009 0203 03090906020009 0703000308 ﾁ03030103000203070801 030006030503 ﾁ030500050209 0209 ﾁ030406030702, 09030803060203 05 0603080300 0308010308070801: 6ｦ1 ｨｬ03080002070103 ﾁ03 07070707070003020703 ﾁ03 010203050706 04030003000302070506 04060702010704070900010203 03080007070903080705 0308 0703 ﾁ0603010302020308 080303060707. 6ｦ1 ｨｦ 080301 0203 0103020303 050803 07070707070003020703 05 ﾁ000503080705 07 ﾁ0503020308, 05040403090807 ﾁ020308 07 0906090707 ﾁ0308 08030306070308 07090103 0403 07030003. 6ｦ1 ｨｹ0809 07 ﾁ05030203070801, 05040403090807 ﾁ0203070801 07 09060907030809 0308090602 ﾁ0908080705 00070401 08030109, 090803 07030907090308 080303060708 07 0709020708 03 020308 ﾁ 0305 0703000708 ﾁ0302020206 0803060107020906, 020907090300010903 050803 ﾁ03030103000203, 09 0203 ﾁ 0803060107020906 080303060708, ﾁ0303020709040706 04030302020303. 09 04030207030609020900 030703000908 04060706030209 0003080002070103 ﾁ09 07070707070003020705 07 030503 03080007070705 0308 0703 ﾁ060301030202030503 0902090007-0309. 0603 0103050908 0704060307070801: 0708030708 0007 0406070209 ﾁ090801 0508030109 0809090303 0302090703020703? 050909-0207090909 0703 ﾁ0603010302020208 090209-000703 000200 070303020902 0703 ﾁ060301030202020107 010908030109080709090107, ｨｬ030800020701 0003 070303020900 0703 ﾁ070301 020609050303 07070707070003020703 0302 000200 07000704090301 030607050702090001020201 01020700070803000301, 0708030002 07030300060308090801 080303060708, 070303020902020908 02060905070107, 02090003 03070007 050807 020609050703 040607040007 0403070003 02030503. ｨｨ030209 ｨｦ.ｨｪ. 090307, 0403070308020208 040603040307070306 ｨｮ0309010707 07070803060707 01090803010908070907 07 030708030708 ﾁ0302020206 02090909 010207 ﾁ0306070708030809 05. 010806030608, 06070203060009020202. 08030603 ﾁ0302 07 0902050007080709030503: ｨ. ｨｦ. 05030802070903 ﾁ.

1301070300020303 04030703000703 ﾁ 00090602090003 ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 08060302030000090301 04090000070909010708 000309010708 0403 09020900070807070307090308 050303010308060707, 0406030707080902020206 090906070902080901 ﾂ0303020203- ﾁ0303020904020308 07020003020306020308 0909090203010707 0701. 04060304. 06. 02. 02090903 ﾁ0709030503. ﾂ 020907080305060301 020301030603 07030203060009080705 08030102 7 07 8. 00030102 5 07 6 0304090000070903 ﾁ090202 ﾁ 04060302020209060301 020301030603 00090602090009. 00030109 7 080605010905 0209 040003070903070807 ﾂ 06090302030003 罍ﾂ0309080306020905 090005030006091 7 0102 0609030609000308090007 0702070806090103020809060708 020005 07070700030203 ﾁ09020705 0503030103080607-070307090706 03000803090803 ﾁ, 09030803060208 080304030601 09090807 ﾁ0203 0009020301 040607000905090801 09 0703090703020708 040605010206, 04000307090307080308, 09 0809090003 090607 ﾁ0206 07 0403 ﾁ030606020307080308 ﾁ080306030503 04030605020909 03070203 ﾁ020206 03000803090803 ﾁ 0406030201030809 罟 0209000708070703-07090905 0503030103080607051 7. ﾂ 020907080305060303 ﾁ06030105 09020900070807070307090905 050303010308060705 ﾁ020603070009 ﾁ 0703 ﾁ030708020908 03080609070001 01090803010908070907 罟 00050300060907070307090905 0503030103080607051 7 0209090909, 040607 ﾁ0003090908060908 09 0703090703020708 0503030103080607070307090706 03000803090803 ﾁ 0703- ﾁ0603010302020908 09000503000609. ｨ 00050300060907070307090905 050303010308060705 02090603020708 04060701030203020703 ﾁ 08030306030807070307090308 040703070903, 03020209 0703 07020803060307020308040706 0309020907 09030803060308 0703030209020703 030207020308 080303060707 04030005, 0304070702 ﾁ0908060308 ﾁ 07 ﾁ030706 060901090906 090909 05000309080607070307090703, 080909 07 050609 ﾁ07080901070302020203 ﾁ03090701030203080708 ﾁ0705. 0407040308030309 03 070906030708 ﾁ03 ﾁ09020707 0809090308 080303060707 ﾁ0202 ﾁ07020900 030603 ｨ. ｨｹ08020408030802. 0103080708 ﾁ07080300010203, 03070007 070609 ﾁ02070801 0309090302 050900030209, 030407-0702 ﾁ0908060708 07070009 04060708050003020705 03090605000302020206 070907080701, 07 0309090302 ﾁ070301070602030503 080505030803020705, 09090709080607080705 04060708050003020705 010908030607090001020206 080300, 0803 0103000203 0309010308070801 0706 08030002030708 ﾁ03020203070801. 070202090903 ﾁ0703 0302090808 03 080301, 070803 070906030708 ﾁ090808 090909 040300030007080300010203 03090605000302020203 07090708070102, 080909 07 030806070109080300010203 03090605000302020203. 0603, 09 070300090003020708, 080300 07 03080607010908030001020308 010907070308 04030909 0203 02090802030203. ﾂ 07 ﾁ050307 07 05080701 ﾁ0303020709090308 0309-0109020707 ﾁ0905 0507040308030309: 03070007 0609030609000308090801 030207020908 080303060708 04030005, 03 09030803060308 010307080900 ｨｹ08020408030802, 0803 030209, ﾁ03030103000203, 04060302070909000308, 090909 0403000907070801 08030009 07 03080607010908030001020308 010907070308, 070803 0103000308 040307000900070801 0308-040609 ﾁ020308 080307090308 0703030006030803020705 0907080603080708 ﾁ, 0300030704030707 ﾁ0908060706 09020807050609 ﾁ070809010708! 080306 ﾁ0905 08030109 09020900070807070307090308 050303010308060707 040605010905 0209 040003070903070807. ｨｲ02030701 020901 040603020708030708 ﾁ02 ﾁ03-070807 060903000707020203 090609 ﾁ0203020705 040605010308, 07070700030203 ﾁ090801 0706 ﾁ03090701020303 060907040300030003020703 07 020909070708010705 060304090801 030902090707, 040307 ﾁ05060302020203 040605010201 0209 040003070903070807. 060907020301 0102, 030708030708 ﾁ03020203, 07 090609 ﾁ0203020708. 07000709020701 ﾁ0206090003020703 縺090609 ﾁ0203020703 0406050103081 7 070007 縺040605010905 0304070702 ﾁ0903080705 090609 ﾁ0203020703011 7. 0503050209 0102 0503 ﾁ03060701 0300 090609 ﾁ020302070506, 0304070702 ﾁ0908060706 0909090703-0803 03000803090802 0209 040003070903070807, 06030701 07020308 03 040003070903070807, ﾁ 09030803060308 04070907070603 ﾁ090209 04060501030905030001020905 07070708030109 090303060207020908 Oxy, 07 090609 ﾁ0203020707, 07030203060009060301 02 ﾁ03 02030703 ﾁ030708020206 (090909 040609 ﾁ070003, 02030703 ﾁ030708020203 0102 0009020301 03000303020907090801 0703060303 x 07 y): F(x; y) = 0; 050203 F(x; y) 0406030703 ﾁ030001020905 04090209010705. 0609040607010306, 2x + 3y 6ﾓ1 2 = 0; x 2 + y 2 6ﾓ1 4 = 0; sin x = cos y 36

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 37 07 08. 02. 070008030908 ( ﾁ 070907080203070807, 040605010905), 0304070702 ﾁ0903010208 090609 ﾁ020302070301, 050803 01020300030708 ﾁ03 ﾁ070306 080306 07 080300010903 080306 0803070309 040003070903070807, 09030306020702090802 09030803060206 090203 ﾁ000308 ﾁ0306050808 0508030109 090609 ﾁ0203020708. ｨｰ090707010308060701 ﾁ 090907030708 ﾁ03 04060701030609 090609 ﾁ0203020703 x 6ﾓ1 2y = 0. ｨｬ03050903 040302030006090801 020307090300010903 030503 06030403-020708: (0; 0), (2; 1), (20; 10),..., 07 ﾁ0303000603, 04090609 (x; y) 090203 ﾁ000308 ﾁ0306050308 090609 ﾁ0203020708, 0903050209 09030306020702090809 x ﾁ 02 ﾁ09 06090309 000300010403 09030306020702090802 y. 02070007 07030300060903070801 罍ﾁ07031 7 0803070907 040003070903070807, 09030306020702090802 09030803060206 090203 ﾁ000308 ﾁ0306050808 0508030109 090609 ﾁ0203020708, 0803, 090909 0703 ﾁ0307080203 030603 0703 0409030001020308 070909010107, 040300090707080705 040605010905 (0701. 060707. 7.1). 06090409 030902090709 ﾁ 05080308 08030103 ﾁ02050702070801, 0909090703 08070402 090609 ﾁ0203020708 030407-0702 ﾁ090808 040605010908 0209 040003070903070807 07 090909 0209040707090801 090609 ﾁ0203020703 09030209060308020308 040605010308, 0309020902020308 090909070107-0803 0903020906030802020107 0409060901030806090107. 3 080603000203 070301 04030603080807 02030403070603020708 ﾁ03020203 09 ﾁ02 ﾁ030209 040306 ﾁ030503 090609 ﾁ0203020705 2 040605010308, 0603080300030701 0002 07040306010900070603 ﾁ090801 03070203 ﾁ020308 040302060302 09 040300090703020708 1 090609 ﾁ0203020708, 0304070702 ﾁ0908060706 040605010203. 0702 07 ﾁ030207080705 09 070003020908060701 02 ﾁ0901-3 -2-1 04090209080901: -1 1 2 3 1) 07040306010900070603 ﾁ090801 09070003 ﾁ0705, 040607 09030803060206 0406030703 ﾁ030001020905 0803070909 M 0406070209020003000708 07070903010308 040605010308, ﾁ 0803060107020906 ﾁ0309080306020308 09000503000602, 2) 04030603040306010900070603 ﾁ090801 050807 09070003 ﾁ0705 ﾁ 0803060107020906 090303060207020908. 080307000302020505 040306010900070603 ﾁ0909 07 02090708 020900020303 090609 ﾁ0203020703. 39. 050902030207070307090303 07 ﾁ02 ﾁ030207010203 0703 02030503 090609 ﾁ0203020705 040605010308 0209 040003070903070807-2 -3 ｨｰ0707. 7.1. 080605010905, 0304070702 ﾁ09-03010905 090609 ﾁ020302070301 x 6ﾓ1 2y = 0 39.1. 050902030207070307090303 090609 ﾁ0203020703. 0803070809 ﾁ0701 0403060302 0703000308 030902090709: ﾁ02040707090801 090609 ﾁ0203020703 040605010308 l 0209 040003070903070807, 04060306030205060308 0703060303 0309020902020908 0803070909 A(x 0 ; y 0 ) 0409060900000300010203 02090202030109 ﾁ030908030609 6ﾓ1 a (p; q) (060707. 7.2). 07080103080701, 070803 ﾁ0309080306 6ﾓ1 a 030002070203 02090302 ﾁ090808 0209040609 ﾁ000508060701 ﾁ03090803060301 040605010308 l. ｨｮ03050009070203 030006030109 0406070201070409, ﾁ030301010301 0406030703 ﾁ030001020908 0803070909 M(x; y) 07 ﾁ020507020701, 040607 0909090301 09070003 ﾁ0707 030209 04030409020308 0209 040605010908 l. 080307090300010909 080603000903010303 09070003 ﾁ0703 0209000203 07040306010900070603 ﾁ090801 0703060303 ﾁ030908030602, 0703030207020701 0803070907 A 07 M 0209040609 ﾁ000302020201 0308060303090301, 090909 050803 0403090903090203 0209 060707. 7.2. 08030205080203, 070803 0803070909 M 0009020308 040607020902000300090801 040605010308 l 0803050209 07 08030001-0903 0803050209, 0903050209 ﾁ030908030602 6ﾓ1 a 07 6ﾓ16ﾓ1 AM 0009020908 0903000007020309060202. ｨｹ0803 07 03070801 0803 09070003 ﾁ0703, 09030803060303 0102 070709090007. 000304030601, 070003020905 03070203 ﾁ02030109 0406070201070409, 020901 040603020708030708 04030603040707090801 020908020302020303 09070003 ﾁ0703 0703060303 09030306020702090802. 010005 0508030503 ﾁ07040301020701, 070803 ﾁ0309- ｨｰ0707. 7.2. 05 ﾁ02 ﾁ030209 090902030207-07030709030503 090609 ﾁ0203020705 040605010308 08030602 6ﾓ1 a 07 6ﾓ16ﾓ1 AM 0903000007020309060202 0803050209 07 080300010903 0803050209, 0903050209 0706 09030306020702090802 040603040306010703020900010202. 05030306020702090802 ﾁ030908030609 6ﾓ1 a (p; q) 0703 ﾁ0307080202 0403 09070003 ﾁ0708, 09 09030306020702090802 ﾁ030908030609 6ﾓ16ﾓ1 AM ﾁ02070707000508080705 090909 6ﾓ16ﾓ1 AM(x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ). 080603040306010703020900010203070801 090303060207020908 ﾁ02050005020708 070003020908060701 03000609030301: ｨｦ080909, 0102 0403000907070007, 070803 x 6ﾓ1 x 0 p = y 6ﾓ1 y 0 : (7.1) q 0803070909 M 07 090303060207020908090107 (x; y) 0406070209020003000708 040605010308 l, 04060306030205060308 0703060303 0309020902020908 0803070909 A(x 0 ; y 0 ) 0409060900000300010203 02090202030109 ﾁ030908030609 6ﾓ1 a (p; q), 0803050209 07 080300010903 0803050209, 0903050209 04090609 0707070300 (x; y) 090203 ﾁ000308 ﾁ0306050308 09070003 ﾁ0708 (7.1). ｨｦ0103020203 04030508030109 0703030802030403020703 (7.1) 05 ﾁ000503080705 07070903010201 090609 ﾁ020302070301, 09030803060303 04060702050803 02090302 ﾁ090801 090902030207070307090701 090609 ﾁ020302070301 040605010308 0209 040003070903070807. ﾂ 020301 040906090103080602 p 07 q 09030306020702090802 0209040609 ﾁ00050806030503 ﾁ0309-08030609, 09 (x 0 ; y 0 ) 09030306020702090802 0909090308-0803 09030209060308020308 0803070907 0209040308 040605010308.

1338 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁｨｰ030403020703 030902090707 0209 0703070809 ﾁ0003020703 09090203020707030709030503 090609 ﾁ0203020705 060903030006090203 ﾁ 04060701030603 7.1. 39.2. 080906090103080607070307090703 090609 ﾁ0203020705. ﾂ 04060302020209060301 06090302030003 0102 0403000907070007 03020203 0703 03070203 ﾁ020206 090609 ﾁ0203020708, 0304070702 ﾁ0908060706 040605010908 0209 040003070903070807. ｨｦ03 02030503 0003050903 ﾁ02 ﾁ030205080705 060903000707020203 ﾁ070202 090609 ﾁ- 0203020708 040605010308. ｨｮ0308070907 0102 04030009070701 080909 02090302 ﾁ0903010203 040906090103080607070307090703 090609 ﾁ0203020705. ｨｦ03 020903 ﾁ09020705 05070203, 070803 040906090103080607070307090703 090609 ﾁ0203020705 050803 090609 ﾁ0203020705 07 04090609010308060301. 000307020303, 050803 07070708030109 090609 ﾁ0203020708 { x = x(t); y = y(t); 0304070702 ﾁ0908060706 040300030003020703 0803070907 07 090303060207020908090107 (x; y) 0209 040003070903070807 ﾁ 0309 ﾁ0707070103070807 0308 0302090703020705 040906090103080609 t (0209040607010306, ﾁ060301030207). ｨｮ08090608090301 07 09090203020707030709030503 090609 ﾁ0203020705 040605010308 (7.1), 0703070809 ﾁ00030202030503 ﾁﾁ070203 040603040306010707: x 6ﾓ1 x 0 p = y 6ﾓ1 y 0 : q 070003030209070701 0903050404070107030208 040603040306010703020900010203070807 0703060303 t 07 03090407040301 050803 090609 ﾁ0203020703 ﾁﾁ070203 07070708030102: 61 x 6ﾓ1 x 0 6462 = t; p 6463 y 6ﾓ1 y 0 = t: q 010102030007 ﾁ 090900020303 0703 090609 ﾁ0203020708 0209 07 ﾁ0308 0302090103020908030001 07 0403060302030705 x 0 07 y 0 ﾁ 040609 ﾁ0908 0709070801, 04030009070701 040906090103080607070307090703 090609 ﾁ0203020705 040605010308 0209 040003070903070807: { x = x0 + pt; (7.2) y = y 0 + qt: ﾂ 020301 (p; q) 09030306020702090802 0209040609 ﾁ00050806030503 ﾁ030908030609 040605010308, 09 (x 0 ; y 0 ) 09030306020702090802 020309030803060308 09030209060308020308 0803070907, 0703060303 09030803060908 0406030603020708 040605010905, t 0409060901030806. 0700060908070803 ﾁ02070109020703, 070803 ﾁ縺020907090001020208 010301030208 ﾁ0603010302071 7 t = 0 0803070909 040605010308 07 090303060207020908090107 (x; y) 0703 ﾁ040902090308 07 080307090308 A(x 0 ; y 0 ). 08030508030109 0803070909 A 0103000203 02090302 ﾁ090801 0308040609 ﾁ020308, 070007 020907090001020308, 080307090308 040906090103080607070307090706 090609 ﾁ0203020708 040605010308 0209 040003070903070807. 080307090300010909 040906090103080607070307090703 090609 ﾁ0203020705 040605010308 0003050903 0403000907070801 0703 09090203020707030709030503 090609 ﾁ0203020705, 09 07090107 040906090103080607070307090703 090609 ﾁ0203020705 0203 0307030201 0709070803 0009020908 ﾁ07080603070908010705 ﾁ 0209040301 0909060703, 0803 090302-09060308020208 040607010306 0209 020706 0102 040607 ﾁ0302070801 0203 0009020301, 03070809 ﾁ07 ﾁ 030503 ﾁ 090907030708 ﾁ03 030902090707 7.15. 39.3. 010609 ﾁ0203020703 040605010308, 04060306030205060308 0703060303 02 ﾁ03 020902020203 0803070907. 0806030204030003000701, 020901 020900-0203 0209040707090801 090609 ﾁ0203020703 040605010308 l 0209 040003070903070807, 04060306030205060308 0703060303 0803070907 A(x 0 ; y 0 ) 07 B(x 1 ; y 1 ) (060707. 7.3). ｨｰ0707. 7.3. 080605010905, 04060306030205-060905 0703060303 02 ﾁ03 0803070907 0609040301020701, 070803 0102 090003 0901030301 ﾁ0204070702 ﾁ090801 090902030207070307090303 090609 ﾁ- 0203020703 040605010308. 010005 0508030503 020901 02030708090803070203 0302090801 09030306020702090802 0909090308-020700090201 0803070907 0209 05080308 040605010308 07 09030306020702090802 0209040609 ﾁ00050806030503 ﾁ030908030609. ｨｦ03 ﾁ0307080202 09030306020702090802 02 ﾁ0906 0803070309 A 07 B, 00030009060706 0209 040605010308. 030306010900010203 020308 080300010903 0209040609 ﾁ00050806030503 ﾁ030908030609. 070202090903 ﾁ0309080306 AB, 6ﾓ1 09030203070203, 04090609000003000302 040605010308 (AB) 07 030503 0103000203 ﾁ03050801 ﾁ 090907030708 ﾁ03 0209-040609 ﾁ00050806030503. 05030306020702090802 ﾁ030908030609 AB 6ﾓ1 ﾁ02070707000508080705 0708090202090608020201 03000609030301: 6ﾓ1 AB(x 1 6ﾓ1 x 0 ; y 1 6ﾓ1 y 0 ): 000304030601 09 020907 03070801 ﾁ0703 0707060302020203 020902020203 020005 020904070709020705 09090203020707030709030503 090609 ﾁ0203020705 (7.1). ﾂ0307040300010309-03010705 070107 07 04030009070701 080603000903010303 090609 ﾁ0203020703 040605010308 0209 040003070903070807, 04060306030205060308 0703060303 02 ﾁ03 0309020902020203 0803070907: x 6ﾓ1 x l: 0 = y 6ﾓ1 y 0 : (7.3) x 1 6ﾓ1 x 0 y 1 6ﾓ1 y 0

