( ( ( 43037 3 0 (Nicolas Bourbaki (Éléments d'histoire des athématiques : 984 b b b n ( b n/b n b ( 0 ( p.3 3500 ( 3500 300 4 500 600 300 (Euclid (Eukleides : EÎkleÐdhc : 300 (StoiqeÐwsic 7 ( 3 p.49 ( 97
( 97 978 0 3 4 5 6 7 8 9 0 ( 3 ( 0 5 3 0 3 0 ( 6 ( 7 3 30 7
( (Rosetta Stone (Napoléon Bonaparte : 7698 799 8 ( 4.4cm 7.3cm 7.9cm 760kg 3 ( 3 ( ( 5 (Ptolemaios : 8 (Jean-François Champollion : 79083 (Thomas Young : 77389 ( 3 ( 3 ( 3m ( ( 0 00 000 0000 0 00 0 0 00,000 0,000 0 00 3 4 5 6 7 0 00 C,000 0,000 ( 0 ( 3
00 ( 43037 4445555 964 http://www-groups.dcs.st-and.ac.uk/history/ HistTopics/Egyptian_numerals.html 0 00 000 0 30 964 0 4 (Rhind athematical Papyrus (oscow athematical Papyrus (Alexander Henry Rhind : 833863 858 ( (August Eisenlohr : 8390 (Ahmes 650 3 (Amenemhat : 849 80 33cm 5.5m (Vladimir Semnoviq Goleniwev (Vladimir Semyonovich Golenishchev : 856947 893 ( 060 580 7.6cm 4.6m 4
m n 3 n n 3 ( n n 3 3 ( 5 0 n n 5 3 5 39 6 78 73 60 9 9 365 7 4 8 4 4 46 38 75 50 50 9 6 8 43 4 86 9 30 77 44 308 6 66 45 30 90 79 60 37 36 790 3 8 5 04 47 30 4 470 8 54 6 5 0 30 49 8 96 83 60 33 45 498 7 5 68 5 34 0 85 5 55 9 76 4 53 30 38 795 87 58 74 4 4 55 30 330 89 60 356 534 890 3 76 57 38 4 9 70 30 5 5 75 59 36 36 53 93 6 86 7 8 54 6 40 44 488 60 95 60 380 570 9 4 58 74 3 63 4 6 97 56 679 776 3 0 4 55 65 39 95 99 66 98 33 66 67 40 335 536 0 0 0 303 606 35 30 4 69 46 38 37 4 96 7 40 568 70 ( n 5 = 5 + 5 = 3 + 5 = 4 + 0 + 0 7 = 4 + 8 = 6 + 4 + ( 5
( ( 0 = = = 4 n (n + ( n+ 0 (i (ii n ( 0 n ( 0 (iii (iv 4 80 ( 69 80 (i 80 0 800 (ii 0 4 0 4 60 (iii 4 4 30 (iv (v 4 80 = (0 + 4 80 = 800 + 30 = 0 4 80 ( + 4 + 8 80 = 60 + 30 + 640 = 0 9 7 6
3 n (i (ii n ( n ( (iii (iv 9 8 ( 4 8 6 4 4 8 (i 8 (ii 4 4 8 8 (iii 9 (iv (v 9 8 = + 4 + 8 696 9 9 58 4 6 8 3 6 464 (i 9 (ii 4 8 6 4 8 6 (iii 696 (iv (v 696 9 = 8 + 6 = 4 n 5 5 = 5 = ( + + = + + = ( + 4 + ( + 4 4 + = 4 + 4 + 4 = + 7 + = 7 + = ( 7 + 4 + 4 = 7 + 4 + 4 5 = 7 + 4 + 4 7