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 39 ｨｲ02030701 (x 0 ; y 0 ), (x 1 ; y 1 ) 09030306020702090802 0803070309, 04060702090200030009060706 040605010308. 05030209060308020905 030902090709 0209 050803 090609 ﾁ0203020703 060304030209 ﾁ 04060701030603 7.2. 40. 0700060303 090609 ﾁ0203020703 040605010308 0209 040003070903070807 40.1. 010609 ﾁ0203020703 040605010308 0403 0803070903 07 02030601090007. 0806030204030003000701, 020901 0309020902 ﾁ0309080306 6ﾓ1 n (A; B) 07 0803070909 M 0 (x 0 ; y 0 ) 07 080603000903080705 0209040707090801 090609 ﾁ0203020703 040605010308 l, 04060306030205060308 0703060303 0803070909 M 0 040306040302-020709090005060203 ﾁ030908030609 6ﾓ1 n (060707. 7.4). 050909 07 0609020303, ﾁ030301010301 0406030703 ﾁ030001020908 0803070909 M(x; y), 0403070806030701 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M 07 03090209010903010705: 040607 0909090706 09070003 ﾁ070506 0803070909 M 04030409020308 0209 040605010908 l? 09070203, 070803 050803 04060307030308020308 0803050209 07 080300010903 0803050209, 0903050209 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M 0009020308 040306040302020709090005060302 ﾁ030908030609 6ﾓ1 n. ﾂ020609030701 080304030601 050803 09070003 ﾁ0703 0703060303 09030306020702090802. 080603000203 ﾁ07030503 03090103080701, 070803 09030306020702090802 ﾁ030908030609 6ﾓ16ﾓ16ﾓ1 M 0 M 050803 (x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ). 080306040302-020709090005060203070801 ﾁ030908030603 ﾁ 0303020907090308, 070803 09050300 ' 0103000209 02070107 0703070809 ﾁ00050308 90 71, 08. 03. 09030707020907 0508030503 09050009 020300000302 00020801 0609 ﾁ0302 0. ﾂ020609000905 09030707020907 09050009 0703060303 070909000506020303 0406030703 ﾁ030203020703, 0403000907090301: cos ' = (6ﾓ1 n ; 6ﾓ16ﾓ16ﾓ1 M 0 M) 6ﾓ1 n 6ﾓ16ﾓ16ﾓ1 M : 0 M M M n ｨｰ0707. 7.4. 080605010905, 09030803060905 030902090209 ﾁ03090803060301 02030601090007 07 080307090308 0009090701 03000609030301, 040306040302020709090005060203070801 ﾁ030908030603 ﾁ 0303020907090308, 070803 0706 070909000506020303 0406030703 ﾁ030203020703 0609 ﾁ0203 0. 0707080900030701 ﾁ0704030102070801, 090909 ﾁ02070707000503080705 070909000506020303 0406030703 ﾁ030203020703 0703060303 09030306020702090802: ( 6ﾓ1 n ; 6ﾓ16ﾓ16ﾓ1 M 0 M) = A(x 6ﾓ1 x 0 ) + B(y 6ﾓ1 y 0 ): ｨｮ00030203 ﾁ09080300010203, 07070903010303 090609 ﾁ0203020703 040605010308 l ﾁ02050005020708 080909: l: A(x 6ﾓ1 x 0 ) + B(y 6ﾓ1 y 0 ) = 0: (7.4) 080607 05080301 A 07 B 07090801 09030306020702090802 ﾁ030908030609 6ﾓ1 n, 0403060403020207090900050602030503 040605010308 l, 09 (x 0 ; y 0 ) 09030306020702090802 020309030803060308 0803070907 0209 040605010308. ﾂ0309080306 6ﾓ1 n (A; B) 0203070708 020903 ﾁ09020703 02030601090007 09 040605010308 l. 40.2. 0700060303 090609 ﾁ0203020703 040605010308. ｨｰ0907090602 ﾁ 070903000907 ﾁ 090609 ﾁ0203020707 (7.4), 04030009070701 Ax + By + (6ﾓ1Ax 0 6ﾓ1 By 0 ) = 0: ﾂ0206090003020703 ﾁ 07090300090906 0707070003, 09030803060303 0103000203 03000303020907070801 0703060303 C 07 04030603040707090801 090609 ﾁ0203020703 ﾁﾁ070203 Ax + By + C = 0: (7.5) ｨｪ02 090003 090003020700070701, 070803 03070007 050803 090609 ﾁ0203020703 0403000907030203 ﾁ 06030309000108090803 060907090602080705 070903000309 ﾁ 090609 ﾁ- 0203020707 (7.4), 0803 030203 0304070702 ﾁ090308 040605010908. ｨｦ02020107 070003 ﾁ090107, 0803070907, 09030306020702090802 09030803060206 090203 ﾁ000308 ﾁ03-06050808 0508030109 090609 ﾁ0203020708, 0300060903090808 020309030803060908 040605010908 0209 040003070903070807. ﾂ0303020709090308 030909030203010306020208 ﾁ0304060307: 09 ﾁ0705090303 0007 090609 ﾁ0203020703 08070409 (7.5) 0304070702 ﾁ090308 0909090908-0803 040605-010908 0209 040003070903070807. 0708 ﾁ0308 04030003000708030001020208, 0309 0302020701 030207020708 ﾁ0302020201 0707090008070302070301: 03070007 A = B = 0, 0803 090609 ﾁ0203020703 0009020308 ﾁ0205000502030801 090909 C = 0. 080307090300010909 C 09030209060308020303 0707070003, 0803 040300090707080705 00070003 08030002030708 ﾁ03 (03070007 C = 0), 0903080306030109 090203 ﾁ000308 ﾁ0306050308 0008000905 04090609 090303060207020908, 08. 03. 0809090303 縺090609 ﾁ02030207031 7 0304070702 ﾁ090308 ﾁ0708 040003070903070801, 00070003 000300020303 0609 ﾁ03020708 ﾁ03 (03070007 C ﾙ 0), 01020300030708 ﾁ03 06030403020708 0903080306030503 0409070803. ｨｮ0308070907 0102 04030909000301, 070803 03070007 A 07 B 03020203 ﾁ06030103020203 ﾁ 02090001 0203 03000609060908080705, 0803 090609 ﾁ0203020703 (7.5) 0304070702 ﾁ090308 040605010908 07 0203060109000108 6ﾓ1 n (A; B). ｨｹ0803 090609 ﾁ0203020703 04060702050803 02090302 ﾁ090801 0300060701 090609 ﾁ020302070301 040605010308 0209 040003070903070807.

1340 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁｨｦ080909, 06090707010308060701 090609 ﾁ0203020703 (7.5), ﾁ 09030803060301 00070003 A, 00070003 B 03080007070203 0308 02090005, 07 020908020301 0909090303-020700090201 03020203 030503 06030403020703. 0909020301, 0209040607010306, 07070708090801, 070803 A ﾙ 0 07 04030003000701 y = 0. 0003050209 050803 090609 ﾁ0203020703 0403060304070403080705 ﾁﾁ070203: Ax = 6ﾓ1C; 0603040302070301 0903080306030503 070009000708 0707070003 x = 6ﾓ1C=A. ｨｲ0209070708, 04090609 (6ﾓ1C=A; 0) 05 ﾁ000503080705 0603040302070301 0707-06030202030503 090609 ﾁ0203020705. 070003030209070701 01020300030708 ﾁ03 0803070309 040003070903070807, 0304070702 ﾁ0903010206 090609 ﾁ020302070301 (7.5), 070701 ﾁ03000301 l. 0003070909 M 0 07 090303060207020908090107 (6ﾓ1C=A; 0) 0406070209020003000708 01020300030708 ﾁ09 l. 0608030002 00020003 0403020508020303 02090403 0609070709000203020703, 040603 ﾁ03020301 030503 020005 0903020906030802030503 070009070905, 0209040607010306, 020005 090609 ﾁ0203020705 3x + 5y + 9 = 0. 080300030007 ﾁ y = 0, 04030009070701 3x = 6ﾓ19, 030809090209 x = 6ﾓ13. 0009090701 03000609030301, 04090609 (6ﾓ13; 0) 06030403020703 070706030202030503 090609 ﾁ0203020705, 070803 0003050903 040603 ﾁ0306070801 02030403070603020708 ﾁ0302020308 0403020708090203 ﾁ- 090308. ｨｮ00030203 ﾁ09080300010203, 0803070909 M 0 (6ﾓ13; 0) 0406070209020003000708 01020300030708 ﾁ09 l (0102 04030909 030603 0203 09 ﾁ0306030202, 070803 050803 040605010905). 0806030300060903090301 090609 ﾁ0203020703 (7.5) 070003020908060701 03000609030301: Ax + By + C = 0 6ﾍ2 A(x + C=A) + B(y 6ﾓ1 0) = 0 07 ﾁﾁ03020301 04090609 ﾁ030908030603 ﾁ: 6ﾓ1 n (A; B) 07 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M(x + C=A; y 6ﾓ1 0). 0003070909 M 0 (6ﾓ1C=A; 0) 0406070209020003000708 01020300030708 ﾁ09 l, 09 0803070909 M 07 090303060207020908090107 (x; y) 0406030703 ﾁ030001020905 0803070909 040003070903070807. ｨｮ03030802030403020703 A(x + C=A) + B(y 6ﾓ1 0) = 0 0103000203 070208030604060308070603 ﾁ090801 n 080909, 070803 0803070909 M(x; y) 0403040902090308 ﾁ 01020300030708 ﾁ03 l, 0903050209 070909000506020303 040603-0703 ﾁ030203020703 ﾁ030908030603 ﾁ 6ﾓ1 n 07 6ﾓ16ﾓ16ﾓ1 M 0 M 0609 ﾁ0203 02090008, 08. 03. 030207 040306040302020709090005060202 (0701. 070806. 39). 0603 050803 0303020907090308, 070803 01020300030708 ﾁ03 l 04060302070809 ﾁ00050308 0703000308 040605010908, 04060306030205060908 0703060303 0803070909 M 0 (6ﾓ1C=A; 0) 040306040302020709090005060203 ﾁ0309-08030609 ｨｰ0707. 7.5. 6ﾓ1 n (A; B) (060707. 7.5), 070803 0102 07 060308030007 0203090903090801. 080603020300090301 0902090003050707020203 040603030006090303 ﾁ09020705 ﾁ 09030209060308020301 04060701030603: 3x + 5y + 9 = 0 6ﾍ2 3(x + 3) + 5(y 6ﾓ1 0) = 0: ｨｲ02030701 6ﾓ1 n (3; 5), M 0 (6ﾓ13; 0), M(x; y) 07 6ﾓ16ﾓ16ﾓ1 M 0 M(x + 3; y 6ﾓ1 0). 08030508030109 040307000302020303 0703030802030403020703 0303020907090308 0609 ﾁ03020708 ﾁ03 02090008 07090900050602030503 0406030703 ﾁ030203020705 ( 6ﾓ1 n ; 6ﾓ16ﾓ16ﾓ1 M 0 M), 08. 03. 040306040302020709090005060203070801 07030308 ﾁ03080708 ﾁ0908060706 ﾁ030908030603 ﾁ. 41. 010609 ﾁ0203020703 040605010308 07 09050003 ﾁ0201 09030504040701070302080301 ｨｰ090707010308060701 0300060303 090609 ﾁ0203020703 040605010308 (7.5) 07 0609030603040701 030503 030802030707080300010203 y: l: Ax + By + C = 0 6ﾍ2 y = 6ﾓ1 A B x 6ﾓ1 C B : 0700060908070803 ﾁ02070109020703, 050803 0103000203 07020300090801 080300010903 0803050209, 0903050209 B ﾙ 0 ( ﾁ 0406030807 ﾁ020301 070009070903 04030603-010302020308 y ﾁ 090609 ﾁ0203020707 040603070803 020308). ﾂﾁ03020301 0300030302090703020705: k = 6ﾓ1A=B, b = 6ﾓ1C=B 07 040306030407040301 090609 ﾁ0203020703: y = kx + b: (7.6) 08030009070700030701 080909 02090302 ﾁ0903010303 090609 ﾁ0203020703 040605010308 07 09050003 ﾁ0201 09030504040701070302080301. 0700080507020701, 040307030109 050803 090609 ﾁ0203020703 02090302 ﾁ0903080705 070103020203 080909. ｨｦ0303000609030701 040605010908 0209 060707. 7.6.

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 41 ｨｰ0707. 7.6. 080605010905 0403 090609 ﾁ0203020708 07 09050003 ﾁ0201 09030504040701070302080301 08060307080201 ﾁ02070707000302070301 09000300020903010705, 070803 05080308 040605010308 0406070209020003000908 0803070907 A(0; b) 07 B(1; k +b). 070807080209 0103000203 07020300090801 ﾁ02 ﾁ0302: 0903050404070107030208 b ﾁ 090609 ﾁ0203020707 050803 0306020702090809 0803070907, ﾁ 09030803060308 6ﾓ1 040605010905 04030603070309090308 090303060207020908020908 030701 Oy. 0506030103 08030503, AB(1; k) 0209040609 ﾁ000508060708 ﾁ0309080306 040605-010308 l. 080300010309050701 0607070902090301, ﾁ02070707000701 0200070202 03080603030903 ﾁ AC 07 BC: 070807080209 0903050404070107030208 k 0207 070803 07020303, 090909 AC = 1; BC = k: tg ' = BC AC ; 08. 03. 08090205030207 09050009 02090900030209 040605010308 l 09 0503060703030208090007. ｨｦ0103020203 04030508030109 090609 ﾁ0203020703 (7.6) 02090302 ﾁ090808 090609 ﾁ020302070301 040605010308 07 09050003 ﾁ0201 09030504040701070302080301. 42. 010609 ﾁ0203020703 040605010308 ﾁ 0308060303090906 0609070803 0002 ﾁ090308 04030003030203 090103020703 ﾁ0204070702 ﾁ090801 090609 ﾁ0203020703 040605010308, 09030803060905 04030603070309090308 030707 0903-03060207020908 ﾁ 09030209060308020206 080307090906, 0308000707020206 0308 020907090009 090303060207020908. 0103040907080701, 020901 04030806030003 ﾁ0900030701 090609 ﾁ0203020703 040605010308 l, 040306030703090908060308 030701 Ox ﾁ 0803070903 M(a; 0), 09 030701 Oy ﾁ 0803070903 N(0; b) (060707. 7.7). 08030402080903010705 040302030006090801 090305040407010703020802 ﾁ 0300060301 090609 ﾁ0203020707 Ax + By + C = 0 040605010308 080909, 0708030002 04030009070700030701 090609 ﾁ0203020703 040605010308 l. ｨｪ02 0302090301 09030306020702090802 02 ﾁ0906 0803070309 0209 040605010308 l. 08030508030109 0103000203 ﾁ02040707090801 07070708030109 090609 ﾁ0203020708: { Aa + B0 = 6ﾓ1C; A0 + Bb = 6ﾓ1C: 070202090903 ﾁ 05080308 07070708030103 080300010903 02 ﾁ09 090609 ﾁ0203020705 07 080607 02030703 ﾁ030708020206: A, B 07 C. ｨｲ090103080701, 070803 03070007 ﾁ 0300060301 090609 ﾁ0203020707 040605010308 0403000300070801 C = 0, 0803 040605010905, 0304070702 ﾁ0903010905 0809090701 090609 ﾁ020302070301, 0009020308 040603060302070801 0703060303 020907090003 090303060207020908, 070803 0203 0703050009070903080705 07 09070003 ﾁ070301 030902090707. 08030508030109 C ﾙ 0 07 0102 0103000301 060903020300070801 0209 02030503 030009 090609 ﾁ0203020705 07070708030102: { AC a + B C 0 = 6ﾓ11; A C 0 + B C b = 6ﾓ11; 030809090209 A C = 6ﾓ11 a ; B C = 6ﾓ11 b 07 020900020303 090609 ﾁ0203020703 ﾁ02050005020708 090909 6ﾓ1 1 a x 6ﾓ1 1 b y + 1 = 0 ｨｰ0707. 7.7. 080605010905, 040603-06030205060905 0703060303 0309020902020203 0803070907 0209 03070506 090303060207020908

1342 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ x 070007 a + y = 1: (7.7) b 0009090308 ﾁ0702 090609 ﾁ0203020705 02090302 ﾁ090808 090609 ﾁ020302070301 040605010308 ﾁ 0308060303090906. 43. 06030601090001020303 090609 ﾁ0203020703 040605010308 ｨｰ090707010308060701 040605010908 l, 0309020902020908 090609 ﾁ020302070301 2x 6ﾓ1 3y + 4 = 0. 02070007 050803 090609 ﾁ0203020703 0901020300070801 0209 4, 04030009070701 030603 03020203 090609 ﾁ0203020703 8x 6ﾓ1 12y + 16 = 0, 09030803060303 0304070702 ﾁ090308 0809 0003 040605010908. 0903-000303 08030503, 09010203000905 090609 ﾁ0203020703 040605010308 0209 0406030703 ﾁ030001020908 020302090003 ﾁ0908 090302070809020809, 0009020301 0403000907090801 060903020203 090609 ﾁ0203020705, 09030803060203 030902090808 03020209 07 0809 0003 040605010908. ｨｹ0803, 09030203070203, 0203090203000203. ｨｨ03080300030701 0002, 0708030002 090900020308 040605010308 07030308 ﾁ03080708 ﾁ03 ﾁ090003 080300010903 03020203 090609 ﾁ0203020703. 01030708070701 0508030503 0103000203 07 04030103060108 020306010900070309010707. 43.1. 0704060302030003020703. 06030601090001020201 090609 ﾁ020302070301 040605010308 02090302 ﾁ0903080705 090609 ﾁ0203020703 ﾁ070209 x + y 6ﾓ1 = 0; 050203 2 + 2 = 1 07 1 7 0. ｨｪ03000209 01020300030708 ﾁ090107 040605010206 0209 040003070903070807 07 02030601090001020206 090609 ﾁ0203020708 070906030708 ﾁ090308 ﾁ030907010203 0302-020303020907020303 07030308 ﾁ03080708 ﾁ0703. ｨｦ02020107 070003 ﾁ090107, 020005 090900020308 040605010308 070906030708 ﾁ090308 02030601090001020303 090609 ﾁ0203020703, 09030803060303 0303 0304070702 ﾁ090308, 040607070301 080300010903 03020203. 010309090309080300010708 ﾁ03 0508030503 0409090809 0102 03070809 ﾁ0701 ﾁ 090907030708 ﾁ03 0403000303020308 030902090707 (030902090709 7.37 6ﾓ5 ). ｨｮ 04030103060108 0203060109000102030503 090609 ﾁ0203020705 0103000203 ﾁ0207070700070801 06090707080305020703 0308 0803070907 0203 040605010308. ｨ 00-05030607080109 0508030503 ﾁ020707070003020705 040307 ﾁ0506030202 08030306030109 07 070003020708 ﾁ0705 0703 020303. 43.2. 00030306030109. 0809070801 x + y 6ﾓ1 = 0 02030601090001020303 090609 ﾁ0203020703 040605010308 l. 0003050209 1) 0200070209 02030601090007 6ﾓ1 n (; ) 09 040605010308 l 0609 ﾁ0209 1; 2) 02030601090001 6ﾓ1 n 0209040609 ﾁ00030209 0308 020907090009 090303060207020908 09 040605010308 l, 090909 0403090903090203 0209 060707. 7.8, 09; 3) 06090707080305020703 0308 020907090009 090303060207020908 0203 040605010308 l 0609 ﾁ0203. M n n ｨｰ0707. 7.8. 05 0203060109000102030109 090609 ﾁ0203020708 040605010308 ｧﾑ) ｧﾒ) 010309090309080300010708 ﾁ03. ｨｲ090103080701, 070803 ﾁ0309080306 6ﾓ1 n (; ) 0203080708 ﾁ07080300010203 05 ﾁ000503080705 0203060109000108 040605010308 l (0701. 070806. 39), 08. 03. 040306040302020709090005060302 0308. 0100070209 ﾁ030908030609 6ﾓ1 n (; ) ﾁ02070707000503080705 090909 6ﾓ1 n = ﾌ 2 + 2. 0803 0304060302030003020708 0203060109000102030503 090609 ﾁ0203020705 ﾁ0206090003020703 040302 090306020301 0609 ﾁ0203 1. 000909 070803 6ﾓ1 n = 1. 010005 020309090309080300010708 ﾁ09 0908 ﾁ0306000203020708 2) 07 3) 08030306030102 03040907080701 04030604030202070909000506 0703 020907090009 09030306-0207020908 0209 040605010908 l 07 030003030209070701 030503 03070203 ﾁ09020703 0703060303 M 0 (x 0 ; y 0 ) (0701. 060707. 7.8, 00). 0003050209 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 OM 0 (x 0 ; y 0 ) 0009020308 04090609000003000302 ﾁ030908030609 6ﾓ1 n (; ). ｨｲ0209070708, 0706 09030306020702090802 040603040306010703020900010202. ｨｦ0202-0107 070003 ﾁ090107, 0209080203080705 0809090303 0707070003 t, 070803 x 0 = t, y 0 = t. 080607070301 t 1 7 0, 03070007 050807 ﾁ030908030602 0009020908 07030209040609 ﾁ00030202 (090909 0209 06070709020903) 07 t < 0, 03070007 030207 0406030807 ﾁ0304030003000203 0209040609 ﾁ00030202. ｨｮ 020609050308 07080306030202, 0803070909 M 0 (x 0 ; y 0 ) 0406070209020003000708 040605010308 l, 04030508030109 09030306020702090802 (x 0 ; y 0 ) 090203 ﾁ000308 ﾁ0306050808 090609 ﾁ0203020708 040605010308, 08. 03. x 0 + y 0 6ﾓ1 = 0:

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 43 080302070809 ﾁ0701 ﾁ 050803 0703030802030403020703 x 0 = t, y 0 = t: 07 ﾁ020203070301 t 0309 070903000907: t + t 6ﾓ1 = 0 t( 2 + 2 ) 6ﾓ1 = 0: 000909 090909 0403 09070003 ﾁ0708 2 + 2 = 1, 0803 0703 04030700030202030503 0703030802030403020705 07000302090308 0609 ﾁ03020708 ﾁ03: t =. ｨｦ080909, 0403 0304060302030003020708 0203060109000102030503 090609 ﾁ0203020705 1 7 0, 030209070708, 07 t 1 7 0, 08. 03. ﾁ030908030602 6ﾓ1 n 07 6ﾓ16ﾓ16ﾓ1 OM 0 07030209040609 ﾁ00030202 07 02030601090001 6ﾓ1 n 0203080708 ﾁ07080300010203 030607030208070603 ﾁ090209 0308 020907090009 090303060207020908 09 040605010308. ｨｰ090707080305020703 0308 020907090009 090303060207020908 0203 040605010308 l 050803 ﾁ 0803070203070807 0200070209 ﾁ030908030609 6ﾓ16ﾓ16ﾓ1 OM 0, 09030803060905 ﾁ02070707000503080705 0703060303 030503 09030306020702090802: 6ﾓ16ﾓ16ﾓ1 OM 0 = ﾌ (t) 2 + (t) 2 = ﾌ t 2 ( 2 + 2 ) = t 1 = : 7ﾁ3 ｨｮ 04030103060108 080300010903 070803 02030909030902020308 08030306030102 0102 0103000301 ﾁ0207070700070801 06090707080305020703 0308 020907090009 090303060207020908 0203 0406030703 ﾁ030001020308 040605010308. ｨｮ01. 07030308 ﾁ03080708 ﾁ0908060708 040607010306 7.4. 0608030002 ﾁ0207070700070801 06090707080305020703 0308 0406030703 ﾁ030001020308 0803070907 040003070903070807 0203 040605010308, 0209000203 ﾁ030704030001-0303 ﾁ0908010705 070003020708 ﾁ070301 08030306030102 (0701. 040607010306 7.5). 43.3. ｨｮ0003020708 ﾁ0703. 0809070801 x + y 6ﾓ1 = 0 02030601090001020303 090609 ﾁ0203020703 040605010308 l. ｨｰ090707080305020703 (A; l) 0308 0803070907 A(x 0 ; y 0 ) 0203 040605010308 l ﾁ02070707000503080705 0403 04030601090003: (A; l) = x 0 + y 0 6ﾓ1 : 010309090309080300010708 ﾁ03. ｨｲ090103080701, 070803 050803 0908 ﾁ0306000203020703 090003 0203090903090203, 0903-050209 09030306020702090802 0803070907 A 050803 (0; 0) (0701. 08030306030109 43.2). 08030508030109 ﾁﾁ03020301 0203 ﾁ0908 07070708030109 090303060207020908 Auv (060707. 7.9), 030707 09030803060308 0409-060900000300010202 03070501 0707060302020308 07070708030102, 09 020907090003 090303060207020908 0703 ﾁ040902090308 07 080307090308 A. ﾂ020507020701, 090909 07 ﾁ0503090202 070809060203 07 0203 ﾁ0203 09030306020702090802. ｨｲ090103080701, 070803 09030306020702090802 0803070907 A ﾁ 070809060308 07070708030103 (x 0 ; y 0 ), 09 ﾁ 0203 ﾁ0308 (0; 0), 0702020107 070003 ﾁ090107, 0903050209 x = x 0, 0803 u = 0, 09 0903050209 y = y 0, v = 0. 060307000300-0203 07030300060903070801, 070803 0309 ﾁ0707070103070801 090303060207020908 ﾁ020609000903080705 07000302090806070107 040306010900090107: u = x 6ﾓ1 x 0 ; v = y 6ﾓ1 y 0 : ﾂ020609030701 0703 05080706 040306010900 x 07 y: ｨｰ0707. 7.9. ｨｮ070708030109 090303060207-020908 Auv ﾁ 07070708030103 090303060207-020908 Oxy. 07 040302070809 ﾁ0701 ﾁ 02030601090001020303 090609 ﾁ0203020703 040605010308 l: x = u + x 0 ; y = v + y 0 (u + x 0 ) + (v + y 0 ) 6ﾓ1 = 0: ｨｪ02 0403000907070007 090609 ﾁ0203020703 040605010308 l ﾁ 0203 ﾁ0308 07070708030103 090303060207020908. ｨｰ0907090602 ﾁ0905 070903000907, 0403000907090301 u + v + (x 0 + y 0 6ﾓ1 ) = 0: 000909 090909 0707060302020303 090609 ﾁ0203020703 00020003 02030601090001020201, 0803 2 + 2 = 1. 000909 070803 07 080307020307080108 0203 0302090909 090609 ﾁ0203020703 ﾁ 0203 ﾁ0308 07070708030103 090303060207020908 08030003 020306010900010203 (020901 02030703 ﾁ0307080302 03020909 07 ﾁ0300030202030503 0700030209). 08030508030109 0103000203 0908 ﾁ03060002090801, 070803 06090707080305020703 0308 020907090009 090303060207020908 0203 ﾁ0308 07070708030102 (08. 03. 0803070907 A) 0203 040605010308 l 0609 ﾁ0203 x 0 + y 0 6ﾓ1. 7ﾁ3

1344 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 44. ﾂ03090701020303 060907040300030003020703 040605010206 0209 040003070903070807 050909 0102 0302090301 0703 0909060709 0409030001020308 0400090207010308060707, 02 ﾁ03 040605010203 0209 040003070903070807 0103050908 00070003 04030603-0703090908010705, 00070003 00020801 04090609000003000102020107, 0203 0203 0703 ﾁ040902090806070107 04060501020107, 00070003 0703 ﾁ040902090801. ｨｮ0308070907 0102 0009020301 07070700030203 ﾁ090801 ﾁ03090701020303 040300030003020703 04090602 040605010206 0209 040003070903070807, 070309070905 0706 090609 ﾁ0203020705. 0809070801 040605010203 l 1 07 l 2 030902090202 07 ﾁ03070107 030006070107 090609 ﾁ02030207050107: l 1 : A 1 x + B 1 y + C 1 = 0; l 2 : A 2 x + B 2 y + C 2 = 0: 02070007 03020203 090609 ﾁ0203020703 0403000907030203 0703 02060905030503 09010203000302070301 0209 020302090003 ﾁ0908 090302070809020809, 0803, 03070803-0708 ﾁ03020203, l 1 = l 2. ﾂ 05080308 0707080909010707 ﾁ0703 090305040407010703020802 090609 ﾁ0203020708 040603040306010703020900010202: A 1 A 2 = B 1 B 2 = C 1 C 2 : 02070007 040605010203 0409060900000300010202, 0803 0409060900000300010202 07 0706 02030601090007 (0701. 060707. 7.10), 09 030209070708, 0706 09030306-020702090802 040603040306010703020900010202. 000909 090909 6ﾓ1 n 1 (A 1 ; B 1 ), 09 6ﾓ1 n 2 (A 2 ; B 2 ), 0803 09070003 ﾁ0703 0409060900000300010203070807 040605010206 ﾁ02050005020708 090909 A 1 = B 1 : A 2 B 2 0700060908070803 ﾁ02070109020703, 03070007 040607 05080301 030603 ｨｰ0707. 7.10. 080906090000030001020203 040605-010203 A 1 = B 1 ﾙ C 1 ; A 2 B 2 C 2 0803 040605010203 0409060900000300010202, 0203 0203 0703 ﾁ040902090808. 06090903020301, 0708030002 040605010203 0209 040003070903070807 040306030703090900070701, 02030300060302070103 07 02030708090803070203, 0708030002 0706 02030601090007 00020007 0203 0409060900000300010202, 08.03. A 1 A 2 ﾙ B 1 B 2 : 45. 0809070309 040605010206 ｨｮ0003 ﾁ03 縺04090703091 7 ﾁ 01090803010908070903 0303020907090308 0406070103060203 0803 0003, 070803 07 ﾁ 0609030503 ﾁ0306020301 0503020903, 09 070103020203, 0203070803, 070307080305060303 0703 030802030001020206, 0203 04030603000706 02060905 0209 0206090509 罍ﾁ0308030703091 7. ﾂ 0209040301 0909060703 罍ﾁ03080307-09071 7 050803 040605010203 (04030909 080300010903 0209 040003070903070807). ｨｰ0903000707090808 02 ﾁ09 08070409 0409070909 040605010206: 070307080305060708 0703 ﾁ070306 040605010206, 04060306030205060706 0703060303 0309020902020908 0803070909 (060707. 7.11, 00), 07 0703 ﾁ070306 040605010206, 040906090000030001-020206 0103000209 0703000308 (060707. 7.11, 09). ﾂ 08030306030807070307090706 03090209070906 0002 ﾁ090808 04030003030202 090609 ﾁ0203020705 0809090706 0409070903 ﾁ. 03090908070703070907 050803 090609 ﾁ0203020703 040605010308 07 04090609010308060301. ｨｮ0308070907 0102 0706 ﾁ02 ﾁ03020301. ｧﾑ) ｧﾒ) ｨｰ0707. 7.11. 0809070309 040605010206: 09) 04030409060203 040906090000030001020206; 00) 0403060307030909080607060705 ﾁ 0302020308 0803070903 060907020301 07 0409070909 040906090000030001020206 040605010206. ｨｲ09040709070706090301 ﾁ0309080306 6ﾓ1 a (p 0 ; q 0 ) 07 030407040301 ﾁ0703 040605010203 07 0809090701 0209040609 ﾁ000508060701 ﾁ03090803060301. ｨｲ02030701 020901 0209000203 ﾁ0307040300010303 ﾁ0908010705 090902030207070307090701 090609 ﾁ020302070301

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 45 040605010308 (7.1). 070202090903 020901 0203 02090209 0803070909, 0703060303 09030803060908 0406030603020708 040605010905. 0203 09030306020702090802 07 0009020908 0409060901030806090107, 070909000301, x 0 =, y 0 =. ﾂ 06030309000108090803 04030009070701: x 6ﾓ1 p 0 = y 6ﾓ1 q 0 : 0608030002 00020003 0403020508020303, ﾁ030301010301 09030209060308020208 ﾁ0309080306, 0209040607010306, 6ﾓ1 a (2; 3). 0003050209 090609 ﾁ0203020703 0409070909 040605010206, 040906090000030001020206 0508030109 ﾁ030908030609, ﾁ02050005020708 090909 x 6ﾓ1 2 = y 6ﾓ1 : 3 080607 00030009020707 0103000203 07030009 ﾁ0708010705 0308 030209010302090803000308 07 0309040707090801 0300060303 090609 ﾁ0203020703 0409070909 ﾁﾁ070203: q 0 x 6ﾓ1 p 0 y + (p 0 6ﾓ1 q 0 ) = 0: 0609040301020701, 070803 (p 0 ; q 0 ) ﾁ 05080301 090609 ﾁ0203020707 09030306020702090802 0209040609 ﾁ00050806030503 ﾁ030908030609, 09 07 0406030703 ﾁ030001020203 ﾁ0306030708 ﾁ0302020203 0707070009. 08030508030109 ﾁ0703 ﾁ0206090003020703 p 0 6ﾓ1 q 0 0103000308 040607020701090801 0008000303 0302090703020703. ﾂ0305 ﾁ 030503 0309 0409060901030806, 040607020301 09 0309030207090803000102030109 ﾁ070209 090609 ﾁ0203020705 0409070909 040906090000030001020206 040605010206: q 0 x 6ﾓ1 p 0 y + = 0: (7.8) 0809060901030806, 0907090708 ﾁ0908060708 ﾁ 090609 ﾁ0203020707 0409070909, 0103000203 ﾁ0307040607020701090801 090909 09030306020702090809 090302-09060308020308 040605010308 0703 02090202030503 0409070909. 0506030103 08030503, 0302 0209040605010908 07 ﾁ05030902 07 0609070708030502070301 0103000209 04060501020107 ﾁ 0409070903. 050909 ﾁ0207070700070801 06090707080305020703 0103000209 04090609000003000102020107 04060501020107, 0403090903090203 ﾁ 040607-01030603 7.6. ｨｮ 040306030703090908060701070705 04060501020107 02030003 03000708030708 020307090300010903 07020803060307020303. 0809070309 040605010206, 04060306030205-060706 0703060303 03020209 0803070909, 05 ﾁ000503080705 01030203000108 04060303090807 ﾁ020308 040605010308, 03 070301 06030701 040308020308 ﾁ 070003020908060301 06090302030003. ｨｦ080909, 0309040709070706090301 0803070909 M 0 (x 0 ; y 0 ) 07 03090407040301 090609 ﾁ0203020703 040605010308, 04060306030205060308 0703060303 020303 0409060900000300010203 090909030109-020700090201 0406030703 ﾁ03000102030109 ﾁ030908030609 6ﾓ1 a (p; q): 070007 x 6ﾓ1 x 0 p = y 6ﾓ1 y 0 ; q q(x 6ﾓ1 x 0 ) 6ﾓ1 p(y 6ﾓ1 y 0 ) = 0: (7.9) ｨｹ0803 07 03070801 090609 ﾁ0203020703 0409070909 0403060307030909080607060705 040605010206 0209 040003070903070807. 02070007 ﾁ 04030009070302020301 090609 ﾁ0203020707 0609070906020801 070903000907 07 ﾁ0206090003020703 py 0 6ﾓ1 qx 0 04060702050801 0309 0909090308-020700090201 0203 ﾁ0208 0409060901030806, 0803 0102 0403080306050301 07020403060109010708 03 0903030602070209080906 0300060308 0803070907. 08030508030109 020005 090609 ﾁ0203020705 0409070909 040605010206 0508030503 020300090801 020300010305! 010609 ﾁ0203020703 (7.9) 040303 ﾁ0300050308 ﾁ0207070700070801 09050300 0103000209 040306030703090908060701070705 04060501020107 (0701. 040607-010306 7.7). 46 6ﾓ5. 08060303090807 ﾁ020905 040605010905 ﾂ 0703 ﾁ0603010302020308 01090803010908070903 (080307020303, 0900050300060907070307090308 050303010308060707) 070906030708 ﾁ090308 0809090303 04030205080703, 090909 縺010203050303000609030703 010302090003081 7. 080302 020701 040302060903090103 ﾁ0903080705 0803, 070803 0703000308 04060302070809 ﾁ00050308 01020300030708 ﾁ03 0909090706-0803 04030603000706 02060905 0209 0206090509 03000803090803 ﾁ 07 0803070907 030603020705 050303010308060707. ﾂ 0709010301 020907090003 0909060709 0102 090003 ﾁ07080603070900070701 07 05080308 0900070806090901070308, 06030805 07 0203 0904030806030000050007 080306010702 縺010203050303000609030703 010302090003081 7. 0103080708 ﾁ07080300010203, 0102 020907090007 0703090703020703 050303010308060707 07 01020300030708 ﾁ09 ﾁ030908030603 ﾁ, 090900020208 0703 09030803060206 0900090707 0509 ﾁ07 ﾁ0900030208020206 0209040609 ﾁ000302020206 03080603030903 ﾁ. 09020003 020304030205080203, 070803 0703-000308 04060302070809 ﾁ00050308 050803 01020300030708 ﾁ03 0203 080306 040306, 04030909 0102 0203 ﾁﾁ030007 09030306020702090802. 02070007 030904070907070603 ﾁ090801

1346 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 0009030707, 0803 090900020208 ﾁ0309080306 0009020308 03020203030209070203 030406030203000508010705 090303060207020908090107 07 ﾁ03030503 0903020109 (0102 0707070809-0301, 070803 020907090003 ﾁ070306 ﾁ030908030603 ﾁ 0703 ﾁ040902090308 07 02090709000301 090303060207020908). 0009090701 03000609030301, 01020300030708 ﾁ03 ﾁ070306 ﾁ030908030603 ﾁ 0209 040003070903070807 07 0803070907 030603020705 050303010308060707 050803 08030003 040003070903070801! ｨｮ0003020908060708 040607010306 010203050303000609030705 01030209000308 050803 0409070309 040906090000030001020206 040605010206, ﾁ 09030803060301 090900020905 040605010905 0409070909 060907070109080607 ﾁ0903080705 090909 0803070909 0203 ﾁ030503 01020300030708 ﾁ09 (010203050303000609030705 01030209000308). 0608030002 04060302070809 ﾁ070801 07030003 050803 01020300030708 ﾁ03, 06090707010308060701 0909090308-0803 0409070309 040906090000030001020206 040605010206 (7.8) 07 040603 ﾁ03020301 0406030703 ﾁ030001020908 040605010908 l, 040306030703090908060908 090900020908 040605010908 0409070909 (060707. 7.12). 0003050209 090900020905 040605010905 l 0409070909, 07010308060905 090609 ﾁ0203020703 ｨｰ0707. 7.12. ｨｪ0203050303000609030703 01030209000308 0409070909 040906090000030001-020206 040605010206 0009020308 0701030801 ﾁ0702: q 0 x 6ﾓ1 p 0 y + = 0; 03020203030209070203 030406030203000503080705 080307090308 0403060307030703020705 07 040605010308 l. ｨｲ0209070708, 07 0803070907 030603020705 050303010308060707, 0409070309 040906090000030001020206 040605010206 050803 040603070803 040605010905 l. 0700060908070803 ﾁ02070109020703, 070803 0409060901030806 040605010206 ﾁ 0409070903 0103000203 07070708090801 0903030602070209080308 0209 010203050303000609030707 01030209000308 (040605010308 l). 000304030601 030006090807010705 09 0409070909 0403060307030909080607060705 040605010206 (7.9), ﾁ02000609 ﾁ 0309 0300060908 0803070909 020907090003 090303060207020908 (060707. 7.13). 0003050209 090609 ﾁ0203020703 0409070909 qx 6ﾓ1 py = 0: (7.10) 060901 0603080300030701 0002 040302050801, 070803 04060302070809 ﾁ00050308 0703000308 01020300030708 ﾁ03, 090900020905 0803070909 0903080306030503 050803 040605010905 0409070909. 080603 ﾁ03020301 0406030703 ﾁ030001020908 040605010908 l, 0203 04060306030205060908 0703060303 020907090003 090303060207020908 (060707. 7.13). 0003050209 090900020905 040605010905 0409070909 (0906030103 0302020308, 09030803060905 0209 06070709020903 03000303020907030209 090909 l 0 ) 040306030703070308 040605010908 l 0603 ﾁ0203 ﾁ 0302020308 0803070903. 08030508030109 07 0803070907 030603020705 050303010308060707 0409070309 0403060307030909-080607060705 040605010206 050803 040605010905 04000807 030603 03020209 0803070909 x ﾞ, 07030308 ﾁ03080708 ﾁ0908060905 040605010308 l 0! ﾂ0304060307 ﾁ 080301, 090909 050809 0803070909 04030209000307 ﾁ0903080705 09 040605010308 l. 07080103080701, 070803 010203050303000609030703 01030209000308 0409070909 0403060307030909080607060705 040605010206 0203070708 020903 ﾁ09020703 04060303090807 ﾁ020308 040605010308 07 030003030209070903080705 090909 P 1. ｨｰ0707. 7.13. 0809070309 040605010206 ｨｰ0707. 7.14. 08030700030203 ﾁ09080300010203070801 040605010206 ｨｮ08060305 010203050303000609030703 01030209000308, 0406070203060007 ﾁ0908080705 07000302090806030503 0406070201070409: 00000703090703 040605010203 0409070909 (09050300 0103000209 0903080306020107 010900) 020300000202 070303000609000908010705 0209 04060303090807 ﾁ020308 040605010308 0000070309070107 08030709090107 (06090707080305020703 0103000209 0903080306020107 010900030201090303). 08030508030109, 0708030002 040302050801 0103070803 0803070907 x ﾞ 0209 04060303090807 ﾁ- 020308 040605010308, ﾁ030301010301 04030700030203 ﾁ09080300010203070801 040605010206 l 1 ; l 2 ; : : :, 0406070000070009080607060705 09 l 0 (0701. 060707. 7.14). 0003070907 0403060307030703020705 05080706 040605010206 07 l 0300060903090808 04030700030203 ﾁ09080300010203070801, 09030803060905 090603020708 ﾁ040609 ﾁ03 ﾁ 00030709030203070203070801. ｨｪ03000203 0609070701030806030801 04030700030203 ﾁ09080300010203070801 040605010206 l 6ﾓ11 ; l 6ﾓ12 ; : : : (0701. 060707. 7.14), 040607-0000070009080607060705 09 l 0 07 020609050308 07080306030202. ｨｮ030308 ﾁ03080708 ﾁ0908060905 04030700030203 ﾁ09080300010203070801 0803070309 0209 l 0009020308 09060302070801 ﾁ0003 ﾁ03 ﾁ 00030709030203070203070801. 070202090903 0406030203000301 090909 040306 ﾁ0308 04030700030203 ﾁ09080300010203070807 0803070309, 080909 07 ﾁ0803060308 020300000209 07000900070801 0803070909 x ﾞ. ｨｲ0209070708, 0708030002 040302090003070801 0803070909 x ﾞ 09 040605010308 l, 0209000203 030803-0002030708 ﾁ070801 0003 ﾁ0908 07 040609 ﾁ0908 縺000307090302030702030708071 7 040605010308 l (060707. 7.15). ﾂ 06030309000108090803 040300090707080705 070803-0803, 020904030107020908060303 03090609000203070801 縺00030709030203070203 0003000104030503 060902070907091 7.

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 47 ｨｰ0707. 7.15. 08060303090807 ﾁ020905 040605010905 07000709020701 09030306020702090802 0209 04060303090807 ﾁ020308 040605010308. 0609040301020701, 070803 04060303090807 ﾁ020905 040605010905 050803 010203050303000609030703 01030209000308 040605010206, 04060306030205060706 0703060303 03020209 0803070909. 010609 ﾁ0203020703 0409070909 050803 090609 ﾁ0203020703 (7.10), ﾁ 09030803060301 090900020905 040605010905 0309 ﾁ07070708 0308 02 ﾁ0906 040906090103080603 ﾁ p 07 q. 0609 040306 ﾁ0208 ﾁ0305000502 050809 04090609 0707070300 (p; q) 07 0103000203 00020003 0002 ﾁ03050801 0309 09030306020702090802. 0603 0406030000030109 ﾁ 080301, 070803 (p; q), (2p; 2q), (6ﾓ12p; 6ﾓ12q),... ﾁ 0203080708 ﾁ07080300010203070807 0304070702 ﾁ090808 03020209 07 0809 0003 040605010908. 08030508030109 09030306020702090802 0209 04060303090807 ﾁ020308 040605010308 050803 04090609 0707070300 07 080307020307080108 0203 040603040306010703020900010203070807, 070803 030904070702 ﾁ0903080705 090909 (p : q). 08060701030602 06030403020705 08070403 ﾁ0206 0309020907 080607010306 7.1. ﾂ02040707090801 090609 ﾁ0203020703 040605010308 l, 04060306030205060308 0703060303 0803070909 A(2; 3) 0409060900000300010203 ﾁ0309-08030609 6ﾓ1 a (6ﾓ11; 4). ｨｰ030403020703. 0608030002 060304070801 0403070809 ﾁ000302020908 030902090709, 02030708090803070203 ﾁ0704030102070801 090902030207070307090303 090609 ﾁ0203020703 040605010308 (7.1), 03040603020300070801 0302090703020705 040906090103080603 ﾁ x 0, y 0, p 07 q 0703 09070003 ﾁ0705 030902090707 07 040302070809 ﾁ070801 0706 ﾁ 090902030207070307090303 090609 ﾁ0203020703. 080906090103080602 x 0, y 0 050803 09030306020702090802 0309020902020308 0803070907, 0703060303 09030803060908 0406030603020708 040605010905. ﾂ 0209040308 0707080909010707 x 0 = 2, y 0 = 3. 050305040407010703020802 p 07 q 09030306020702090802 0209-040609 ﾁ00050806030503 ﾁ030908030609; 09 020907 p = 6ﾓ11, q = 4. 080302070809 ﾁ000505 020908020302020203 0302090703020705 ﾁ 090609 ﾁ0203020703 (7.1), 0403000907090301 0308 ﾁ0308: x 6ﾓ1 2 l: 6ﾓ11 = y 6ﾓ1 3 4 : ﾂ0703 00020003 0002 030901030709080300010203, 03070007 0002 0203 03020203 縺02031 7! 010005 06030403020705 030902090707 090909030902020201 01030803020301 02030300060302070103 04030102070801 090909 090902030207070307090303 090609 ﾁ0203020703, 080909 07 0701020700 ﾁ070306 ﾁ06030205060706 ﾁ 02030503 040906090103-080603 ﾁ. 020708030708 ﾁ03020203, 030904030102070801 080300010903 050803 0203 080909 0900 07 070003000203. 0603 080300010903 ﾁ 0209040301 0909060703 080909030503 0703060809 040306010900 0305060301020303 0707070003, 09 040901050801 020308060302070603 ﾁ090202030503 07030003 ﾁ030909 ﾁ0307010109 0305060902070703020209. 0803-0508030109 0102 0703 ﾁ0308090301 03090403010702090801 01070207010901 縺04030601090001020308 070204030601090107071 7, 090203000505 030703000303 ﾁ02070109020703 03070203 ﾁ020201 0702030501 0609070709000203020708 07 0503030103080607070307090701 03000609030901, 070007 090906080702090901. 000909 07 ﾁ 05080308 0707080909-010707 040609 ﾁ070001020303 ﾁ02 ﾁ03070807 090902030207070307090303 090609 ﾁ0203020703 020005 0903020906030802030503 070009070905, 07040306010900070603 ﾁ090202030503 ﾁ 09070003 ﾁ0707 02030403070603020708 ﾁ03020203. 060907020301 07 06070709020909 (060707. 7.16), 0209 09030803060301 070303000609030701 07070903010908 040605010908, 0803070909 A(2; 3), ﾁ0309080306 6ﾓ1 a (6ﾓ11; 4) 07 0803070907 M(x; y): 0209 040605010308 l 07 ﾁ0203 0303. 0700060908070803 ﾁ02070109020703, 070803 06070709020309 07060301090807070302. ｨｮ03 ﾁ0306040302-0203 0203 0300050309080300010203 07030300060900090801 07070708030109 090303060207020908 07 0308010307090801 ﾁ 020308 040300030003020703 0803070309 090007030008080203 0803070203. 01030708090803070203, 0708030002 06070709020309 0209050005020203 04060302070809 ﾁ000500 0707060302020203 020902020203 07 090302010302080607-0603 ﾁ0900 ﾁ02070109020703. ｨｦ03 06070709020909 090007030008080203 05070203, 070803 M ﾊ l 0803050209 07 080300010903 0803050209, 0903050209 ﾁ030908030602 6ﾓ1 a 07 6ﾓ16ﾓ1 AM 0409060900000300010202, 09 09070003 ﾁ0703 0409060900-000300010203070807 0300030704030707 ﾁ0903080705 04060304030601070302090001020307080108 090303060207020908 05080706 ﾁ030908030603 ﾁ, 040307090300010909 03020702 0703 02060905030503 0103000203 0403000907070801 ｨｰ0707. 7.16. ｨｰ070709020309 09 04060701030609 7.1 09010203000302070301 0209 0707070003 (0903050404070107030208 040603040306010703020900010203070807). 0707080903080705 00070401 ﾁ02040707090801 0903030602070209-0802 ﾁ030908030609 6ﾓ16ﾓ1 AM(x 6ﾓ1 2; y 6ﾓ1 3) 07 09070003 ﾁ0703 0706 040603040306010703020900010203070807 0903030602070209080901 ﾁ030908030609 6ﾓ1 a (6ﾓ11; 4): l: x 6ﾓ1 2 6ﾓ11 = y 6ﾓ1 3 4 :