( 30 3 0 0 3 0 0 3 3 0 3 5 4 3 5 8 6 0 30 3 0 3 9 3 0 5 0 30 30 30 30 3 0 3 30 30 3 0 3 3 3 ( x 3 + = 0 x 0 0 ( + ( 3 0 3 = + 3 0 ( + 4 + 8 = ( + ( 3 0 + + + ( 3 5 + 5 + + + 3 5 5 ( 3 + 0 4 = 8 = + 3 3 3 8 = 8 = 4 = + 0 0 5 5 5 = ( + ( 3 0 + + + + ( 3 3 5 + 5 + + + + + 3 3 5 3 5 = ( + ( ( 3 0 + 3 + 5 + 6 + 5 = ( 3 + 0 + ( 3 + 5 = 9 + 3 + 0 + 5 + 0 + 30 + ( 6 + 0 + 30 = 9 + 0+3++3+ = 9 + 9 30 30 3 0 30 ( + 30 3 0 ( 3 + 0 ( 3 + 3 30 = 60 30 + 30 0 = 3 ( 3 + 0 = 9 + 3 + 0 + 5 + 0 + 30 + 30 3 + 3 3 = 30 = 0 3 7 5 8
(3 ( ( 500 3 3000 ( 890 595 : /3 3 600 59 ( : Y (0 : < http://www-groups.dcs.st-and.ac.uk/history/histtopics/babylonian_numerals.html 59 60!! Y 60 3600 = 60 60 9
( 60 60 60 3 60 60 3 60 3600 = 60 60 3 60 60 603 (i (ii ( (iii ( 43037 43037 = 3600 + 57 60 + 7 60 n = 60 + 57 60 + 7 57 7 8 0 47 8 3600 + 0 60 + 47 = 00847 60 n 3 + 60 + 3 60 = 3600 3600 + 0 3600 + 3 3600 = 373 3600 = 4 00 =.03466.05 + 5 00 = 05 00 = 4 0 = 3 60 = + 3 60 3 4 964 0
YBC789 8cm ( YBC the Yale Babylonian Collection 30, 4, 5, 0 4, 5, 35 http://cerebro.xu.edu/~otero/math47/plimpton/ybc789.html 3 30 a = 0 30 =, 4, 5, 0 b = 4, 5, 0 4, 5, 35 c = 0 4, 5, 35 b = + 4 60 + 5 60 + 0 60 3 = 30547 =.44969696.4496 600 c = 4 60 + 5 60 + 35 60 3 = 30547 = 0.70706484848 0.7070648 4300 a b = c b.4496.44356 5!! a b = c 0 30 0 4, 5, 35 ( = 0.7070648 (>Hrwn (Heron of Alexandria : 60? x a min( x max( x b i = x a i a i+ = a i + b i (i = a a x b r = a r x = a r
(4 60 59 59? 36 36 36 36 9 5, 4 36 7 0, 36, 36 0 6 (6, 0 36 8 0, 48 36 3, 48 36 6, 36 36 9, 4 36 4, 4 36 7, 36 0 (, 0 36 5 3 (3, 0 36 3 7, 48 36 30 8 (8, 0 36 6 3, 36 36 4 8, 4 36 40 4 (4, 0 36 7 4, 36 5 9 (9, 0 36 50 30 (30, 0 36 8 4, 48 36 6 9, 36 (60 3, 40, 8 36 3, 40, 8 36 4, 48 8 36 = 4, 48 4, 0 40 36 = 4, 0 7, 48 3 36 = 7, 48 7, 7, 4, 48 7 =, 8,, 4, 48 3, 40, 8 36 = 8,, 4, 48 ( 3 53 = (30 + (50 + 3 = 30 50 + 30 3 + 50 + 3 = 5, 0 +, 30 +, 40 + 6 = 7, 76 = 8, 6
a b = a b 30 6 3, 45 45, 0 3 0 8 3, 0 48, 5 4 5 0 3 50, 5 4, 30 54, 6, 40 6 0 5, 4 8 7, 30 7, 3, 0, 4 56, 5 9 6, 40 30, 50 0 6 3, 5, 30, 5 48 5 36, 40, 0 45 5 4 40, 30, 44, 6, 40 6 7 6 7 = 6 = 6 0 ;, 3, 0 = 0 ;, 78, 0 = 0 ;, 80 7 = 0 ; 3, 0 7, 9, 4 09 64 7, 9, 4 = 7, 9, 4 = 7, 9 0 ; 0, 56, 5 = 6 ; 4, 4, 5 7, 9 0 ; 0, 56, 5 55, 35 95, 504 95, 759, 35 6 ; 4, 4, 5 5 8, 50 36 6 3 3
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