1348 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 0803000907070801 0703 09090203020707030709030503 090609 ﾁ0203020705 0300060303 030902090709 050003010302080906020308 09060704010308070907 07 0102 0203 0009020301 05080701 03090207010908010705, 02090203050701 0209 0803, 070803 090900020208 0707080908030001 070103000308 050803 07020300090801 0709010307080305080300010203! 080607010306 7.2. ﾂ02040707090801 090609 ﾁ0203020703 040605010308 l, 04060306030205060308 0703060303 0803070907 A(2; 3) 07 B(2; 7). ｨｰ030403020703. ｨｪ03000203 ﾁ0307040300010303 ﾁ0908010705 ﾁ02 ﾁ03020302020201 090609 ﾁ020302070301 (7.3), 0203 0009070403 040306090707090002090801 07 ﾁ02 ﾁ03070807 030503 ﾁ 09030209060308020301 070009070903. 060907020301 07 06070709020909 (060707. 7.17). 0003070907 A(2; 3) 07 B(2; 7), 04060702090200030009060703 040605010308 0403 09070003 ﾁ0708 030902090707, 030902090808 ﾁ0309080306 AB(0; 6ﾓ1 4). ﾂ030301010301 0406030703 ﾁ030001020908 0803070909 M(x; y) 0209 040003070903070807 07 0403070806030701 ﾁ0309080306 6ﾓ16ﾓ1 AM(x 6ﾓ1 2; y 6ﾓ1 3). 09070203, 070803 0803070909 M 0009020308 000300090801 0209 040605010308 l 0803050209 07 080300010903 0803050209, 0903050209 ﾁ0309080306 6ﾓ16ﾓ1 AM 0009020308 04090609000003000302 ﾁ030908030609 AB, 6ﾓ1 08. 03. 0706 0903-0306020702090802 0009020908 040603040306010703020900010202. ﾂ0204070702 ﾁ0905 07030308 ﾁ03080708 ﾁ0908060908 040603040306010708, 04030009070701 0308 ﾁ0308: ｨｰ0707. 7.17. ｨｰ070709020309 09 04060701030609 7.2 x 6ﾓ1 2 l: = y 6ﾓ1 3 0 4 : 050909 07080609020203! 05090003080705, 06090707090002090007 ﾁ03060203, 0906070401030807070307090706 030407000309 08030003 0203 020304090708070007, 09 ﾁ 0302090103020908030003 0003 ﾁ0308 0709070807 090609 ﾁ0203020705 0708030708 02090001. ｨ縺0209 02090001 020300070801 020300010305!1 7 070708070209, 0907 ﾁ030302020905 030603 ﾁ 0409030003. 060803 050803? 0806030807 ﾁ030603070703 ﾁ 01090803010908070903 070007 0102 ﾁ0703 0003 050203-0803 0304070000070701? 0609 0709010301 02030003 0207090909030503 0406030807 ﾁ030603070705 020308 07 030407000909 0203 ﾁ09060900090701 ﾁ 02090407 ﾁ020707070003020705. 01030003 ﾁ 080301, 070803 040603040306010708, 09030803060908 0102 0309040707090007, 0203 ﾁ0703050209 0103000203 060907070109080607 ﾁ090801 090909 0609 ﾁ03020708 ﾁ03 020603-000308! ﾂ 020902020308 0707080909010707 0303 0209000203 ﾁ0307040607020701090801 070103020203 090909 縺0609 ﾁ020303 030802030403020703 07070703001 7. ｨ 0708030002 02090001 ﾁ 0302090103020908030003 縺0203 0603030900 050009031 7, ﾁ030704030001030903010705 07 ﾁ03080708 ﾁ090107 040603040306010708: x 6ﾓ1 2 = y 6ﾓ1 3 0406030703 ﾁ030203020703 07060302020706 0700030203 ﾁ 6ﾍ2 0 4 0609 ﾁ0203 0406030703 ﾁ030203020708 09060908020706 6ﾍ2 4 (x 6ﾓ1 2) = 0 (y 6ﾓ1 3) 6ﾍ2 x 6ﾓ1 2 = 0: 0009090701 03000609030301, 090609 ﾁ0203020703 07070903010308 040605010308 050803 x = 2. 080607010306 7.3. 0609040707090801 090609 ﾁ0203020703 040605010308 l, 04060306030205060308 0703060303 0803070909 M 0 (6ﾓ11; 0) 04030604030202070909000506-0203 ﾁ030908030609 6ﾓ1 n (5; 2). ｨｰ030403020703. 060907020301 07 06070709020909 (060707. 7.18), 0209 09030803060301 03080103080701 ﾁ0703 0703 ﾁ030708020203 020902020203 07 0803070909 M(x; y) 07 0406030703 ﾁ03000102020107 090303060207020908090107. 070703 ﾁ07020203, 070803 0803070909 M 0009020308 000300090801 0209 07070903010308 040605-010308 0803050209 07 080300010903 0803050209, 0903050209 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M(x + 1; y) 0009020308 040306040302020709090005060302 ﾁ030908030609 6ﾓ1 n. 01070003 ﾁ0703 040306040302020709090005060203070807 ﾁ030908030603 ﾁ 0103000203 0309040707090801 07 04030103060108 07090900050602030503 0406030703 ﾁ030203020705: ｨｰ0707. 7.18. ｨｰ070709020309 09 04060701030609 7.3 ｨｲ0209070708, 080603000903010303 090609 ﾁ0203020703 0701030308 ﾁ0702: 6ﾓ16ﾓ16ﾓ1 M 0 M ﾍ 6ﾓ1 n 6ﾍ2 ( 6ﾓ16ﾓ16ﾓ1 M 0 M; 6ﾓ1 n ) = 0: ｨｮ0909000506020303 0406030703 ﾁ030203020703 6ﾓ1 n (5; 2) 07 6ﾓ16ﾓ16ﾓ1 M 0 M(x+1; y) ﾁ02070707000503080705 0703060303 09030306020702090802 070003020908060701 03000609030301: 5(x + 1) + 2y = 0: ( 6ﾓ16ﾓ16ﾓ1 M 0 M; 6ﾓ1 n ) = 5(x + 1) + 2y: 080607010306 7.4. 0609080807 06090707080305020703 0308 020907090009 090303060207020908 0203 040605010308 l: 2x 6ﾓ1 y + 4 = 0. ｨｰ030403020703. 060901 0209000203 040607 ﾁ03070807 090609 ﾁ0203020703 040605010308 09 0203060109000102030109 ﾁ070209 07 ﾁ0307040300010303 ﾁ0908010705 0803030603-010308 43.2. ｨｦ03 090609 ﾁ0203020705 040605010308 02090603020701 09030306020702090802 02030601090007 6ﾓ1 N (2; 6ﾓ11). 0203 0200070209 6ﾓ1 N = ﾌ 4 + 1 = ﾌ 5.

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 49 02070007 080304030601 ﾁ0309080306 6ﾓ1 N 0403020300070801 0209 030503 0200070209, 04030009070701 030207020707020208 ﾁ0309080306 6ﾓ1 n ( 2 ﾌ5 ; 6ﾓ11 ﾌ 5 ), 07030209040609- ﾁ000302020208 07 6ﾓ1 N. 02070007 080304030601 060903020300070801 ﾁ0703 0707060302020303 090609 ﾁ0203020703 040605010308 l 0209 ﾌ 5, 04030009070701 090609 ﾁ0203020703 2 ﾌ 5 x 6ﾓ1 1 ﾌ 5 y + 4 ﾌ 5 = 0; 0304070702 ﾁ0908060303 0809 0003 040605010908, 09030803060303 0701030308 0403070807 02030601090001020208 ﾁ0702, 080909 090909 ( ) 2 2 ( ) 6ﾓ11 2 ﾌ5 + ﾌ = 1: 5 070203 03080007070903080705 0308 0203060109000102030503 090609 ﾁ0203020705 00070401 030209090301 07 ﾁ0300030202030503 0700030209, 080909 090909 ﾁ 02030601090001020301 090609 ﾁ0203020707 07 ﾁ03000302020208 07000302 6ﾓ1, 050203 1 7 0, 09 09 020907 + ﾌ 4 5. 010102030007 ﾁﾁ0703 090609 ﾁ0203020703 0209 (6ﾓ11), 04030009070701 02030601090001020303 090609 ﾁ0203020703: 0803 08030306030103 43.2 07070903010303 06090707080305020703 0609 ﾁ0203 4 ﾌ 5. 6ﾓ1 2 ﾌ 5 x + 1 ﾌ 5 y 6ﾓ1 4 ﾌ 5 = 0 080607010306 7.5. 0609080807 06090707080305020703 0308 0803070907 A(1; 2) 0203 040605010308 l: 2x 6ﾓ1 y + 4 = 0. ｨｰ030403020703. 0803 070003020708 ﾁ0708 43.3 020901 0209000203 040607 ﾁ03070807 090609 ﾁ0203020703 040605010308 09 0203060109000102030109 ﾁ070209, 040302-070809 ﾁ070801 ﾁ 02030503 09030306020702090802 0803070907 A 07 ﾁ03050801 010302090001 0403000907030202030503 0707070009. 05 0203060109000102030109 ﾁ070209 090609 ﾁ0203020703 05080308 040605010308 00020003 090003 040607 ﾁ0302030203 ﾁ 04060302020209060301 04060701030603: 6ﾓ1 ﾌ 2 5 x + ﾌ 1 5 y 6ﾓ1 ﾌ 4 5 = 0. 080302070809 ﾁ0701 ﾁ 02030503 09030306020702090802 0803070907 A 07 04030009070701 0308 ﾁ0308: ｨO (A; l) = ｨO 6ﾓ1 ﾌ 2 1 + ﾌ 1 2 6ﾓ1 4 ｨO ｨOｨOｨO ﾌ = ﾌ 4 : 5 5 5 5 080607010306 7.6. ﾂ0207070700070801 06090707080305020703 0103000209 04090609000003000102020107 04060501020107: l 1 : 2x 6ﾓ1 3y + 4 = 0; l 2 : 2x 6ﾓ1 3y + 2 = 0: ｨｰ030403020703. ﾂ 04060701030603 7.4 0102 ﾁ0207070700050007 06090707080305020703 0308 020907090009 090303060207020908 0203 040605010308. ｨ 02090003050707-020303 ﾁ020707070003020703 0103000203 0406030703 ﾁ03070807 07 ﾁ 05080301 04060701030603 (060707. 7.19). O = ｧﾑ) ｧﾒ) ｨｰ0707. 7.19. ﾂ020707070003020703 06090707080305020705 0103000209 04090609000003000102020107 04060501020107 060901 0209000203 ﾁ0207070700070801 06090707080305020703 0308 020907090009 090303060207020908 0203 090900020308 0703 040605010206, 09 0309080301 070003-00070801 070007 ﾁ03050801 010302090001 0609030203070807 04030009070302020206 0302090703020708 ﾁ 0309 ﾁ0707070103070807 0308 040300030003020705 020907090009 090303060207020908 030802030707080300010203 040605010206 (0701. 060707. 7.19). 08030909 03080003000701 ﾁ0205070203020703 ﾁ030406030709 03 040300030003020707 020907090009 090303060207020908 07 ﾁ02070707000701 06090707080305020703 0308 0803070907 O(0; 0) 0203 0300030706 040605010206, 040300010309050701 09000503060708010301 04060701030609 7.4.

1350 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁｨｮ020907090009 040607 ﾁ03020301 090609 ﾁ0203020705 040605010206 09 0203060109000102030109 ﾁ070209, 06090302030007 ﾁ 0706 0209 0203060107060908060708 010203000708030001 (6ﾓ1 ﾌ 13): l 1 : 6ﾓ1 2x ﾌ 13 + 3y ﾌ 13 6ﾓ1 4 ﾌ 13 = 0; l 2 : 6ﾓ1 2x ﾌ 13 + 3y ﾌ 13 6ﾓ1 2 ﾌ 13 = 0: 070807080209 (O; l 1 ) = ﾌ 4 13, (O; l 2 ) = ﾌ 2 13. 000304030601, 070706030205 0703 02030601090001020206 090609 ﾁ0203020708 040605010206, 0102 020300000202 03040603020300070801: 070900090202 ﾁ090801 050807 06090707080305020705 070007 ﾁ02070708090801. 06090403010208, 070803 0403 08030306030103 43.2 02030601090001 09 040605010308, 09030306020702090802 0903-0803060308 0708030508 090909 090305040407010703020802 ﾁ 02030601090001020301 090609 ﾁ0203020707, 0209040609 ﾁ00030209 0308 020907090009 090303060207020908 09 040605010308! ﾂ 0209040308 0707080909010707 6ﾓ1 n 1 = 6ﾓ1 n 2 (6ﾓ1 ﾌ 2 13 ; ﾌ3 13 ). 08030508030109 020907090003 090303060207020908 0003000708, 090909 0403090903090203 0209 060707. 7.19, 09. ｨｮ00030203 ﾁ09080300010203, 06090707080305020703 0103000209 04060501020107 04030009070903080705 090909 0609030203070801 (l 1 ; l 2 ) = (O; l 1 ) 6ﾓ1 (O; l 2 ) = 4 ﾌ 13 6ﾓ1 2 ﾌ 13 = 2 ﾌ 13 : 080607010306 7.7. ﾂ0207070700070801 09050300 0103000209 04060501020107 l 1 : x + 3y 6ﾓ1 4 = 0; l 2 : 2x 6ﾓ1 y + 7 = 0: ｨｰ030403020703. 0803060307030909080607030705 040605010203 0300060903090808 070308020603 0403040906-0203 0609 ﾁ020206 09050009 (060707. 7.20). 0609040301020701, 070803 0905000301 0103000209 04060501020107 02090302 ﾁ0903080705 080308 09050300 ', ﾁ03000707070209 0903080306030503 0203 040603- ﾁ03070603020708 =2. 0803 090609 ﾁ020302070501 040605010206 0103000203 03040603020300070801 09030306020702090802 0203060109000308 ( ﾁ 0209040301 070009070903 6ﾓ1 n 1 (1; 3) 07 6ﾓ1 n 2 (2; 6ﾓ11)). ｨｪ03000308 030909030908010705, 070803 09050300 0103000209 020306010900050107 030708060208 070007 040605010308. 0003050209, 09030203070203, 09050300 0103000209 04060501020107 0703 ﾁ040902090308 07 0905000301 0103000209 020306010900050107. 070202090903 09050300 0103000209 020306010900050107 0103000308 00020801 0809040201. 0003050209 ' + = 07 cos = 6ﾓ1 cos ' < 0. 0603 ﾁ 0008000301 070009070903, 09030707020907 09050009 0103000209 04060501020107 0609 ﾁ0302 09000703-000808020308 ﾁ03000707070203 0903070702090709 09050009 0103000209 020306010900050107. ﾂ02070707000701 09030707020907 09050009 0103000209 ﾁ0309080306090107 6ﾓ1 n 1 07 6ﾓ1 n 2. ｨｹ0803 0103000203 07020300090801 0703060303 070909000506020303 0406030703 ﾁ030203020703: cos = (6ﾓ1 n 1 ; 6ﾓ1 n 2 ) ｨｰ0707. 7.20. 05 04060701030609 7.7 6ﾓ1 n 1 6ﾓ1 n 2 : ｨｮ0909000506020303 0406030703 ﾁ030203020703 ﾁ030908030603 ﾁ, 090909 07 0706 0200070209, 0103000203 ﾁ02-07070700050801 0703060303 09030306020702090802 030802030707080300010203 0306080302030601070603 ﾁ090202030503 000903070709: ( 6ﾓ1 n 1 ; 6ﾓ1 n 2 ) = 1 2 + 3 (6ﾓ11) = 2 6ﾓ1 3 = 6ﾓ11; 6ﾓ1 n 1 = ﾌ 1 2 + 3 2 = ﾌ 10; 6ﾓ1 n 2 = ﾌ 2 2 + (6ﾓ11) 2 = ﾌ 5: ｨｦ080909, cos = 5 6ﾓ11 ﾌ. 000909 090909 cos 0308060701090803000302, 0803 09050300 0809040308. 0003050209 07070903010208 030708060208 09050300 2 ' = 6ﾓ1 07 cos ' = cos( ) = 5 ﾌ1 2. ｨｮ00030203 ﾁ09080300010203, ' = arccos 1 5 ﾌ 2. 080607010306 7.8. 0609080807 090609 ﾁ0203020703 0007070703090806070702 09050009, 030006090303 ﾁ090202030503 04060501020107 l 1 : x + 3y 6ﾓ1 4 = 0; l 2 : 2x 6ﾓ1 y + 7 = 0: ｨｰ030403020703. ｨｲ02030701 02090203 ﾁ0307040300010303 ﾁ0908010705 0302020701 0703 030406030203000508060706 07 ﾁ03080708 ﾁ 0007070703090806070702, 09 070103020203: 0007070703090806070709 07030708030708 0703 0803070309, 0609 ﾁ0203090209000302020206 0308 070803060302 09050009. ｨｦ02020107 070003 ﾁ090107, 020005 0008000308 0803070907 M(x; y) 0209 0007070703090806070703 ﾁ0204030002030203 0609 ﾁ03020708 ﾁ03: (M; l 1 ) = (M; l 2 ).

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 51 ｨｰ090707080305020703 0308 0803070907 0203 040605010308 0102 090003 ﾁ0207070700050007 ﾁ 04060701030603 7.6. 010005 0508030503 0209000203 04030603080807 09 0203060109000102030109 090609 ﾁ0203020708: l 1 : x ﾌ + ﾌ 3y 6ﾓ1 ﾌ 4 = 0; l 2 : 6ﾓ1 ﾌ 2x + ﾌ y 6ﾓ1 ﾌ 7 = 0: 10 10 10 5 5 5 000304030601 (M; l 1 ) = ｨO x ﾌ + ﾌ 3y 6ﾓ1 4 ｨO ｨOｨOｨO ﾌ ; (M; l 2 ) = 10 10 10 ｨO 6ﾓ1 2x ﾌ 5 + y ﾌ 5 6ﾓ1 7 ﾌ 5 ｨO ｨOｨOｨO : 0806070609 ﾁ02050301 050807 06090707080305020705: ｨO x ﾌ + ﾌ 3y 6ﾓ1 4 ｨO ｨOｨOｨO ﾌ = 10 10 10 ｨO 6ﾓ1 2x ﾌ 5 + y ﾌ 5 6ﾓ1 7 ﾌ 5 ｨO ｨOｨOｨO : 0803 07 ﾁ03080708 ﾁ09 0007070703090806070702 0803070909 M(x; y) 0003000708 0209 07070903010308 0007070703090806070703 0803050209 07 080300010903 0803050209, 0903050209 0303 09030306020702090802 090203 ﾁ000308 ﾁ0306050808 04030700030202030109 0703030802030403020708. 070202090903 050803 0609 ﾁ03020708 ﾁ03 0203 03080203-0707080705 0207 09 030202030109 0703 0703 ﾁ030708020206 020901 08070403 ﾁ 090609 ﾁ0203020708 040605010206, 040307090300010909 0703020306000708 010302090007. ｨｦ030009 ﾁ07010705 0308 020706, 0403010205. 070803 a = b 0803050209 07 080300010903 0803050209, 0903050209 a = ﾀb: x ﾌ + ﾌ 3y 6ﾓ1 ﾌ 4 = 6ﾓ1 ﾌ 2x + ﾌ y 6ﾓ1 ﾌ 7 ; 10 10 10 5 5 5 x ﾌ + ﾌ 3y 6ﾓ1 ﾌ 4 = ﾌ 2x 6ﾓ1 ﾌ y + ﾌ 7 : 10 10 10 5 5 5 08030009070700030701 02 ﾁ09 090609 ﾁ0203020705, 070803 09090003080705 0708060902020201. ﾂ030201 020901 0209000203 00020003 080300010903 090609 ﾁ0203020703 000707-0703090806070702. 0609 0709010301 02030003 ﾁ0703 040609 ﾁ0700010203. 01030003 ﾁ 080301, 070803 040605010203 0209 040003070903070807 0300060903090808 0203 03020207 09050300, 09 070308020603. 08030508030109 ﾁ0303020709090308 070308020603 0007070703090806070702, 040607070301 0007070703090806070702 ﾁ0306080709090001020206 09050003 ﾁ 0703 ﾁ040902090808. ｨｮ00030203 ﾁ09080300010203, ﾁ 0308 ﾁ030803 020300000203 00020801 02 ﾁ09 090609 ﾁ0203020705 00070707030908060707 b 1 07 b 2. 05030203070203, 04030009070302020203 090609 ﾁ0203020705 02030400030603 00020003 0002 090406030708070801: b 1 : (1 + 2 ﾌ 2)x + (3 6ﾓ1 ﾌ 2)y 6ﾓ1 4 + 7 ﾌ 2 = 0; b 2 : (1 6ﾓ1 2 ﾌ 2)x + (3 + ﾌ 2)y 6ﾓ1 4 6ﾓ1 7 ﾌ 2 = 0: 0503020806030001020203 ﾁ030406030702 7.1. ｨｮ040306010900070609080803 03070203 ﾁ020308 040302060302 09 040300090703020708 090609 ﾁ0203020708 040605010206. 7.2. ｨｲ09040704070803 0300060303 090609 ﾁ0203020703 040605010308 0209 040003070903070807. 05090903 ﾁ 0701020700 090305040407010703020803 ﾁ, 07080305060706 0403060302 0403060301030202020107 x 07 y? 7.3. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040605010308 0403 0803070903, 04060702090200030009060308 040605010308, 07 0209040609 ﾁ00050806030109 ﾁ030908030609. 7.4. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040605010308 0403 0803070903, 04060702090200030009060308 040605010308, 07 ﾁ030908030609 02030601090007. 7.5. ｨｲ09040704070803 090609 ﾁ0203020703 040605010308 07 09050003 ﾁ0201 09030504040701070302080301. 060803 0303020907090808 040906090103080602 k 07 b? 7.6. ｨｲ09040704070803 090609 ﾁ0203020703 040605010308 ﾁ 0308060303090906 0209 03070506. 0509090703 040605010203 0203 0304070702 ﾁ0908080705 05080701 090609 ﾁ- 020302070301? 7.7. ｨｲ09040704070803 090609 ﾁ0203020703 0409070909 040605010206, 04060306030205060706 0703060303 0803070909 M 0 (x 0 ; y 0 ). 0509090905 040605010905, 04060306030205060905 0703060303 0803070909 M 0, 0203 0304070702 ﾁ0903080705 05080701 090609 ﾁ020302070301? 7.8. 07040704070803 0703 ﾁ030708020203 ﾁ0901 07040307030002 0304060302030003020705 09050009 0103000209 04060501020107. 7.9. ｨｮ040306010900070609080803 09070003 ﾁ0705 0409060900000300010203070807 07 040306040302020709090005060203070807 040605010206. ｨｲ0902090707 7.1 71. ｨｬ03000908 0007 0803070907 M 1 (2; 6ﾓ13), M 2 (6ﾓ12; 6ﾓ13), M 3 (2; 3) 0209 040605010308 x 6ﾓ1 3y + 7 = 0?

1352 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 7.2 71. ｨｲ09040704070803 090609 ﾁ0203020705 040605010206, 04060306030205060706 0703060303 020907090003 090303060207020908 07 0703070809 ﾁ000508060706 07 0403-0003000708030001020201 0209040609 ﾁ000302070301 030707 Ox 09050300: 09) 45 o ; 00) 90 o ; ﾁ) 120 o ; 05) 135 o : 080307080603080803 050807 040605010203. 7.3 71. 080605010905 0406030603020708 0703060303 0803070909 A(2; 0) 040302 0905000301 45 o 09 0403000300070803000102030109 0209040609 ﾁ0003020708 030707 Ox. 0609040704070803 090609 ﾁ0203020703 05080308 040605010308. 7.4 71. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040605010308, 04060306030205060308 0703060303 0803070907 A(2; 4) 07 B(6ﾓ11; 3). 0509090703 03080603030907 0209 090303060207020908020206 03070506 0308070309090308 050809 040605010905? 7.5 71. 080307080603080803 040605010203 x + 2y 6ﾓ1 6 = 0; y = 6ﾓ12x + 1; x 3 + y 4 = 1; 2x + 5 = 0, y + 3 = 0. 01090900070803 0706 09050003 ﾁ0203 090305040407010703020802. 7.6 71. 0006030905030001020709 0309020902 090303060207020908090107 07 ﾁ030706 ﾁ0306040702 A(8; 6ﾓ12), B(2; 5), C(0; 0). ｨｮ03070809 ﾁ010803 090609 ﾁ- 0203020705 030503 070803060302 07 09090900070803 09050002 02090900030209 05080706 070803060302 09 0403000300070803000102030109 0209040609 ﾁ0003020708 030707 Ox. 7.7 71. 080605010905 0406030603020708 0703060303 0803070909 M(1; 3) 0409060900000300010203 040605010308 3x 6ﾓ1 4y + 1 = 0. ｨｲ09040704070803 090609 ﾁ0203020703 05080308 040605010308. 0509090703 03080603030907 0209 090303060207020908020206 03070506 030209 0308070309090308? 7.8 71. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040605010308, 04060306030205060308 0703060303 0803070909 P(6ﾓ12; 1) 040306040302020709090005060203 040605010308 2x + 3y + 5 = 0. 7.9 71. 06090802070803 09030306020702090802 0803070907 0403060307030703020705 040605010206 2x 6ﾓ1 3y 6ﾓ1 1 = 0 07 4x 6ﾓ1 y + 3 = 0. 7.10 71. ｨｮ080306030202 080603090503000102070909 0003000908 0209 040605010206, 0309020902020206 090609 ﾁ02030207050107 3x 6ﾓ1y 6ﾓ12 = 0; y = x 6ﾓ12, x 6ﾓ1 2 = 0. 06090802070803 09030306020702090802 ﾁ0306040702 080603090503000102070909. 7.11 71. 080605010905 0406030603020708 0703060303 0803070907 A(2; 0) 07 B(0; 4). 0603060303 0803070909 C(1; 1) 040603 ﾁ0302030209 040605010905, 04030604030202070909000506020905 040306 ﾁ0308 040605010308. 0609040704070803 090609 ﾁ0203020705 0300030706 040605010206. 7.12 71. 080605010905 0406030603020708 0703060303 0803070907 A(1; 6ﾓ11) 07 B(3; 1). 0603060303 0803070909 C(3; 2) 040603 ﾁ0302030209 040605010905, 040906090000030001020905 040306 ﾁ0308 040605010308. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020705 0300030706 040605010206. 7.13 71. 080605010905 0308070309090308 0209 090303060207020908020206 03070506 Ox 07 Oy 03080603030907 a = 2 07 b = 5 07030308 ﾁ03080708 ﾁ03020203. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 05080308 040605010308 07 02090802070803 0303 09050003 ﾁ0308 0903050404070107030208. 7.14. 0609040704070803 090609 ﾁ0203020703 0703060302070202030503 0403060403020207090900050609 09 03080603030909, 09030201090107 0903080306030503 070009000908 0803070907 A(6ﾓ13; 3), B(5; 5). 7.15. ﾂ02040704070803 040906090103080607070307090703 090609 ﾁ0203020705 040605010308 0209 040003070903070807, 04060306030205060308 0703060303 0803070909 A(1; 6ﾓ11) ﾁ 0209040609 ﾁ0003020707 ﾁ030908030609 6ﾓ1 a (2; 7). 7.16. ｨｦ03 ﾁ0307080203, 070803 0803070907 O(0; 0) 07 A(4; 0) 05 ﾁ000508080705 ﾁ0306040702090107 040906090000030003050609010109, 09 030503 0207090503-02090007 040306030703090908080705 ﾁ 0803070903 B(0; 2). ｨｮ03070809 ﾁ010803 090609 ﾁ0203020705 070803060302 07 02070905030209000308 040906090000030003-050609010109. 7.17. 06090802070803 0406030309010708 0803070907 M(6ﾓ16; 12) 0209 040605010908 4x + 7y + 5 = 0. 7.18. 06090802070803 0406030309010708 0803070907 P(6ﾓ13; 6) 0209 040605010908, 04060306030205060908 0703060303 0803070907 A(7; 6ﾓ19) 07 B(0; 6ﾓ15).

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 53 7.19. 0609040704070803 090609 ﾁ0203020703 040605010308, 04060306030205060308 0703060303 0803070909 A(4; 3) 07 03080703090908060308 0308 090303060207-020908020206 03070308 0806030905030001020709 0400030609020108 S = 3. 7.20. 010709050302090007 09 ﾁ090206090809 040306030703090908080705 ﾁ 0803070903 M(1; 6), 09 03020209 0703 030503 070803060302 0003000708 0209 040605010308 x + 2y = 23. 0609040704070803 090609 ﾁ0203020705 08060306 020609050706 070803060302 0508030503 09 ﾁ090206090809. 7.21. 0006030905030001020709 0309020902 090303060207020908090107 07 ﾁ030706 ﾁ0306040702 A(6ﾓ13; 4); B(5; 2), C(8; 2). 0609040704070803 090609 ﾁ- 0203020705 01030207090202, ﾁ0207030802 07 0007070703090806070702, 040603 ﾁ03020302020206 0703 ﾁ030604070202 B 09 07080306030203 AC. 7.22. 06090802070803 09030306020702090802 0803070907 0403060307030703020705 010302070902 ﾁ 080603090503000102070903 ABC, 03070007 A(3; 0), B(1; 6ﾓ13), C(1; 3). 7.23. 06090802070803 09050300 0103000209 04060501020107, 03070007: 09) l 1 : 3x 6ﾓ1 y + 11 = 0; l 2 : x + 3y 6ﾓ1 7 = 0. 00) l 1 : 3x + 2y 6ﾓ1 1 = 0; l 2 : A(1; 4); B(6ﾓ15; 6ﾓ111). ﾁ) l 1 : A(0; 1); B(6; 6ﾓ13); l 2 : M(3; 8); N(6ﾓ11; 2). 7.24. 06090802070803 ﾁ020908060302020703 09050002 ﾁ 080603090503000102070903 ABC, 0309020902020301 090303060207020908090107 ﾁ0306040702 A(1; 6ﾓ13), B(0; 0), C(3; 9). 7.25. 07040603020300070803 06090707080305020703 0308 0803070907 A(2; 6ﾓ15) 0203 040605010308 3x 6ﾓ1 y 6ﾓ1 5 = 0. 7.26. 06090802070803 06090707080305020703 0308 0803070907 M(6ﾓ18; 12) 0203 040605010308 (AB); 03070007 A(2; 6ﾓ13); B(6ﾓ15; 1). 7.27. ﾂ0207070700070803 06090707080305020703 0103000209 04060501020107 x 6ﾓ1 2y = 3 07 2x 6ﾓ1 4y = 7, 040603000203 020309090309 ﾁ, 070803 030207 0409060900000300010202. 7.28. ﾂ02040704070803 090609 ﾁ0203020705 040605010206, 04060306030205060706 0209 06090707080305020707 4 030207020701 0409060900000300010203 040605010201: 09) 3x 6ﾓ1 4y + 5 = 0; 00) y = 3 x + 2; ﾁ) x = 3; 05) y = 6ﾓ11: 4 7.29. 06090802070803 090609 ﾁ0203020705 040605010206, 04060306030205060706 0703060303 0803070909 A(2; 0) 0209 06090707080305020707 3 030207020701 0308 0803070907 B(6; 0). 7.30. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040605010308, 040906090000030001020308 02 ﾁ0901 020902020201 040605010201 l 1 07 l 2 07 0209060302050603080705 0209 03020702090903 ﾁ0301 0308 020706 06090707080305020707, 03070007 l 1 : 2x 6ﾓ1 5y + 7 = 0, l 2 : 4x 6ﾓ1 10y + 9 = 0. 7.31. ﾂ 080603090503000102070903 ABC 0703 ﾁ0307080202 ﾁ030604070209 A(5; 6ﾓ13) 07 090609 ﾁ0203020705 02 ﾁ0906 ﾁ02070308: 2x 6ﾓ1 y = 0, 3x 6ﾓ1 7y + 16 = 0. 06090802070803 090609 ﾁ0203020705 070803060302 080603090503000102070909. 7.32. ﾂ 080603090503000102070903 ABC 0703 ﾁ0307080202 ﾁ030604070209 A(2; 6), 090609 ﾁ0203020703 ﾁ0207030802 5x + 2y 6ﾓ1 27 = 0 07 01030207090202 4x + 5y 6ﾓ1 8 = 0, 040603 ﾁ03020302020206 0703 0302020308 ﾁ030604070202. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020705 070803060302 080603090503000102070909. 7.33. ﾂ 080603090503000102070903 ABC 0703 ﾁ0307080202 ﾁ030604070209 A(1; 3) 07 090609 ﾁ0203020705 02 ﾁ0906 010302070902 x 6ﾓ12y +1 = 0, y 6ﾓ1 1 = 0. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020705 070803060302 080603090503000102070909. 7.34. 010005 0803070907 P(0; 10) 02090802070803 090609 ﾁ0203020703 0809090308 040605010308, 0708030002 0303 03080603030309, 0309090008070302020208 0103000209 04060501020107 x 6ﾓ1 3y + 10 = 0 07 2x + y 6ﾓ1 8 = 0 02030007000705 ﾁ 0803070903 P 04030403000901. 7.35. ﾂ 04060501030905030001020301 080603090503000102070903 ABC 0703 ﾁ0307080202 09030306020702090802 0903020103 ﾁ 05070403080302090302 A(2; 3), B(1; 0). 06090802070803 090609 ﾁ0203020705 090908030803 ﾁ. 7.36. 01090202 ﾁ030604070202 080603090503000102070909 ABC: A(6ﾓ18; 8), B(2; 6ﾓ17), C(6ﾓ15; 6ﾓ13). 0609040704070803 090609 ﾁ0203020703 0403060403020207090900050609, 040603 ﾁ0302030202030503 0703 ﾁ030604070202 A 09 01030207090203, 040603 ﾁ03020302020308 0703 ﾁ030604070202 B. 7.37 6ﾓ5. 0103090900070803, 070803 020005 090900020308 040605010308 070906030708 ﾁ090308, 040607070301 080300010903 03020203, 02030601090001020303 090609 ﾁ0203-020703, 09030803060303 0303 0304070702 ﾁ090308. 7.38 6ﾓ5. 0103090900070803, 070803 08090205030207 09050009 0103000209 02 ﾁ090105 040306030703090908060701070705 04060501020107 l 1 07 l 2, 030902090202020107 090609 ﾁ02030207050107 y = k 1 x + b 1 07 y = k 2 y + b 2, ﾁ02070707000503080705 0403 04030601090003 tg ' = k 2 6ﾓ1 k 1 1 + k 1 k 2 :

1300030109 8 080003070903070801 ｨｮ0003020908060708 0403 070003000203070807 030008030908 0403070003 040605010308 0209 040003070903070807 050803 040003070903070801 ﾁ 0406030708060902-0708 ﾁ03. 070202090903 ﾁ0703 09070003000203020703 07 ﾁ030207080705 00070401 09 0203040300020708030001020308 09030306020702090803. 08030508030109 0707080908030001, 0907 ﾁ0307 ﾁ040708 0109080306070900 04060302020209060308 08030102, 000303 03070300030503 0806090209 040308010308 07 050809 08030109. 47. 010609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 020902020908 0803070909 040306040302020709090005060203 02090202030109 ﾁ030908030609 ｨｰ0707. 8.1. 080003070903070801, 0406030603-0205060905 0703060303 0309020902020908 0803070909 040306040302020709090005060203 ﾁ030908030609 0809070801 02090209 0803070909 M 0 (x 0 ; y 0 ; z 0 ) 07 ﾁ0309080306 6ﾓ1 n (A; B; C). 000603000903080705 0209040707090801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 M 0 040306-040302020709090005060203 ﾁ030908030609 6ﾓ1 n (060707. 8.1). 050909 07 ﾁ 070009070903 040605010308, ﾁ030301010301 0406030703 ﾁ030001020908 0803070909 M(x; y; z) 07 ﾁ020507020701, 040607 0909090706 09070003 ﾁ070506 030209 0009020308 040607020902000300090801 040003070903070807. 0803 09070003 ﾁ0708 040003070903070801 040306040302020709090005060209 ﾁ030908030609 6ﾓ1 n, 04030508030109 0008000905 040605010905, 04060702090200030009060905 05080308 040003070903070807, 0809090003 030109 040306040302-020709090005060209. ﾂ 070907080203070807, 040605010905 (M 0 M) (09 030209070708, 07 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M) 040306040302020709090005060209 6ﾓ1 n 0803050209 07 080300010903 0803050209, 0903050209 0803070909 M 0403040902090308 0209 040003070903070801 (0701. 060707. 8.1). 05030306020702090802 ﾁ030908030609 6ﾓ16ﾓ16ﾓ1 M 0 M ﾁ02070707000508080705 0708090202090608020201 03000609030301: 6ﾓ16ﾓ16ﾓ1 M 0 M(x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ), 09 040306040302020709090005060203070801 ﾁ030908030603 ﾁ 0609 ﾁ0203070700010209 08030109, 070803 0706 070909000506020303 0406030703 ﾁ030203020703 0609 ﾁ0203 02090008: ( 6ﾓ1 n ; 6ﾓ16ﾓ16ﾓ1 M 0 M) = 0. 0009090701 03000609030301, 07070903010303 090609 ﾁ0203020703 0701030308 ﾁ0702: : A(x 6ﾓ1 x 0 ) + B(y 6ﾓ1 y 0 ) + C(z 6ﾓ1 z 0 ) = 0: (8.1) ﾂ 05080301 090609 ﾁ0203020707 6ﾓ1 n (A; B; C) ﾁ0309080306, 04030604030202070909000506020208 040003070903070807, 09030803060208 04060702050803 02090302 ﾁ090801 0203060109000108 09 040003070903070807, 09 (x 0 ; y 0 ; z 0 ) 09030306020702090802 0803070907, 0703060303 09030803060908 0406030603020708 040003070903070801. 48. 0700060303 090609 ﾁ0203020703 040003070903070807 02070007 ﾁ 090609 ﾁ0203020707 (8.1) 0609070906020801 070903000907 07 070506090404070603 ﾁ090801 0700030202, 04030009070701 Ax + By + Cz 6ﾓ1 (Ax 0 + By 0 + Cz 0 ) = 0: 000909 090909 ﾁ0206090003020703 (6ﾓ1(Ax 0 +By 0 +Cz 0 )) 040603070803 090302070809020809, 0102 0303 0103000301 03000303020907070801 0703060303 D. ﾂ 06030309000108090803 090609 ﾁ0203020703 040607010308 ﾁ0702: Ax + By + Cz + D = 0: (8.2) 0009090303 090609 ﾁ0203020703 02090302 ﾁ0903080705 0300060701 090609 ﾁ020302070301 040003070903070807. ｨｪ02 040301020701, 070803 (A; B; C) 09030306-020702090802 02030601090007 09 040003070903070807. 050909 030002070203, ﾁ0303020709090308 ﾁ0304060307: 0008000303 0007 090609 ﾁ0203020703 080909030503 08070409 0304070702 ﾁ090308 020309030803060908 04000307-0903070801? 080603000203 ﾁ07030503 03090103080701, 070803 03070007 (A; B; C) = (0; 0; 0), 0803 090609 ﾁ0203020703 00070003 0203 0701030308 06030403020708 (03070007 D ﾙ 0), 00070003 030109 090203 ﾁ000308 ﾁ0306050308 0008000905 0803070909 04060307080609020708 ﾁ09 (03070007 D = 0). 08030508030109 0009020301 07070708090801, 070803 06030805 0002 03020203 0703 0707070300 A; B; C 0203 0609 ﾁ0203 02090008. 070003030209070701 ﾁ0309080306 07 090303060207020908090107 (A; B; C) 0703060303 6ﾓ1 n 07 04030402080903010705 0209080807 0909090908-020700090201 0803070909, 09030306020702090802 09030803060308 090203 ﾁ000308 ﾁ0306050808 090609 ﾁ0203020708 (8.2). 54

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 55 000909 090909 6ﾓ1 n (A; B; C) ﾙ 0, 0803 03020209 0703 030503 090303060207020908 0300050309080300010203 03080007070209 0308 02090005. 090303 03050609-02070703020705 0300060203070807 0406030204030003000701, 070803 A ﾙ 0. 080300030007 ﾁﾁ 090609 ﾁ0203020707 y = z = 0, 04030009070701 04060307080303 0703030802030403020703 020005 x: Ax + D = 0 6ﾍ2 x = 6ﾓ1D=A: 0009090701 03000609030301, 0803070909 M 0 (6ﾓ1D=A; 0; 0) 0406070209020003000708 01020300030708 ﾁ09 06030403020708 090609 ﾁ0203020705 (8.2). 02070007 04030603040707090801 090609 ﾁ0203020703 (8.2) ﾁﾁ070203 A(x + D=A) + By + Cz = 0; 0803 030503 0003 ﾁ0908 0709070801 0103000203 070208030604060308070603 ﾁ090801 090909 070909000506020303 0406030703 ﾁ030203020703 ﾁ030908030603 ﾁ 6ﾓ1 n (A; B; C) 07 6ﾓ16ﾓ16ﾓ1 M 0 M(x + D=A; y; z); 09 07090103 090609 ﾁ0203020703 090909 0609 ﾁ03020708 ﾁ03 02090008 0508030503 07090900050602030503 0406030703 ﾁ030203020703, 08. 03. 04030604030202070909-0005060203070801 ﾁ030908030603 ﾁ 6ﾓ1 n (A; B; C) 07 6ﾓ16ﾓ16ﾓ1 M 0 M(x + D=A; y; z). ｨｲ0209070708, 09030306020702090802 (x; y; z) 0803070907 M 090203 ﾁ000308 ﾁ0306050808 090609 ﾁ0203020708 (8.2) 0803050209 07 080300010903 0803050209, 0903050209 6ﾓ1 n (A; B; C) ﾍ 6ﾓ16ﾓ16ﾓ1 M 0 M(x + D=A; y; z): 0603 050803 0303020907090308, 070803 0803070909 M(x; y; z) 0406070209020003000708 040003070903070807, 04060306030205060308 0703060303 0803070909 M 0 040306040302020709090005060203 ﾁ030908030609 6ﾓ1 n (A; B; C). ｨｦ080909, 0102 0203090903090007, 070803 03070007 6ﾓ1 n (A; B; C) ﾙ 0, 0803 090609 ﾁ0203020703 (8.2) 0304070702 ﾁ090308 020309030803060908 04000307-0903070801, 040607070301 6ﾓ1 n (A; B; C) 02030601090001 09 05080308 040003070903070807! 49. 010609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 020902020908 0803070909 0409060900000300010203 02 ﾁ0901 0203090300000702030906020201 ﾁ03090803060901 0806030204030003000701, 020901 0209000203 0209040707090801 090609 ﾁ0203020703 040003070903070807, 0406030603-0205060308 0703060303 0803070909 M 0 (x 0 ; y 0 ; z 0 ), 0409060900000300010203 ﾁ03090803060901 6ﾓ1 a (a x ; a y ; a z ) 07 6ﾓ1 b (b x ; b y ; b z ). ｨｲ090103080701, 070803 ﾁ030908030602 020300000202 00020801 02030903000007020309060202, 080909 090909 ﾁ 0406030807 ﾁ020301 070009070903 040003070903070801 03040603020300030209 020303020203030209070203! 070006090807010705 09 060707. 8.2. 0609 020301 07030300060900030202 0707060302020203 020902020203 07 040603-0703 ﾁ030001020905 0803070909 04060307080609020708 ﾁ09 M(x; y; z). ｨｲ090209010903010705, 040607 0909090706 09070003 ﾁ070506 0803070909 M 0009020308 040607020902000300090801 0209040308 040003070903070807? 09070203, 070803 ｨｰ0707. 8.2. 050301040009020906020203 ﾁ030908030602 6ﾓ1 a, 6ﾓ1 b 07 6ﾓ16ﾓ16ﾓ1 M0M 050803 04060307030308020308 0803050209 07 080300010903 0803050209, 0903050209 ﾁ030908030602 6ﾓ1 a, 6ﾓ1 b 07 6ﾓ16ﾓ16ﾓ1 M 0 M 0009020908 0903010400090209060202. 080307000302020303 09070003 ﾁ0703 0609 ﾁ0203070700010203 08030109, 070803 0706 070103-040902020303 0406030703 ﾁ030203020703 0609 ﾁ0203 02090008. 0707080900030701 0309040707090801 070103040902020303 0406030703 ﾁ030203020703 ﾁ 0903030602070209080906 07 0406070609 ﾁ02050801 030503 02090008: : ｴ 6ﾓ16ﾓ16ﾓ1 M 0 M; 6ﾓ1 a ; 6ﾓ1 b ｵ = ｨO x 6ﾓ1 x 0 y 6ﾓ1 y 0 z 6ﾓ1 z 0 a x a y a z b x b y b z ｨO = 0: (8.3) 0803010205 03 080301, 090909 060907090602 ﾁ0903080705 030406030203000708030001, 0003050903 040603030006090303 ﾁ090801 04030009070302020303 090609 ﾁ0203020703 09 030006030109 ﾁ070209: ｨO ｨO x 6ﾓ1 x 0 y 6ﾓ1 y 0 z 6ﾓ1 z 0 a x a y a z b x b y b = z ｨO = (x 6ﾓ1 x 0 )(a y b z 6ﾓ1 a z b y ) 6ﾓ1 (y 6ﾓ1 y 0 )(a x b z 6ﾓ1 a z b x ) + (z 6ﾓ1 z 0 )(a x b y 6ﾓ1 a x b y ) = 0: 070202090903 0203 07000302090308 03090006070801 040307000302020808 04030601090009. ｨｬ09070403 0307030302090801 0900050306070801 ﾁ02 ﾁ030209 090609 ﾁ0203020705 (8.3). 0903000303 08030503, 0308 ﾁ03070905 0209 07030308 ﾁ03080708 ﾁ0908060708 ﾁ0304060307 0209 0509030901030203, 0103000203 030708090203 ﾁ0708010705 0209

1356 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 090609 ﾁ0203020707 (8.3), 0203 060907090602 ﾁ0905 030406030203000708030001, 09 040607 ﾁ0302070801 090609 ﾁ0203020703 040003070903070807 09 030006030109 ﾁ070209, 03070007 080300010903 ﾁ 05080301 ﾁ0303020709090308 02030300060302070103070801 040607 06030403020707 09030209060308020308 030902090707 (0209040607010306, 03070007 0209000203 ﾁ0207070700070801 09030306020702090802 02030601090007 09 05080308 040003070903070807). 06030400030603 00020003 0002 ﾁ 05080308 010301030208 030902090801 07030003 ﾁ0304060307: 09 040307030109, 0703000708 ﾁ03020203, 090609 ﾁ0203020703 (8.3) 020308-0708 ﾁ07080300010203 0304070702 ﾁ090308 080603000903010908 040003070903070801. 0109 ﾁ09080803 0900030207010705 ﾁ 05080301. 080603000203 ﾁ07030503 040603 ﾁ03060701, 070803 0803070909 M 0 (x 0 ; y 0 ; z 0 ) 0406070209020003000708 040003070903070807, 040302070809 ﾁ07 ﾁ 0303 09030306020702090802 ﾁ0103070803 04030603010302020206 (x; y; z) ﾁ 090609 ﾁ0203020703. 08030009070701 030406030203000708030001 07 02090003 ﾁ0308 07080603090308 ｨO x 0 6ﾓ1 x 0 y 0 6ﾓ1 y 0 z 0 6ﾓ1 z 0 a x a y a z b x b y b z 09030803060208, 09030203070203, 0609 ﾁ0302 02090008. ｨｲ0209070708, 09030306020702090802 0803070907 M 0 090203 ﾁ000308 ﾁ0306050808 090609 ﾁ0203020708 (8.3), 08. 03. 0803070909 M 0 ﾊ. ﾂ030301010301 080304030601 0406030703 ﾁ030001020908 0803070909 M 1 (x 1 ; y 1 ; z 1 ) 040003070903070807 07 040302070809 ﾁ0701 0303 09030306020702090802 ﾁ 0003 ﾁ0908 0709070801 090609 ﾁ0203020705 (8.3): ｨO x 1 6ﾓ1 x 0 y 1 6ﾓ1 y 0 z 1 6ﾓ1 z 0 a x a y a z b x b y b z 03090908070703070907 09000703000808020905 ﾁ03000707070209 0508030503 030406030203000708030005 0609 ﾁ0209 030008030109 040906090000030003040704030209, 0403070806030302-02030503 0209 ﾁ03090803060906 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1, 6ﾓ1 a 07 6ﾓ1 b, 04030508030109 0302 0609 ﾁ0302 02090008 0803050209 07 080300010903 0803050209, 0903050209 050807 ﾁ030908030602 0009020908 0409060900000300010202 0302020308 040003070903070807, 09 070103020203, 040003070903070807. ｨｹ0803 07 0303020907090308, 070803 M 1 ﾊ. 50. 080906090103080607070307090703 090609 ﾁ0203020705 040003070903070807 0803020308020301 09 06030403020708 030902090707, 07040306010900070603 ﾁ0902020308 ﾁ 020907090003 0406030202020906030503 ﾁ030406030709, 020307090300010903 0702090703. 0609040301020701, 070803 020901 0209000203 ﾁ02040707090801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 M 0 (x 0 ; y 0 ; z 0 ) 0409060900000300010203 ﾁ03090803060901 6ﾓ1 a (a x ; a y ; a z ) 07 6ﾓ1 b (b x ; b y ; b z ). ｨｪ02 090003 ﾁ02050702070007, 070803 0803070909 M 0009020308 040607020902000300090801 040003070903070807 0803050209 07 080300010903 0803050209, 0903050209 ﾁ030908030602 6ﾓ1 a, 6ﾓ1 b 07 6ﾓ16ﾓ16ﾓ1 M 0 M 0903010400090209060202. 0506030103 08030503, 080607 ﾁ030908030609 0903010400090209060202 0803050209 07 080300010903 0803050209, 0903050209 030207 00070203080203 0309 ﾁ0707070102. ｨｮ 020609050308 07080306030202, ﾁ030908030602 6ﾓ1 a 07 6ﾓ1 b 02030903000007020309060202, 08. 03. 00070203080203 02030309 ﾁ0707070102. 08030508030109 0007020308020905 0309 ﾁ0707070103070801 ﾁ030908030603 ﾁ 6ﾓ1 a, 6ﾓ1 b 07 6ﾓ16ﾓ16ﾓ1 M 0 M ﾁ03030103000209 080300010903 0803050209, 0903050209 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M 00070203080203 ﾁ020609000903080705 0703060303 6ﾓ1 a 07 6ﾓ1 b : 6ﾓ16ﾓ16ﾓ1 M 0 M = t 6ﾓ1 6ﾓ1 1 a + t 2 b ; 050203 t 1 07 t 2 020309030803060203 ﾁ0306030708 ﾁ0302020203 0707070009. 080302070809 ﾁ0701 ﾁ 040307000302020303 0703030802030403020703 09030306020702090802, 0403010205 03 080301, 070803 0203080708 ﾁ0705 020902 ﾁ0309080306090107 07030308 ﾁ03080708 ﾁ090808 0203080708 ﾁ070501 020902 090303060207020908090107. 0609040301020701 0809090003, 070803 ﾁ030908030602 0609 ﾁ0202 0803050209 07 080300010903 0803050209, 0903050209 0703 ﾁ040902090808 0706 09030306020702090802: (x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ) = t 1 (a x ; a y ; a z ) + t 2 (b x ; b y ; b z ) 6ﾍ2 6ﾍ2 (x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ) = (t 1 a x ; t 1 a y ; t 1 a z ) + (t 2 b x ; t 2 b y ; t 2 b z ) 6ﾍ2 6ﾍ2 (x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ) = (t 1 a x + t 2 b x ; t 1 a y + t 2 b y ; t 1 a z + t 2 b z ): 070807080209 040906090103080607070307090703 090609 ﾁ0203020705 040003070903070807 0103000203 0309040707090801 ﾁﾁ070203 07070708030102: : 61 62 63 ; ｨO : ｨO x = x 0 + t 1 a x + t 2 b x ; y = y 0 + t 1 a y + t 2 b y ; z = z 0 + t 1 a z + t 2 b z : ｨｲ02030701 (x 0 ; y 0 ; z 0 ) 09030306020702090802 0803070907, 0703060303 09030803060908 0406030603020708 040003070903070801, (a x ; a y ; a z ) 07 (b x ; b y ; b z ) 09030306020702090802 ﾁ030908030603 ﾁ, 09030803060201 040003070903070801 0409060900000300010209, 09 t 1 07 t 2 040906090103080602. (8.4)

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 57 51. 010609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 02 ﾁ03 020902020203 0803070907 0409060900000300010203 030902090202030109 ﾁ030908030609 0806030204030003000701, 020901 0209000203 ﾁ02040707090801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 020902020203 080307-0907 M 0 (x 0 ; y 0 ; z 0 ), M 1 (x 1 ; y 1 ; z 1 ) 0409060900000300010203 ﾁ030908030609 6ﾓ1 a (a x ; a y ; a z ). ｨｰ090707010308060701 07030308 ﾁ03080708 ﾁ0908060708 06070709020309 (060707. 8.3, 09), 0209 09030803060301 03080103080701 0406030703 ﾁ030001020908 0803070909 04060307080609020708 ﾁ09 M(x; y; z). 080307090300010909 0803070907 M 0 07 M 1 0406070209020003000908 040003070903070807, 0803 ﾁ0309080306 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1 0009020308 0308 04090609000003000302 (060707. 8.3, 00). 0009090701 03000609030301, 030902090709 07 ﾁ030207080705 09 0703070809 ﾁ0003020708 090609 ﾁ0203020705 040003070903070807, 04060306030205060308 0703060303 0803070909 M 0 0409060900000300010203 02 ﾁ0901 ﾁ03090803060901 6ﾓ1 a 07 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1, 070803 0102 090003 0901030301 020300090801 (070806. 55). ｨｰ0707. 8.3. 080003070903070801, 04060306030205060905 0703060303 02 ﾁ03 0803070907 0409060900000300010203 030902090202030109 ﾁ030908030609 ｨｮ 020609050308 07080306030202, 04030003030203 030603 060903 040603020901090801, 090909 04030009070908080705 0809090703 090609 ﾁ0203020705. ｨｦ07070003020905 060707. 8.3, 00, 0003050903 040302050801, 070803 0803070909 M 04030409020308 0209 040003070903070801 0803050209 07 080300010903 0803050209, 0903050209 ﾁ030908030602 6ﾓ1 a, 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1 07 6ﾓ16ﾓ16ﾓ1 M 0 M 0903010400090209060202, 08. 03. 0706 070103040902020303 0406030703 ﾁ030203020703 0609 ﾁ0203 02090008. 010005 ﾁ020707070003020705 07010304090202030503 0406030703 ﾁ030203020705 0403080603000908080705 09030306020702090802 ﾁ030908030603 ﾁ 6ﾓ1 a (a x ; a y ; a z ), 6ﾓ16ﾓ16ﾓ1 M 0 M(x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ) 07 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1 (x 1 6ﾓ1 x 0 ; y 1 6ﾓ1 y 0 ; z 1 6ﾓ1 z 0 ). ｨｮ0103040902020303 0406030703 ﾁ030203020703 ﾁ02070707000503080705 0703060303 030406030203000708030001: ｴ 6ﾓ16ﾓ16ﾓ1 M 0 M; 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1 ; 6ﾓ1 a ｵ = ｨO x 6ﾓ1 x 0 y 6ﾓ1 y 0 z 6ﾓ1 z 0 x 1 6ﾓ1 x 0 y 1 6ﾓ1 y 0 z 1 6ﾓ1 z 0 a x a y a z 0707080900030701 0406070609 ﾁ02050801 05080308 030406030203000708030001 02090008 07 0403000907070801 07070903010303 090609 ﾁ0203020703: : ｨO x 6ﾓ1 x 0 y 6ﾓ1 y 0 z 6ﾓ1 z 0 x 1 6ﾓ1 x 0 y 1 6ﾓ1 y 0 z 1 6ﾓ1 z 0 a x a y a z ｨO : ｨO = 0: (8.5) 000304030601 04030003030203 040603 ﾁ0306070801, 070803 (8.5) 0203080708 ﾁ07080300010203 05 ﾁ000503080705 090609 ﾁ020302070301 080603000903010308 040003070903-070807. 08060302030009080803 050803 0709010307080305080300010203, 070003020905 060907070900020302070501, 040607 ﾁ03020302020201 0209 070806. 56. 52. 010609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 080607 020902020203 0803070907 ﾂ 05080301 06090302030003 020901 040603020708030708 ﾁ02040707090801 090609 ﾁ0203020703 040003070903070807, 03070007 0703 ﾁ0307080203, 070803 030209 0406030603020708 0703060303 0803070907 M 0 (x 0 ; y 0 ; z 0 ), M 1 (x 1 ; y 1 ; z 1 ) 07 M 2 (x 2 ; y 2 ; z 2 ). ﾂ 0302020301 0703 04060302020209060706 ﾁ030406030703 ﾁ (070806. 55) 060903030006090203, 090909 ﾁ0204070702 ﾁ0903080705 090609 ﾁ0203020703 040003070903-070807, 03070007 0703 ﾁ0307080202 09030306020702090802 040906090000030001020206 0308 ﾁ030908030603 ﾁ 07 0803070909, 00030009060905 ﾁ 040003070903070807. 0009090703 ﾁ030908030602 040300090709080705, 03070007 070303020702070801 0803070907 M 0 07 M 1, M 0 07 M 2. 05030306020702090802 ﾁ030908030603 ﾁﾁ020707070005-08080705 0708090202090608020201 03000609030301: 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 1 (x 1 6ﾓ1 x 0 ; y 1 6ﾓ1 y 0 ; z 1 6ﾓ1 z 0 ); 6ﾓ16ﾓ16ﾓ16ﾓ1 M 0 M 2 (x 2 6ﾓ1 x 0 ; y 2 6ﾓ1 y 0 ; z 2 6ﾓ1 z 0 ): ﾂﾁ03020301 0406030703 ﾁ030001020908 0803070909 04060307080609020708 ﾁ09 M(x; y; z) 07 06090707010308060701 ﾁ0309080306 6ﾓ16ﾓ16ﾓ1 M 0 M(x 6ﾓ1 x 0 ; y 6ﾓ1 y 0 ; z 6ﾓ1 z 0 ):

1358 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 0803 0902090003050707 07 0406030202020906070107 0700090709050107 ﾁ020407040301 090609 ﾁ0203020703: : ｨO x 6ﾓ1 x 0 y 6ﾓ1 y 0 z 6ﾓ1 z 0 x 1 6ﾓ1 x 0 y 1 6ﾓ1 y 0 z 1 6ﾓ1 z 0 x 2 6ﾓ1 x 0 y 2 6ﾓ1 y 0 z 2 6ﾓ1 z 0 080603 ﾁ0306010803, 070803 050803 090609 ﾁ0203020703 0203080708 ﾁ07080300010203 0304070702 ﾁ090308 020900020908 040003070903070801! ｨO = 0: (8.6) 53. ﾂ03090701020303 060907040300030003020703 04000307090307080308 ｨｦ03 040903000102030503 0909060709 050303010308060707 0703 ﾁ0307080203, 070803 02 ﾁ03 040003070903070807 0103050908 040306030703090908010705 070007 00020801 04090609000003000102020107. 080607070301 ﾁ03 ﾁ0803060301 070009070903 030207 0103050908 0703 ﾁ040902090801. ｨｦ02090703 0503 ﾁ030605, 040003070903070807 1 07 2 0103050908 02090603020708010705 ﾁ 0302020301 0703 08060306 040300030003020708: 1) 0703 ﾁ040902090808: 1 = 2 ; 2) 0409060900000300010202, 0203 0203 0703 ﾁ040902090808: 1 2, 1 ﾙ 2 ; 3) 040306030703090908080705 0403 040605010308 l: 1 ﾉ 2 = l. ｨｲ0902090709 07030708030708 ﾁ 080301, 0708030002 020909070708010705 03040603020300050801 ﾁ03090701020303 060907040300030003020703 04000307090307080308 0403 0706 0300060701 090609 ﾁ020302070501 (8.2): 1 : A 1 x + B 1 y + C 1 z + D 1 = 0; 2 : A 2 x + B 2 y + C 2 z + D 2 = 0: ｨｲ090103080701, 070803 03070007 ﾁ0803060303 0703 05080706 090609 ﾁ0203020708 04030009070903080705 0703 040306 ﾁ030503 09010203000302070301 0209 020302090003 ﾁ0303 0707070003, 0803 090609 ﾁ0203020705 0609 ﾁ0203070700010202, 08. 03. 01020300030708 ﾁ09 0706 06030403020708 0703 ﾁ040902090808. ｨｲ0209070708, 07 07030308 ﾁ0308-0708 ﾁ0908060703 040003070903070807 0703 ﾁ040902090808. ｨｹ080308 04090908 0103000203 0309040707090801 070003020908060701 03000609030301: 0806030204030003000701 080304030601, 070803 040307000302020303 0703 0609 ﾁ03020708 ﾁ 02090609040903080705: 000909 090909 040607 05080301 A 1 A 2 = B 1 B 2 = C 1 C 2 = D 1 D 2 : (8.7) A 1 A 2 = B 1 B 2 = C 1 C 2 ﾙ D 1 D 2 : (8.8) A 1 = B 1 = C 1 ; A 2 B 2 C 2 0803 09030306020702090802 ﾁ030908030603 ﾁ 6ﾓ1 n 1 (A 1 ; B 1 ; C 1 ) 07 6ﾓ1 n 2 (A 2 ; B 2 ; C 2 ) 040603040306010703020900010202, 09 030209070708, 050807 ﾁ03090803-0602 0903000007020309060202. 070202090903 6ﾓ1 n 1 02030601090001 09 040003070903070807 1 (070806. 55), 09 6ﾓ1 n 2 02030601090001 09 040003070903070807 2 (070806. 55). ｨｲ0209070708, 030207 0009020908 0409060900000300010202 0803050209 07 080300010903 0803050209, 0903050209 07090107 040003070903070807 0409060900-000300010202. 08030508030109 09070003 ﾁ0703 (8.8) 0303020907090308 0409060900000300010203070801 02030703 ﾁ0409020908060706 04000307090307080308 1 07 2. 06090903020301, 040003070903070807 0009020908 040306030703090908010705 0803050209 07 080300010903 0803050209, 0903050209 0706 02030601090007 02030409060900-000300010202. ｨｦ02090703 0503 ﾁ030605, 09030306020702090802 0203060109000308 020300000202 00020801 0203040603040306010703020900010202. 54. 010609 ﾁ0203020703 040003070903070807 ﾁ 0308060303090906 ｨｰ090707010308060701 030603 03020203 090609 ﾁ0203020703 040003070903070807, 040303 ﾁ03000508060303 090203000203 0304070702 ﾁ090801 060907040300030003020703 040003070903070807 030802030707080300010203 090303060207020908020206 03070308 07 090303060207020908020206 04000307090307080308 02030909060803 ﾁ0308 07070708030102 090303060207020908.

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 59 54.1. 0700060708 070009070908 090609 ﾁ0203020705 040003070903070807 ﾁ 0308060303090906. 0809070801 090609 ﾁ0203020703 040003070903070807 030902090203 0300060701 090609 ﾁ020302070301 (8.2) 07 A ﾙ 0, B ﾙ 0, C ﾙ 0 07 D ﾙ 0. 0806030300060903090301 050803 090609 ﾁ0203020703 070003020908060701 03000609030301: Ax + By + Cz + D = 0 6ﾍ2 Ax + By + Cz = 6ﾓ1D 6ﾍ2 6ﾍ2 6ﾓ1 A D x 6ﾓ1 B D y 6ﾓ1 C D z = 1 6ﾍ2 x 6ﾓ1D=A + y 6ﾓ1D=B + z 6ﾓ1D=C = 1: ﾂﾁ03020301 0300030302090703020705 a = 6ﾓ1D=A, b = 6ﾓ1D=B, c = 6ﾓ1D=C 07 040306030407040301 04030009070302020303 090609 ﾁ0203020703 040003070903070807 ﾁﾁ070203: x a + y b + z = 1: (8.9) c 0009090303 090609 ﾁ0203020703 02090302 ﾁ090808 090609 ﾁ020302070301 040003070903070807 ﾁ 0308060303090906. ﾂ 090609 ﾁ0203020707 (8.9) 040906090103080602 a; b; c 0103050908 040607020701090801 090909 04030003000708030001020203, 080909 07 03080607010908030001020203 0302090703020705. 060903 ﾁ09020703 090609 ﾁ0203020705 0300080507020503080705 0503030103080607070307090701 07010207000301 ﾁ06030205060706 ﾁ 02030503 040906090103080603 ﾁ a; b; c. 0103080708 ﾁ07080300010203, 04030009050905 y = 0, z = 0 0703 090609 ﾁ0203020705 (8.9) 0403000907090301 0803070909 P(a; 0; 0) 0803070909 0403060307030703020705 040003070903070807 07 03070108 Ox (0701. 060707. 8.4). ｨ 020900030507070203 Q(0; b; 0) 0803070909 040306030703-0703020705 040003070903070807 07 03070108 Oy, 09 R(0; 0; c) 0803070909 0403060307030703020705 040003070903070807 07 03070108 Oz. 050909 ﾁ07020203 0703 060707. 8.4, a, b 07 c 0200070202 03080603030903 ﾁ, 03080703090903010206 04000307090307080108 0308 090303060207020908020206 03070308, 04030508030109 090609 ﾁ0203020703 (8.9) 02090302 ﾁ090808 090609 ﾁ020302070301 040003070903070807 ﾁ 0308060303090906. 54.2. 08030708060303020703 040003070903070807 ﾁ 02030909060803 ﾁ0308 07070708030103 090303060207020908. ﾂ 04060302020209060706 ﾁ03040603-070906 0102 060907070109080607 ﾁ090007 040003070903070801, 0309020902020908 08030107 070007 0702020107 0409060901030806090107. 070202090903, 07030300060903070801 040003070903070801, 0209040607010306, 0403 0309020902020308 0803070903 07 ﾁ030908030609 02030601090007 070003000203 07 08060300090308 0603060304030503 ﾁ0303000609-0003020705. 080307080603070801 040003070903070801 0403 08060301 080307090901 070007 0403 0803070903 07 02 ﾁ0901 ﾁ03090803060901 040003070903070807 0203070003000203, 0203 0809090703 04030708060303020705 0203 040303 ﾁ03000508 03040603020300070801 040300030003020703 040003070903070807 ﾁ 07070708030103 090303060207020908. 0009090701 03000609030301, 03070007 04030708060303020703 040605010308 0209 040003070903070807 (0209040607010306, 0403 090609 ﾁ0203020708 070007 0403 02 ﾁ0901 080307090901) 0203 04060302070809 ﾁ00050308 070003000203070807, 0803 04030708060303020703 040003070903070807 0709070803 ﾁ020302 ﾁ090308 02030406030302030007010203 080609020203070807. 02070007 040003070903070801 030902090209 ﾁ 0308060303090906 0209 03070506, 0803, 090909 050803 00020003 07020300090203 ﾁ020403 0209 060707. 8.4, 07030300060903070801 040003070903070801 0003050903 07 040603070803. 0103080708 ﾁ07080300010203, 020005 0703030006090003020705 040003070903070807 070806030701 0803070907 0403-060307030703020705 040003070903070807 07 09030306020702090802020107 0307050107 P; Q; R. ｨｲ09080301, 04030708060307 ﾁ 040605010203 (P Q), (QR), (P R), 0403000907090301 0703030006090003020703 04000307-0903070807. 080607 ﾁ02 ﾁ030203 090609 ﾁ0203020705 (8.9) 0102 040603020403000905090007, 070803 A ﾙ 0, B ﾙ 0, C ﾙ 0 07 D ﾙ 0. ｨｰ090707010308060701 0203040300020203 090609 ﾁ0203020705 040003070903-070807, 0903050209 03020702 070007 04090609 090305040407010703020803 ﾁ 0703 A; B; C 0609 ﾁ0202 02090008. 0809070801 A = 0, 0803050209 0300060303 090609 ﾁ0203020703 040003070903070807 (8.2) 04060702070109-0308 ﾁ0702 By + Cz + D = 0; ｨｰ0707. 8.4. 010609 ﾁ0203020703 040003070903070807 ﾁ 0308060303090906 09 090609 ﾁ0203020703 ﾁ 0308060303090906 0209 03070506 0009020308 y b + z c = 1: 000909 090909 090609 ﾁ0203020703 040003070903070807 0203 0703020306000708 04030603010302020308 x, 0803 0809090905 040003070903070801 0409060900000300010209 030707 Ox.

1360 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁｨｰ0707. 8.5. 06090708020203 070009070907 060907040300030003020705 040003070903070807 ﾁ 07070708030103 090303060207020908 010005 04030708060303020705 040003070903070807, 040906090000030001020308 030707 Ox, 0308010307090301 0803070907 Q(0; b; 0) 07 R(0; 0; c) 0403-060307030703020705 040003070903070807 07030308 ﾁ03080708 ﾁ03020203 07 0307050107 Oy 07 Oz (0701. 060707. 8.5, 09). ｨｮ0806030701 040605010908 (QR). 0109000303 070806030701 040605010203 QM 1 07 RM 2, 04060306030205060703 0703060303 0803070907 Q 07 R 07 040906090000030001020203 030707 Ox. ﾂ 06030309000108090803 0403000907090301 0703030006090003020703 040003070903070807, 040906090000030001020308 030707 Ox, (0701. 060707. 8.5, 09). 080607 A = 0 07 B = 0 0300060701 090609 ﾁ020302070301 040003070903070807 (8.2) 05 ﾁ000503080705 Cz + D = 0; 090609 ﾁ0203020703 ﾁ 0308060303090906 0209 03070506: z c = 1: 000909 090909 090609 ﾁ0203020703 040003070903070807 0203 0703020306000708 04030603010302020206 x 07 y, 0803 0809090905 040003070903070801 0409060900000300010209 07 030707 Ox, 07 030707 Oy, 08. 03. 040003070903070801 0409060900000300010209 040003070903070807 Oxy (0701. 060707. 8.5, 00). 010005 04030708060303020705 040003070903070807, 040906090000030001020308 040003070903070807 Oxy, 0703060303 0803070909 R(0; 0; c) 0403060307030703020705 040003070903070807 07 03070108 Oz 0708060305080705 040605010203 (RM 1 ) 07 (RM 2 ), 040906090000030001020203 090303060207020908020201 03070501 Oy 07 Oz (00030009060703 07030308 ﾁ03080708 ﾁ03020203 ﾁ 090303060207020908020206 04000307090307080506 Oyz 07 Oxz), 090909 0209 060707. 8.5, 00. ｨｰ0907040704070803 07 04060307000008070806070609080803 0709010307080305080300010203 030708090001020203 07090708020203 070009070907, 0903050209 040003070903070801 0409060900000300010209 020609050701 090303060207020908020201 03070501 070007 090303060207020908020201 04000307090307080501. 0707080900030701 0609070701030806030801 070009070908, 0903050209 D = 0 040607 A ﾙ 0, B ﾙ 0, C ﾙ 0. 0700060303 090609 ﾁ0203020703 040003070903-070807 (8.2) 040607020701090308 ﾁ0702 Ax + By + Cz = 0: 080607 D = 0 050803 090609 ﾁ0203020703 020300010305 040607 ﾁ03070807 09 090609 ﾁ0203020708 ﾁ 0308060303090906 0209 03070506. ｨｰ0707. 8.6. 080003070903070801, 0406030603-0205060905 0703060303 020907090003 090303060207-020908 000909 090909 0803070909 O(0; 0; 0) 090203 ﾁ000308 ﾁ0306050308 0403000907030202030109 090609 ﾁ0203020708, 0803 040003070903070801 0406030603020708 0703060303 020907090003 090303060207020908. ﾂ030704030001030903010705 05080701 040909-080301 020005 04030708060303020705 040003070903070807. ﾂ02, 0209 ﾁ03060203, 0300060908070007 ﾁ02070109020703, 070803 0209 060707. 8.4, 060707. 8.5 040607 0703030006090003020707 040003070903070807 070806030700070701 0007020707 0403060307030703020705 040003070903070807 07 09030306020702090802020107 0400030709030708050107. ﾂ030704030001030903010705 0809090701 0003 04060703010301 040607 04030708060303020707 040003070903070807, 04060306030205060308 0703060303 020907090003 090303060207020908. ﾂ 090303060207020908020308 040003070903070807 Oyz x = 0, 04030508030109 090609 ﾁ0203020703 0007020707 0403060307030703020705 040003070903070807 07 Oyz 0701030308 ﾁ0702 { x = 0; By + Cz = 0: ｨｮ0806030701 050809 040605010908, 09030803060905 0406030603020708 0703060303 020907090003 090303060207020908 (0701. 060707. 8.6).

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 61 0009090003 070806030701 0007020708 0403060307030703020705 040003070903070807 07 Oxz: { y = 0; Ax + Cz = 0: 0803070806030302020203 040605010203 070000080708060706090808 040003070903070801 (0701. 060707. 8.6). 55. 06030601090001020303 090609 ﾁ0203020703 040003070903070807 000304030601 020901 0209000203 020909070708010705 ﾁ0207070700050801 06090707080305020703 0308 0803070907 0203 040003070903070807, 03070007 0803070909 030902090209 07 ﾁ03070107 090303060207020908090107, 09 040003070903070801 090609 ﾁ020302070301. ｨｲ02030701 0809090003 0209000008020903080705 040300020905 0902090003050705 07 040605010308 (070806. 42). 55.1. 0704060302030003020703. 010609 ﾁ0203020703 040003070903070807 x + y + z 6ﾓ1 = 0 02090302 ﾁ0903080705 02030601090001020201, 03070007 1) 2 + 2 + 2 = 1; 2) 1 7 0. 000304030601 0209090707010705 ﾁ0207070700050801 06090707080305020703 0308 020907090009 090303060207020908 0203 040003070903070807, 0309020902020308 020306-01090001020201 090609 ﾁ020302070301. 55.2. 00030306030109. 0809070801 040003070903070801 030902090209 02030601090001020201 090609 ﾁ020302070301 x + y + z 6ﾓ1 = 0. 0003050209 1) 02030601090001 09 040003070903070807 0701030308 030207020707020908 0200070209 6ﾓ1 n = 1; 2) 02030601090001 6ﾓ1 n 0209040609 ﾁ00030209 0308 020907090009 090303060207020908 09 040003070903070807; 3) 06090707080305020703 0308 020907090009 090303060207020908 0203 040003070903070807 0609 ﾁ0203. 010309090309080300010708 ﾁ03. 080306 ﾁ0303 0908 ﾁ0306000203020703 02030403070603020708 ﾁ03020203 07000302090308 0703 09070003 ﾁ0705 08030306030102 07 080306 0409090803 ﾁ, 070803 02030601090001 09 040003070903070807 0701030308 09030306020702090802 6ﾓ1 n (; ; ) (070806. 55), 09 0200070209 ﾁ030908030609 0703060303 030503 09030306020702090802 ﾁ02070707000503080705 0403 0708090202090608020308 04030601090003. 010005 020309090309080300010708 ﾁ09 040307000302020706 0908 ﾁ0306000203020708 0703 020907090009 09030306-0207020908 03040907080701 04030604030202070909000506 0209 040003070903070801 07 030003030209070701 030503 03070203 ﾁ09020703 0703060303 M 0. 0003050209 M 0 ﾊ (060707. 8.7). 0809070801 M 0 (x 0 ; y 0 ; z 0 ). 080307090300010909 6ﾓ16ﾓ16ﾓ1 OM 0 040306040302020709090005060302 040003070903-070807, 0803 6ﾓ16ﾓ16ﾓ1 OM 0 6ﾓ1 n. ｨｲ0209070708, 0706 09030306020702090802 040603040306010703020900010202. ｨｦ02020107 070003 ﾁ090107, 0209080203080705 0809090303 0707070003, 070803 x 0 =, y 0 =, z 0 = (09030306020702090802 ﾁ030908030609 6ﾓ16ﾓ16ﾓ1 OM 0 0609 ﾁ0202 (x 0 ; y 0 ; z 0 )). 0700060908070803 ﾁ02070109020703, 070803 03070007 1 7 0, 0803 ﾁ030908030602 6ﾓ16ﾓ16ﾓ1 OM 0 07 6ﾓ1 n 07030209040609 ﾁ00030202 (090909 0209 060707. 8.7), 070803 0303020907090308 07040609 ﾁ03020007 ﾁ03070801 ﾁ080306030503 0908 ﾁ0306000203020705. 0506030103 08030503, 050803 ﾁ 0803070203070807 0200070209 ﾁ030908030609 6ﾓ16ﾓ16ﾓ1 OM 0 (080909 090909 6ﾓ16ﾓ16ﾓ1 OM 0 = 6ﾓ1 n 07 6ﾓ16ﾓ16ﾓ1 OM 0 = 6ﾓ1 n = 1 = ). 080307090300010909 0803070909 M 0 ﾊ, 0303 09030306020702090802 (; ; ) 020300000202 090203 ﾁ000308 ﾁ0306050801 090609 ﾁ0203020708 040003070903070807, 08. 03. 0703030802030403020703 () + () + () 6ﾓ1 = 0 05 ﾁ000503080705 0707080702020201 0609 ﾁ03020708 ﾁ0301. 0806030300060903090301 030503: ｨｰ0707. 8.7. 06030601090001020303 090609 ﾁ0203020703 040003070903070807 () + () + () 6ﾓ1 = 0 6ﾍ2 ( 2 + 2 + 2 ) 6ﾓ1 = 0 6ﾍ2 = : ｨｦ080909, 0102 0403000907070007, 070803 = 1 7 0. 070807080209 07000302090308, 070803, ﾁ03-040306 ﾁ0206, 06090707080305020703 0308 020907090009 090303060207020908 0203 040003070903070807 0609 ﾁ0203, 09, ﾁ03- ﾁ0803060206, 02030601090001 6ﾓ1 n 0209040609 ﾁ00030209 0308 020907090009 090303060207020908 09 040003070903070807, 090909 0209 060707. 8.7 (040307030109?). 7ﾁ3

1362 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 000304030601, 090909 07 ﾁ 070009070903 040605010308, ﾁ02070707000701 06090707080305020703 0308 0406030703 ﾁ030001020308 0803070907 0203 040003070903070807, 0309020902020308 02030601090001020201 090609 ﾁ020302070301. 55.3. 00030306030109. 02070007 040003070903070801 030902090209 02030601090001020201 090609 ﾁ020302070301 x + y + z 6ﾓ1 = 0, 0803 06090707080305020703 0308 0803070907 M 0 (x 0 ; y 0 ; z 0 ) 0203 05080308 040003070903070807 0609 ﾁ0203 ｨO ｨOx 0 + y 0 + z 0 6ﾓ1 ｨO ｨO: 010309090309080300010708 ﾁ03. ｨｪ02 0302090301, 090909 ﾁ0207070700070801 06090707080305020703 0308 020907090009 090303060207020908 0203 040003070903070807. 0803-0508030109 020005 06030403020705 0403070809 ﾁ000302020308 030902090707 0708030708 ﾁﾁ03070807 0203 ﾁ0908 07070708030109 090303060207020908 M 0 uvw, 020907090003 09030803060308 0703 ﾁ040902090308 07 080307090308 M 0 (060707. 8.8). ｨｦ03 06070709020909 ﾁ07020203, 070803 u = x6ﾓ1x 0, v = y6ﾓ1y 0 07 w = z6ﾓ1z 0. ﾂ020609000905 030807080209 x, y 07 z 07 040302070809 ﾁ000505 0706 ﾁ 090609 ﾁ0203020703 040003070903070807, 0403000907090301 090609 ﾁ0203020703 040003070903070807 ﾁ 0203 ﾁ0308 07070708030103 090303060207020908: ｨｰ09070906030301 070903000907 07 040607 ﾁ03020301 0403020300020203 0700030202: : (x 0 + u) + (y 0 + v) + (z 0 + w) 6ﾓ1 = 0: : u + v + w 6ﾓ1 ( 6ﾓ1 x 0 6ﾓ1 y 0 6ﾓ1 z 0 ) = 0: (8.10) ｨｮ03050009070203 040306010900070603 ﾁ0903 08030306030102, 090609 ﾁ0203020703 040003070903070807 ﾁ 07070708030103 090303060207020908 Oxyz 05 ﾁ000503080705 02030601090001020201, 030209070708 2 + 2 + 2 = 1. 08030508030109, 03070007 (6ﾓ1x 0 6ﾓ1y 0 6ﾓ1z 0 ) 1 7 0, 0803 090609 ﾁ0203020703 (8.10), 0304070702 ﾁ0908060303 0809 0003 040003070903070801 ﾁ 07070708030103 090303060207020908 M 0 uvw, 08030003 02030601090001020303 07 06090707080305020703 0308 020907090009 090303060207020908 05080308 07070708030102 (08. 03. 0308 M 0 ) 0203 0609 ﾁ0203 6ﾓ1 x 0 6ﾓ1 y 0 6ﾓ1 z 0 (0403 08030306030103 55.2). 02070007 0003 ( 6ﾓ1 x 0 6ﾓ1 y 0 6ﾓ1 z 0 ) < 0, 0803 02030601090001020201 0009020308 090609 ﾁ0203020703 : 6ﾓ1 u 6ﾓ1 v 6ﾓ1 w 6ﾓ1 (6ﾓ1 + x 0 + y 0 + z 0 ) = 0 07 0803050209 07070903010303 06090707080305020703 0609 ﾁ0203 (6ﾓ1 + x 0 + y 0 + z 0 ). ｨｰ0707. 8.8. ｨｮ070708030109 090303060207020908 M0uvw ﾁ 07070708030103 090303060207020908 Oxyz 0009090701 03000609030301, ﾁ 0008000301 070009070903 0103000203 0908 ﾁ03060002090801, 070803 06090707080305020703 0308 0803070907 M 0 (x 0 ; y 0 ; z 0 ) 0203 040003070903070807, 0309020902020308 02030601090001020201 090609 ﾁ020302070301 x + y + z 6ﾓ1 = 0, 0609 ﾁ0203 (M 0 ; ) = ｨO ｨOx 0 + y 0 + z 0 6ﾓ1 ｨO ｨO: 7ﾁ3 (8.11)

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 63 08060701030602 06030403020705 08070403 ﾁ0206 0309020907 080607010306 8.1. 0609040707090801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 A(1; 2; 6ﾓ13) 04030604030202070909-0005060203 ﾁ030908030609 6ﾓ1 n = 6ﾓ13 6ﾓ1 { + 5 6ﾓ1 + 2 6ﾓ1 k. ｨｰ030403020703. 0809070801 M(x; y; z) 0406030703 ﾁ030001020905 0803070909 040003070903070807. 060908020301 09030306020702090802 ﾁ030908030609 6ﾓ16ﾓ1 AM: 6ﾓ16ﾓ1 AM(x 6ﾓ1 1; y 6ﾓ1 2; z + 3): 000909 090909 ﾁ030908030602 6ﾓ16ﾓ1 AM 07 6ﾓ1 n 040306040302020709090005060202, 0803 0706 070909000506020303 0406030703 ﾁ030203020703 0609 ﾁ0203 02090008, 070803 ﾁ 090303060207020908020308 0403060103 030904070403080705 070003020908060701 03000609030301: 6ﾓ13(x 6ﾓ1 1) + 5(y 6ﾓ1 2) + 2(z + 3) = 0: 070807080209 0403070003 090406030603020705 04030009070903080705 090609 ﾁ0203020703 040003070903070807: 3x 6ﾓ1 5y 6ﾓ1 2z + 1 = 0: 080607010306 8.2. 080003070903070801 0406030603020708 0703060303 0803070909 M(0; 1; 2) 0409060900000300010203 ﾁ03090803060901 6ﾓ1 l = 6ﾓ1 6ﾓ1 { +2 6ﾓ1 + +3 6ﾓ1 k 07 6ﾓ1 m = 6ﾓ1 6ﾓ1 + 6ﾓ1 k. 0609040707090801 090609 ﾁ0203020703 05080308 040003070903070807. ｨｰ030403020703. ｨｦ03 0304060302030003020705 ﾁ030908030602030503 0406030703 ﾁ030203020705 ﾁ03090803060301 02030601090007 09 040003070903070807 05 ﾁ000503080705 ﾁ0309080306 6ﾓ1 n = [ 6ﾓ1 l ; 6ﾓ1 m] = ｨO 6ﾓ1 k ｨO 6ﾓ1 { 6ﾓ1 6ﾓ11 2 3 = 0 6ﾓ11 1 ｨO 56ﾓ1 { + 6ﾓ1 + 6ﾓ1 k : 01090001020308040708 060302 06030403020705 040300020307080108 07030308 ﾁ03080708 ﾁ090308 080301 0203080708 ﾁ070501, 09030803060203 00020007 ﾁ0204030002030202 ﾁ 04060302020209060308 030902090703: 5 (x 6ﾓ1 0) + 1 (y 6ﾓ1 1) + 1 (z 6ﾓ1 2) = 0 6ﾍ2 5x + y + z 6ﾓ1 3 = 0: 010609 ﾁ0203020703 040003070903070807 0403000907030203, 030902090709 060304030209. 000301 0203 0103020303, 06090707010308060701 06030403020703 07 020609050308 0803070907 030603020705. 0700060908070803 ﾁ02070109020703, 070803 07020907090009 00020003 02090802030203 ﾁ0309080306020303 0406030703 ﾁ030203020703 02 ﾁ0906 ﾁ030908030603 ﾁ, 09 0309-080301 04030009070302020208 ﾁ0309080306 0709090005060203 09010203000302 0209 ﾁ0309080306 6ﾓ16ﾓ1 AM, 08. 03. 04090908070703070907 ﾁ0207070700030203 070103040902020303 0406030703 ﾁ030203020703 ﾁ030908030603 ﾁ 6ﾓ16ﾓ1 AM(x; y 6ﾓ1 1; z 6ﾓ1 2), 6ﾓ1 l (6ﾓ11; 2; 3) 07 6ﾓ1 m(0; 6ﾓ11; 1), 09030803060203 05 ﾁ000508080705 090301040009-02090602020107 (040302090109080803, 040307030109). ｨｲ090407040301 070103040902020303 0406030703 ﾁ030203020703 090301040009020906020206 ﾁ030908030603 ﾁ: ｴ 6ﾓ16ﾓ1 AM; 6ﾓ1 l ; 6ﾓ1 m ｵ = 0 6ﾍ2 ｨO x y 6ﾓ1 1 z 6ﾓ1 2 6ﾓ11 2 3 0 6ﾓ11 1 ｨO ｨO = 0 6ﾍ2 6ﾍ2 x (2 1 6ﾓ1 3 (6ﾓ11) ) 6ﾓ1 (y 6ﾓ1 1) ( 6ﾓ11 1 6ﾓ1 3 0 ) + (z 6ﾓ1 2) ( (6ﾓ11) (6ﾓ11) 6ﾓ1 2 0 ) = 0 6ﾍ2 6ﾍ2 5x + y 6ﾓ1 1 + z 6ﾓ1 2 = 0 6ﾍ2 5x + y + z 6ﾓ1 3 = 0: ｨｦ080909, 04030009070700030701 0809090303 0003 090609 ﾁ0203020703 040003070903070807. 080607010306 8.3. 0609040707090801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070907 A(0; 1; 2) 07 B(6ﾓ12; 1; 0) 0409060900000300010203 ﾁ030908030609 6ﾓ1 s = 6ﾓ1 { 6ﾓ1 2 6ﾓ1 + 6ﾓ1 k. ｨｰ030403020703. ﾂ020003060301 0406030703 ﾁ030001020908 0803070909 M(x; y; z), 04060702090200030009060908 020902020308 040003070903070807. ｨｲ090407-040301 09030306020702090802 070003020908060706 ﾁ030908030603 ﾁ: 6ﾓ16ﾓ1 AM(x; y 6ﾓ1 1; z 6ﾓ1 2); 6ﾓ1 AB(6ﾓ12; 0; 6ﾓ12):

1364 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁﾂ030908030602 6ﾓ16ﾓ1 6ﾓ1 AM, AB 07 6ﾓ1 s 0903010400090209060202, 09 030209070708, 0706 070103040902020303 0406030703 ﾁ030203020703 0609 ﾁ0203 02090008, 070803 0103000203 0309040707090801 0703060303 030406030203000708030001: ｨO x y 6ﾓ1 1 z 6ﾓ1 2 6ﾓ12 0 6ﾓ12 1 6ﾓ12 1 ｨO ｨO = 0 6ﾍ2 x 6ﾓ1 z + 2 = 0: 0700060908070803 ﾁ02070109020703, 070803 ﾁ 04030009070302020301 090609 ﾁ0203020707 03080709080708 ﾁ090308 04030603010302020905 y, 04030508030109 020902020905 040003070903070801 0409060900000300010209 030707 Oy. 080607010306 8.4. 0609040704070803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070907 A(1; 2; 6ﾓ11), B(2; 1; 3), C(0; 6ﾓ12; 4). ｨｰ030403020703. 0809070801 M(x; y; z) 08030909060905 0803070909 040003070903070807. 0003050209 ﾁ0703 070308020603 0803070907 M, A, B, C 0003000908 ﾁ 040003070903070807. ｨｲ090407040301 09030306020702090802 08060306 0209040609 ﾁ000302020206 03080603030903 ﾁ 07 0300060701 02090709000301, 04060702090200030009060706, 0209040607010306 6ﾓ16ﾓ1 6ﾓ1 6ﾓ1 AM(x 6ﾓ1 1; y 6ﾓ1 2; z + 1); AB(1; 6ﾓ11; 4); AC(6ﾓ11; 6ﾓ14; 5): 000909 090909 ﾁ030908030602, 0701070107 050303010308060707030709070107 060309000703090107050107 05 ﾁ000508080705 050807 0209040609 ﾁ000302020203 03080603030907, 0903010400090209060202, 0803 070103040902020303 0406030703 ﾁ030203020703 05080706 ﾁ030908030603 ﾁ 0609 ﾁ0203 02090008: ｨｲ0902090709 060304030209. ｨO x 6ﾓ1 1 y 6ﾓ1 2 z + 1 1 6ﾓ11 4 6ﾓ11 6ﾓ14 5 ｨO = 0 6ﾍ2 11x 6ﾓ1 9y 6ﾓ1 5z + 2 = 0: 080607010306 8.5. ﾂ0207070700070803 06090707080305020703 0308 0803070907 M(5; 6ﾓ12; 0) 0203 040003070903070807 2x + y 6ﾓ1 2z + 4 = 0. ｨｰ030403020703. ｨｹ0809 030902090709, 090909 07 010203050703 020609050703, 0103000203 060304070801 0203070903000109070107 070403070300090107. 0609040607010306, 07070903010303 06090707080305020703 0308 0803070907 0203 040003070903070807 0103000203 0209080807, 030904070709 ﾁ 090609 ﾁ0203020703 0309020902020308 040003070903070807 ﾁ 02030601090001020301 ﾁ070203 07 04060701030207 ﾁ 08030306030109 55.3. 000301 0203 0103020303, 020005 06030403020705 06050209 0309020907 0701030308 0701020700 0403000907070801 05030803 ﾁ0908 04030601090009 ﾁ020707070003020705 06090707080305020705 0308 0803070907 0203 040003070903070807, 0309020902020308 0300060701 090609 ﾁ020302070301. 08030603060302 0308 030006030503 090609 ﾁ0203020705 040003070903070807 09 0203060109000102030109 03070906030708 ﾁ0701, 040302030007 ﾁ 040609 ﾁ0908 07 0003 ﾁ0908 0709070801 090609 ﾁ0203020705 Ax + By + Cz + D = 0; 0209 ﾁ03000707070209 ﾌ A 2 + B 2 + C 2, 03070007 D < 0, 070007 0209 ﾁ03000707070209 6ﾓ1 ﾌ A 2 + B 2 + C 2, 03070007 D 1 7 0. ﾂ 0603-0309000108090803 03020203 0703 090609 ﾁ0203020708 Ax + By + Cz + D ﾌ A 2 + B 2 + C 2 = 0 070007 Ax + By + Cz + D 6ﾓ1 ﾌ A 2 + B 2 + C 2 = 0 05 ﾁ000503080705 02030601090001020201. ｨｮ040609 ﾁ03020007 ﾁ03070801 0508030503 0908 ﾁ0306000203020705 040603 ﾁ0306010803 0709010307080305080300010203 07 04030103-060108 0304060302030003020705 55.1. 010005 000800030503 0403000907030202030503 090609 ﾁ0203020705 0703050009070203 08030306030103 55.3 06090707080305020703 0308 0803070907 M(x 0 ; y 0 ; z 0 ) 0203 040003070903070807 ﾁ02070707000503080705 0403 04030601090003 (M 0 ; ) = Ax 0 + By 0 + Cz 0 + D ﾌ A 2 + B 2 + C 2 : (8.12) 010005 0309030207090803000102030503 06030403020705 030902090707 020901 0307080900030701 040607010302070801 04030601090009 (8.12) 09 0707060302020201 020902-020201, 08. 03. 2 5 + 1 (6ﾓ12) 6ﾓ1 2 0 + 4 = ﾌ 2 2 + 1 2 + (6ﾓ12) 2 = 12 3 = 4:

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 65 080607010306 8.6. 01090202 040003070903070807 1 : x 6ﾓ1 y + 2z 6ﾓ1 3 = 0 07 2 : 2x 6ﾓ1 2y + 4z 6ﾓ1 5 = 0. ﾂ02050702070803, 0409060900000300010202 0007 050807 040003070903070807, 07 03070007 0209, 0803 02090802070803 06090707080305020703 0103000209 02070107. ｨｰ030403020703. ｨｮ020907090009 070309070701 ﾁ03090701020303 060907040300030003020703 0309020902020206 04000307090307080308. ｨｮ03050009070203 04030601090003 (8.8), 040003070903070807 1 07 2 0409060900000300010202, 080909 090909 090305040407010703020802 ﾁ 090609 ﾁ020302070506 040607 x, y 07 z 040603040306-010703020900010202: 1 2 = 6ﾓ11 6ﾓ12 = 2 4 : 07080103080701, 070803 040003070903070807 1 07 2 0203 0703 ﾁ040902090808, 080909 090909 09070003- ﾁ0703 (8.7) 0203 ﾁ02040300020503080705: D 1 D 2 = 6ﾓ13 6ﾓ15 = 3 5 ﾙ 1 2 : 0608030002 0209080807 06090707080305020703 0103000209 0400030709030708050107, ﾁ020003060301 0803070909 0209 0302020308 0703 04000307090307080308 07 020908020301 06090707080305020703 0308 05080308 0803070907 0203 ﾁ0803060308 040003070903070807 (0701. 060707. 8.9). 0609 040003070903070807 1 ﾁ030301010301 0406030703- ﾁ030001020908 0803070909 M 0 (x 0 ; y 0 ; z 0 ), 020005 090303060207020908 09030803060308 07040609 ﾁ03020007 ﾁ03 ｨｰ0707. 8.9. ｨｰ070709020309 09 030902090703 8.6 0609 ﾁ03020708 ﾁ03 x 0 6ﾓ1 y 0 + 2z 0 6ﾓ1 3 = 0 6ﾍ2 x 0 6ﾓ1 y 0 + 2z 0 = 3: ｨｰ090707080305020703 0308 0803070907 M 0 0203 040003070903070807 2 02090603020701 0403 04030601090003 (8.12): = 2x 0 6ﾓ1 2y 0 + 4z 0 6ﾓ1 5 ﾌ 2 2 + (6ﾓ12) 2 + 4 2 = 2(x 0 6ﾓ1 y 0 + 2z 0 ) 6ﾓ1 5 ﾌ 24 : 080302070809 ﾁ07 ﾁ 04030009070302020303 ﾁ020403 0609 ﾁ03020708 ﾁ03 x 0 6ﾓ1 y 0 + 2z 0 = 3 ﾁ 040307000302020303 0703030802030403020703, 0403000907090301 ﾌ 2 3 6ﾓ1 5 6 = ﾌ = 24 12 : 02070801 07 020609050308 070403070300 ﾁ020707070003020705 06090707080305020705 0103000209 04090609000003000102020107 0400030709030708050107. 0702 090209-00030507070302 010308030209, 07 04030103060108 0903080306030503 ﾁ02070707000500030701 06090707080305020703 0103000209 04090609000003000102020107 04060501020107 0209 040003070903070807 (070806. 49). ｨｰ0304070803 030902090709 0508030503 04060701030609 0809090701 0704030703000301 0709010307080305080300010203. 080607010306 8.7. 01090202 040003070903070807 1 : x + y + 2z 6ﾓ1 3 = 0 07 2 : 2x 6ﾓ1 y + 4z 6ﾓ1 5 = 0. 06090802070803 ﾁ03000707070209 02 ﾁ090506090202030503 09050009 0103000209 02070107. ｨｰ030403020703. 0803060307030909080607030705 040003070903070807 0300060903090808 070308020603 02 ﾁ0905060902020206 09050009 ﾁ 04060307080609020708 ﾁ03. ｨｦ06 ﾁ03-000707070202 ' 07 04030409060203 0609 ﾁ0202, 040607070301 '+ =. 0105000301 0103000209 0400030709030708050107 02090302 ﾁ0903080705 ﾁ03000707070209 0103020104030503 0703 09050003 ﾁ ' 07. ﾂ030301010301 02030601090007 09 05080701 04000307090307080501 6ﾓ1 n 1 (1; 1; 2) 07 6ﾓ1 n 2 (2; 6ﾓ11; 4). 02070007 09050300 0103000209 02070107 0203 040603- ﾁ03070603020708 =2, 0803 0302 0703 ﾁ040902090308 07 0905000301 0103000209 0400030709030708050107 (040307030109?). ｨ 03070007 05080308 09050300 0809040308, 0803 0709010109 09050003 ﾁ 0103000209 020306010900050107 07 0400030709030708050107 0703070809 ﾁ0708. ﾂ 0008000301 070009070903 09030707020907 09050009 0103000209 0400030709030708050107 ﾁ02070707000503080705 090909 cos ' = ｨO cos(6ﾓ1 n 0ｼ86ﾓ1 1 ; n 2 ) ｨO : 01050300 0103000209 ﾁ0309080306090107 ﾁ02070707000503080705 0703060303 070909000506020303 0406030703 ﾁ030203020703: cos ' = ｨO ｨO 1 2 + 1 (6ﾓ12) + 2 4 ｨOｨOｨOｨO ﾌ 1 2 + 1 2 + 2 2 ﾌ 2 2 + (6ﾓ11) 2 + 4 2 = ﾌ 4 : 126

1366 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 0503020806030001020203 ﾁ030406030702 8.1. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807 ﾁ 0300060301 ﾁ070203. 05090903 ﾁ 0503030103080607070307090708 0701020700 09030504040701070302-0803 ﾁ, 07080305060706 ﾁ 05080301 090609 ﾁ0203020707 0403060302 x, y, z? 8.2. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807 0403 0803070903, 04060702090200030009060308 05080308 040003070903070807, 07 ﾁ030908030609 020306-01090007. 8.3. 050909 0703070809 ﾁ070801 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 080607 0803070907? 8.4. 07040704070803 060903000707020203 070009070907 0203040300020206 090609 ﾁ0203020708 04000307090307080308. 8.5. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807 ﾁ 0308060303090906. 01090900070803 09030306020702090802 0909090308-00070003 0703 0203060109000308 09 05080308 040003070903070807. 0509090703 040003070903070807 0203 0304070702 ﾁ0908080705 090609 ﾁ020302070301 ﾁ 0308060303090906? 8.6. 0509090303 090609 ﾁ0203020703 040003070903070807 02090302 ﾁ0903080705 02030601090001020201? 050909 03040603020300070801 06090707080305020703 0308 020907090009 090303060207020908 0203 040003070903070807? 8.7. ｨｮ040306010900070609080803 09070003 ﾁ0705 0409060900000300010203070807 07 040306040302020709090005060203070807 04000307090307080308. 8.8. 0509090701 03000609030301 0103000203 03040603020300070801 09050300 0103000209 0400030709030708050107? ｨｲ0902090707 8.1 71. 080307080603080803 040003070903070807: 09) 2x + 3y + z = 6; 00) x 6ﾓ1 4y + z 6ﾓ1 5 = 0; ﾁ) x 6ﾓ1 y 6ﾓ1 z = 0; 05) x + 2y 6ﾓ1 3z = 0; 02) 4x + y = 8; 03) x + z 6ﾓ1 2 = 0; 00) x 6ﾓ1 3 = 0; 03) 2y = 5: ﾂ 0909090706 080307090906 050807 040003070903070807 04030603070309090808 090303060207020908020203 030707? 8.2 71. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 M(1; 6ﾓ12; 6ﾓ11) 040306040302020709090005060203 ﾁ030908030609 6ﾓ1 n = 2 6ﾓ1 { 6ﾓ1 6ﾓ1 +5 6ﾓ1 k. 8.3 71. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 A(1; 1; 0) 07 040906090000030001020308 ﾁ03090803-060901 6ﾓ1 a = 6ﾓ1 { + 2 6ﾓ1 6ﾓ1 5 6ﾓ1 k 07 6ﾓ1 b = 6ﾓ12 6ﾓ1 + 3 6ﾓ1 k. 8.4 71. 080003070903070801 0406030603020708 0703060303 0803070907 A(6ﾓ12; 3; 4) 07 B(1; 0; 1) 0409060900000300010203 ﾁ030908030609 6ﾓ1 l (1; 6ﾓ11; 2). 06090802070803 090609 ﾁ0203020703 05080308 040003070903070807. 8.5 71. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 080607 0803070907 A(0; 6ﾓ11; 6), B(1; 1; 5) 07 C(1; 4; 5). 8.6 71. 010609 ﾁ0203020705 020902020206 04000307090307080308 0309040704070803 ﾁ 02030601090001020301 ﾁ070203: 09) 2x 6ﾓ1 2y + z 6ﾓ1 3 = 0; 00) x + 2y 6ﾓ1 z + 1 = 0; ﾁ) 4x 6ﾓ1 4y 6ﾓ1 2z + 1 = 0; 05) 3y 6ﾓ1 z + 2 = 0; 02) 3x + 4z 6ﾓ1 1 = 0; 03) 6ﾓ1 x + 3 = 0: 8.7. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070907 A(2; 3; 0) 07 B(6ﾓ12; 0; 1) 040906090000030001-0203 030707 Ox. 8.8. 080003070903070801 0703020306000708 030701 Oy 07 0803070909 C(1; 3; 2). ｨｲ09040704070803 090609 ﾁ0203020703 05080308 040003070903070807. 8.9. ｨｲ09040704070803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 D(6ﾓ12; 6ﾓ13; 1) 0409060900000300010203 09030306-0207020908020308 040003070903070807 Oyz. 8.10. 01090202 0803070907 P(4; 6ﾓ17; 2) 07 Q(5; 6ﾓ13; 1). 080003070903070801 0406030603020708 0703060303 0803070909 P 040306040302020709090005060203 ﾁ030908030609 QP. 6ﾓ1 06090802070803 090609 ﾁ0203020703 05080308 040003070903070807. 8.11. 06090802070803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070909 A(0; 1; 6ﾓ12) 0409060900000300010203 040003070903070807 2x 6ﾓ1 y 6ﾓ1 4z + 3 = 0. 8.12. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0803070907 M(6ﾓ12; 3; 1) 07 K(1; 0; 3) 040306040302-020709090005060203 040003070903070807 5x + 2y + z 6ﾓ1 1 = 0.

13ｨｬ0309010707 0403 09020900070807070307090308 050303010308060707 67 8.13. 01090202 090609 ﾁ0203020705 04000307090307080308: 09) x 6ﾓ1 2y + z + 3 = 0; 00) 4x + 2y 6ﾓ1 1 = 0; ﾁ) 2x 6ﾓ1 y + 7 = 0; 05) 3x 6ﾓ1 6y + 3z + 1 = 0; 02) 3x 6ﾓ1 1 = 0; 03) z = 2: ｨｦ03 05080706 04000307090307080308 ﾁ02000306070803 04090602 040906090000030001020206 07 04030604030202070909000506020206 04000307090307080308. 8.14. 080003070903070801 0308070309090308 0209 090303060207020908020206 03070506 Ox, Oy, Oz 03080603030907 1; 5; 4 07030308 ﾁ03080708 ﾁ03020203. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 05080308 040003070903070807 07 09090900070803 09030306020702090802 0302020308 0703 0203060109000308 09 05080308 040003070903070807. 8.15. 080003070903070801 0409060900000300010209 030707 Ox 07 0308070309090308 0209 03070506 Oy 07 Oz 03080603030907 2 07 3 07030308 ﾁ03080708 ﾁ03020203. ｨｲ09040704070803 090609 ﾁ0203020703 05080308 040003070903070807. 8.16. 06090802070803 09050300 0103000209 0400030709030708050107: 09) x + y + 1 = 0; y 6ﾓ1 z + 1 = 0; 00) x 6ﾓ1 3y 6ﾓ1 2z + 1 = 0; x + y 6ﾓ1 z + 2 = 0; ﾁ) x 6ﾓ1 y + 1 = 0; 6ﾓ14x + 4y + 3 = 0; 05) z = 1; z = x; 02) 3x 6ﾓ1 y = 0; 2x + y + 2 = 0; 03) 4x + 3z + 7 = 0; x + 2y + 2z + 3 = 0: 8.17. 06090802070803 06090707080305020703 0308 0803070907 M(5; 6ﾓ12; 0) 0203 040003070903070807 2x + y 6ﾓ1 2z + 4 = 0. 8.18. 07040603020300070803 06090707080305020703 0103000209 04090609000003000102020107 0400030709030708050107 x 6ﾓ1 2y + 2z + 1 = 0 07 4x 6ﾓ1 8y + +8z 6ﾓ14 = 0. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 050303010308060707030709030503 0103070809 0803070309, 0609 ﾁ0203090209000302020206 0308 05080706 04000307090307080308. 8.19. 0609040704070803 090609 ﾁ0203020705 04000307090307080308, 040906090000030001020206 040003070903070807 6x6ﾓ12y+3z+1 = 0 07 030807080305060706 0308 020303 0209 06090707080305020707, 0609 ﾁ020301 2. 8.20. 07040603020300070803 09030306020702090802 0803070907 0403060307030703020705 04000307090307080308 2x 6ﾓ1 y + z = 2; 3x + 2y + 2z = 6ﾓ12; x 6ﾓ1 2y + z = 1. 8.21. ｨｮ03070809 ﾁ010803 090609 ﾁ0203020703 040003070903070807, 04060306030205060308 0703060303 0007020708 0403060307030703020705 04000307090307080308 x6ﾓ12y+ +z = 4, 2x + 3y 6ﾓ1 z = 3 07 0803070909 A(0; 1; 2). 8.22. 080607 ﾁ0302070803 090609 ﾁ0203020705 04000307090307080308 09 0203060109000102030109 ﾁ070209 07 03040603020300070803 06090707080305020703 0308 020907090009 090303060207020908 0203 05080706 04000307090307080308: 09) 2x + y 6ﾓ1 2z + 3 = 0; 00) 3x 6ﾓ1 y + z + 2 = 0; ﾁ) x 6ﾓ1 y + 2z 6ﾓ1 3 = 0; 05) 4x + 2y 6ﾓ1 z + 2 = 0: 8.23 6ﾓ5. 06090802070803 09030306020702090802 0406030309010707 0803070907 A(2; 6ﾓ11; 2) 0209 040003070903070801 3x 6ﾓ1 y + z + 2 = 0. 8.24 6ﾓ5. ﾂ0207070700070803 09030306020702090802 0803070907 Q, 070701010308060707020308 0803070903 P(2; 1; 1) 030802030707080300010203 040003070903070807 x 6ﾓ1 2y 6ﾓ1 z + 3 = 0. 8.25 6ﾓ5. 06090802070803 090609 ﾁ0203020705 04000307090307080308, 02030005060706 04030403000901 02 ﾁ0905060902020208 09050300, 030006090303 ﾁ0902020208 04000307-09030708050107: 09) x + y = 0; x + z = 1; 00) 2x + 2y + z + 9 = 0; 4y + 3z 6ﾓ1 1 = 0: 0109090309020703: 0803070907 040003070903070807, 02030005060308 04030403000901 02 ﾁ0905060902020208 09050300, 03080708030508 0308 030503 050609020308 0209 03020702090903 ﾁ0206 0609070708030502070506. 8.26 6ﾓ5. 080003070903070801 2x 6ﾓ1 y + 2z = 0 05 ﾁ000503080705 000707070309080306020308 04000307090307080108 02 ﾁ090506090202030503 09050009, 03000609-0303 ﾁ090202030503 04000307090307080108 1 : 2x + 4y 6ﾓ1 4z 6ﾓ1 5 = 0 07 04000307090307080108 2. 06090802070803 090609 ﾁ0203020703 040003070903070807 2. 8.27 6ﾓ5. 06090802070803 080308 09050300 0103000209 0400030709030708050107 x 6ﾓ14y 6ﾓ12z 6ﾓ18 = 0 07 6ﾓ16x 6ﾓ13y +z 6ﾓ16 = 0, ﾁ 09030803060301 0003000708 0803070909 A(0; 6ﾓ12; 4). 8.28 6ﾓ5. 06090802070803 0103020806 04090609, ﾁ040707090202030503 ﾁ 0803080609050206, 030902090202030503 ﾁ0306040702090107 A(6ﾓ16; 4; 4), B(6ﾓ11; 0; 6ﾓ13), C(6ﾓ13; 6ﾓ12; 6ﾓ12) 07 D(1; 6ﾓ14; 2).

1368 ｨｮ. 050900030403 ﾁ, ｨ. ｨｮ0900070103 ﾁ09, ｨｮ. ｨｮ0809 ﾁ0103 ﾁ 050900030403 ﾁｨｮ0306050308 ｨ 000309070303 ﾁ0707, 02040102, 040603040307070306 09090403020602 ﾂ0207040905 01090803010908070909" ﾂ0303020203- ﾁ0303020904020308 ｨ 09090203010707 0701030207 04060304. 06. 02. 02090903 ﾁ0709030503. Email: KuleshovSergej@rambler.ru ｨｮ0900070103 ﾁ09 ｨ 0001040705 0309070303 ﾁ0209, 090402, 020301030208 080308 0003 09090403020602. Email: afsalimova@mail.ru ｨｮ0809 ﾁ0103 ﾁｨｮ08090207070009 ﾁｨｬ030302070203 ﾁ0707, 09040102, 020301030208 080308 0003 09090403020602. Email: stav@inm.ras.ru

13ｨｦ020403060109010705 0708 0603020909010707 ｨｹ00030908060302020203 06030709060702 ｨ. 04. ｨｪ0509070403 ﾁ09 08090000070909010707 020904030503 0403070803050202030503 09 ﾁ08030609 ｨ. 04. ｨｪ0509070403 ﾁ09 0103000203 0209080807 0403 090206030709: http://www.geometry.ru/persons/myakishev/text.htm ﾂ 0500030908060302020301 00090602090003 08030007020301", 0203010306 2 0304090000070903 ﾁ090209 030503 070809080105 03 0806030905030001020206 04060909-0809000906: http://www.mathedu.ru/e-journal/ ｨｹ00030908060302020905 ﾁ0306070705 070809080107 ｨ. ｨ. 0603060308070209 ｨｹ00030908060302020905 ﾁ0306070705 070809080107 ｨ. ｨ. 0603060308070209, 0304090000070903 ﾁ0902020308 ﾁ 020301030603 2(50), 2009 05., 02090603-0207080705 0209 0709080803 www.polit.ru ｨｲ090103070302020905 0304030709080909 ﾁ 020301030603 2(50), 2009 05. 0609 070806. 1 (03050009 ﾁ0003020703), 070806030909 12 0702070309: 02090403070908090203: 07030602060306090503000102070909"; 07000302090308 070708090801: 07030802060306090503000102070909". 0003 0003 0209 070806. 31, 070806030909 2 07 ﾁ03060609. 69

1307 0303020203 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 03030202 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 070303020902 ﾁ 0903020103 1996 05. 07 0103000108 070403-0703000708 ﾁ03 ﾁ090801 07030606090203020708 00030509080206 0806090207010708 010908030109080707030709030503 030006090303 ﾁ09020705 07 0209090907 ﾁｨｰ0307070707. 03030202 070308060902020707090308 07 03060509020703090107050107 07 05060900020902090107, 000300090806070107 0907090708 ﾁ03 ﾁ090801 ﾁ 0000090503060302020301 02030003 07030606090203020705 ﾁ02070309030503 090907030708 ﾁ09 0603070707080709030503 010908030109080707030709030503 030006090303 ﾁ09020705. 03030202 040302020306-0007 ﾁ090308 030006090303 ﾁ0908030001020203 0702070107090807 ﾁ02, 0209040609 ﾁ000302020203 0209 02030708070003020703 0403070809 ﾁ000302020308 01030007. 070703000303 ﾁ02070109020703 0309090302 ﾁ0903080705 030006090303 ﾁ0908030001020201 0702070107090807 ﾁ0901 ﾁ 040603 ﾁ0702010707, 090909 ﾁﾁ070203 070302090803000107090308 040302020306000907, 080909 07 04070209020703 ﾁ0308 040301030607. 03030202 0704030703000708 ﾁ090308 07030209020708 02090907020308, 09070300020308 07 01030803-0207070307090308 00070803060908090602 ﾁ 03000009070807 01090803010908070907 07 07010300020206 02090909. 01070003 ﾁ0705 0403020407070907 07 040607030109 010908030607090003 ﾁ 0803 ﾁ03040603070901 0403020407070907 0209 000906020900 0300060906090808030701 0403 0803000304030209: (495) 107-31-46. ｨ 02060307 020005 090306060307040302020302010707 0303020209: 141075 05. 050306030003 ﾁｨｪ03070903 ﾁ07090308 030000., 0406-08 05030701030209 ﾁ0803 ﾁ 9-167. E-mail: matob@yandex.ru ｨｮ0803070103070801 0403020407070907 0209 090900020208 0703 020301030603 ﾁ 1-4 0309 2009 050302 ( ﾁ090008070905 070803070103070801 040306030702000907) { 60 060900000308. 010005 040300090703020705 020301030603 ﾁ 00090602090009 02030300060302070103 ﾁ020700090801 ﾁ 0902060307 0603020909010707 0903040708 04000908030002030503 020309090103020809, 04030208 ﾁ03060002090806030503 030400090809 0403020407070907. ｨｮ03030006070803 0902060307, 0403 0903080306030109 ﾁ02 060308030007 0002 0403000907090801 000906020900. ﾂ 040009080300020301 020309090103020803 09090900070803, 070803 04030603 ﾁ0302 0203000903080705 020005 00090602090009 ｨｪ090803-01090807070307090303 030006090303 ﾁ09020703", 0203010306 00090602090009 0309 2009 05., 0903000707030708 ﾁ03 05090303010400050603 ﾁ. ｨｰ0309 ﾁ0703070802 020005 040306030707070003020705: 08030009070908030001: ｨｦ0606 7725080165 03030202 010908030109080707030709030503 030006090303 ﾁ09020705 07 04060307 ﾁ030603020705 ｨｰ0907070308020208 07070308 07 00090209 04030009070908030005: 06/07 40703810700010001416 ﾁ 07ｨ 07 09090209 ｨｰ0903 ﾁ07080703-ｨｮ080300070109", 05. ｨｪ030709 ﾁ09, 09/07 30101810000000000984, 09ｨｦ05 044525984, 07050807 45084342 ﾂ02 0809090003 010300030803 0309090903090801 0203030006030207010303 ﾁ0901 0903000707030708 ﾁ03 030802030001020206 020301030603 ﾁ 00090602090009 0309 040603-02020209060703 05030202. ﾂ 05080301 070009070903 040306030702000909 03070906030708 ﾁ000503080705 02090003000302020201 0400090803000301 070007 0209 03070203- ﾁ09020707 04000908030002030503 020309090103020809 (060309 ﾁ0703070802 0803 0003). ﾂ 030909090303 ( ﾁ 040009080300020301 020309090103020803) 09090900070803, 0309 0909090703 020301030609 07 ﾁ 0909090301 0903000707030708 ﾁ03 05090303010400050603 ﾁ 0309 0203010306, 0203000903080705 040306030707070003020703. ｨｮ0803070103070801 030202030503 05090303010400050609 00090602090009 (07 090703080301 040306030702000907) 50 060900. ｨｰ03020909010705 040607020701090308 0609090304070707 010908030607090003 ﾁ 07 0703080903 04060306070703 ﾁ090202020107 040306010900090107. 0803 0703050009-0703 ﾁ09020708 07 060302090901070308 0406070207010908080705 010908030607090002 ﾁ 0500030908060302020301 ﾁ070203, 0300050309080300010203 040607000905090801 060907-04030709080909. ｨｰ09090304070707 0203 ﾁ0303 ﾁ0609060908080705 07 0203 06030103020307060908080705. 0803070003 04090000070909010707 09 ﾁ08030607090703 040609 ﾁ09 0703060609-020508080705 0309 09 ﾁ080306090107 010908030607090003 ﾁ. ｨﾁ08030602 0304090000070903 ﾁ0902020206 010908030607090003 ﾁ 0403000907090808 000307040009080203 0403 10 050903. 07030308 ﾁ03080708 ﾁ090806030503 ﾁ020409070909 00090602090009. ｨｪ0203020703 0603020909010707 0203 ﾁ0703050209 0703 ﾁ040902090308 07 01020302070301 09 ﾁ08030603 ﾁ.

13Mathematical Education 6 54(52), 2009 Contents V. Drozdov. Seven Geometric Problems 2 Let G be the mass center of a triangle, H be the orthocenter, and L be the center of the inscribed circle. The conditions for GH, GL, HL to be parallel or/and orthogonal to a side of the triangle are analyzed. The exposition is based on vector approach. E. Potoskuev. On Necessity of Argument while Solving Stereometric Problems 11 Argument is still necessary if some stereometric fact seems to be intuitively clear" or evident". This is illustrated by numerous examples. V. Motanov. Reduction of Optimization Problem with a Homographic Functional to that with a Linear Functional 19 It is shown that a problem of optimization with a homographic functional can be reduced to that with a linear functional by a projective transformation which conserves nonnegativity of variables. H.J.M. Bos. Basic Concepts of Leibnitz Calculus 24 It is shown that Leibnitz calculus based on the concept of variable" and progression of a variable" (in opposition to the modern concept of function) is a self-consistent, beautiful and applicable theory. S. Kuleshov, A. Salimova, S. Stavtsev. Lectures on Analytic Geometry (continued) 36 Themes 7 and 8, equation of a straight line in plane and equation of a plane in space are considered. Information 69

13ｨｪｨ 0002ｨｪｨ 00ｨｦ1 702ｨｮ ｨｰｨ ｨｲ071 7ｨ 06ｨｦ02, ISSN

13ｨｪｨ 0002ｨｪｨ 00ｨｦ1 702ｨｮｨｰｨｨｲ071 7ｨ 06ｨｦ02, ISSN