Pierre Simon Laplace : 749827) 2 Christopher Columbus : 45506) Vasco da Gama : 469524) 400 650 024 2 0 ) 048576 2 20 ) 024 048576 07374824 log 2 024 048576) 2 30 0 + 20 30 2 n!! log a MN = log a M + log a N M log a N = log a M log a N log a M k = k log a M log a k M = log a M k = k log a M a n = M log a M = n 6 7 a n n sin α sin β = 2 {cosα + β) cosα β)}
i) M C F Richter : 900985) 935 00 km 2800) A µm) M L = log 0 A 20 933 8 20 90 ) ii) ph ph mol/l [H + ] ph = log 0 [H + ] = log 0 [H + ] 909 Søren Peter Lauritz Sørensen : 868939) 25 C ph 7 ph 7 ph 7 ph 7 ) ph 2 3 5 8 iii) db 2 ) A B n db) B n = 0 log 0 A A mw 0 2 W 2
) John Napier : 55067) Merchiston Castle) 594 64 Mirici logarithmorum canonis constructio : 69 ) 3 pp78 92) 2 2 26 T g d g S b c i a a TS ds g T d bi i a g T b i a c bc ds 28 o T d S g g g b c a i ST T o os TS TS ds ds bc Td ot 3
24 ) ot Td TS os g o T g T d ) a b c ot Td bc g T o T T d T 26 ) a a bc g ot g Td bc 2 ot Td ot bc Td 26 TS bi g TS T S a bi b i T b g g g 2 g 3 a a a 2 a 3 TS : Tg = g S : g g 2 = g 2 S : g 3 g 3 = = r : g ba = a a 2 = a 2 a 3 = a T g g 2 g 3 g S b a a 2 a 3 a i 2 g a ba gs TS : Tg = r : Tg = TS r g S = TS Tg = TS r TS = ) TS r g g 2 = r g S g 2 S = g S g g 2 = ) g S = r r n g n S = ) n TS r ) r TS r = g n S = ) n a a n ba n = n ) TS = ) 2 TS r 4
) n n [ ) n ] n Nog = ) y y = Nog ) e = lim n + n = n=0 = 27828 log n! e = ) y = ) y log e = log e ) y = y log e ) log e t) = t t2 2 t3 3 log e ) = 2 0 4 3 02 log e y log e y ) = y = 07 log e Nog log e y Nog = 07 log e = 07 log e log e = y log e ) y = Nog = log e = log e log e log e = e n 036788 log e log e log e ) log e 5
= ) 0 Nog = 0 = ) Nog ) = Nog L = Nog M = y Nog N = z L = ) M = ) y N = MN L = 07 ) y ) 0 0 7 z 7 0 7 = Nog MN L Nog MN L ) y+z ) = 07 = y + z = Nog M + Nog N Nog L L = = 0 Nog MN = Nog M + Nog N M = y = 0 Nog N ) = Nog N Nog L L Nog M 2 ) z ) y ) z ) = Nog MM = Nog M + Nog M = 2 Nog M Nog Nog M 2 + Nog M = 2 Nog M + Nog M = 3 Nog M 07 Nog M k k ) = k Nog M M 3 = Nog MN = Nog M + Nog N Nog M N = Nog M Nog N sin 6
Mirici logarithmorum canonis descriptio : 64 ) 4 ) Gr 0 0 + 0 0 0 0000000 60 2909 842530 842530 0 0000000 59 2 588 74493838 74493836 2 9999998 58 27 78539 48467450 4846742 308 9999692 33 28 8448 4803756 4803424 332 9999668 32 29 84357 47752826 47752470 356 9999644 3 30 87265 4743909 4743528 38 999969 30 Gr 0 0 + 30 87265 4743909 4743528 38 999969 30 3 9074 47085992 47085585 407 9999593 29 32 93083 46768488 46768055 433 9999567 28 57 65799 4099564 40994266 375 9998625 3 58 68707 4082769 40820346 423 9998577 2 59 766 40650809 40649336 473 9998527 60 74524 4048278 4048258 523 9998477 0 Gr 44 44 + 30 7009093 3553768 7454 3379227 732504 30 3 7067 3550809 68723 3382086 730465 29 32 70324 3547852 62906 3384946 728426 28 57 7064894 347447 7454 345707 7077236 3 58 7066953 347557 635 3459922 707580 2 59 70690 3468645 587 3462828 707324 60 707068 3465736 0 3465736 707068 0 7
r = O P H POH = α PH = POH = α ) = Nog log e = r log PH e OP = r log e sin α Nog sin α r Nog 30 sin 30 = 05 = sin 30 = 5000000 5000000 = ) = Nog 5000000 69347459 69347 log e sin 30 69347806 45 sin 45 07070678 = sin 45 707068 707068 = ) = Nog 707068 3465735463 3465735 3465736 log e sin 45 3465735903 60 sin 60 08660254038 = sin 60 8660254 8660254 = ) = Nog 8660254 43840338 43840 log e sin 60 43840362 O α P H log Nog = e log e log e ) log e Nog 8
2) Henry Briggs : 556?630) 596 69 Sir Henry Savile : 549622) 69 65 66 0 0 0 ) 67 000 Logarithmorum chilias prima) 624 Arithmetica logarithmica) 5 p) 2 4 8 6 32 64,28 A A B C D 5 5 35 2 2 6 8 32 4 3 7 29 8 4 8 4 26 6 5 9 7 23 32 6 0 20 20 64 7 23 7 28 8 2 26 4 B C D logarithmus lìgoc ) Ćrijmìc ) Log Log Nog Log = Nog Nog Nog Nog 0 = log 0 Nog Nog = Nog ) = k = 07 ) k 9
log 0 = log 0 ) k log = k log 0 0 ) Nog Nog 0 = Nog ) = l 0 0 = 07 log 0 0 = log 0 ) l = l log 0 ) Log = k l = log 0 log 0 ) log 0 ) = log 0 ) l 5 ) 0,00000,00000,0000 4343,8370 2 0,3002,99956,6398 99995 4,99997,82847,3302 7609,2590,5568 4343,4026 3 0,4772,2547,966 99996 4,99998,26278,7328 2493,87366,0830 43430,9683 4 0,60205,9993,2796 99997 4,99998,69709,70 969,0030,0806 43430,5340 5 0,69897,00043,3602 99998 4,99999,340,235 798,2460,4762 43430,0996 6 0,7785,2503,8364 99999 4,99999,56570,3347 6694,67896,3062 43429,6653 00000 5,00000,00000,0000 0300 0477 3,) 00000 5 4 Log MN = Log M + Log N Log M = Log M Log N N Log M k = k Log M Log 0 n M = n + Log M 4 0
3) Jost Bürgi : 552632) 588 620 Arithmetische und geometrische Progress-Tabulen) 0 7 + 0 4 0 8 Bog = 0 8 + 0 4 ) y = 0 8 + ) y 0 4 y = Bog 0 0y 0 230000 7 ) 0y 7 ) 0 500 000 2500 3000 3500 0 00000000 0050227 0004966 0253384 03045299 0356790 0 0000 277 5067 4637 55603 7246 20 2000 2328 2568 589 65909 82503 30 30003 3380 3527 6246 7626 9286 40 40006 4433 45374 72403 86523 0360322 50 5000 5488 55479 82660 96832 358 450 5099 54479 60490 93792 0350024 28844 460 6037 64574 70636 0300409 20375 39247 470 7083 7467 80783 439 30727 4965 480 830 84768 9093 24693 4080 60056 490 978 94867 050080 34995 5435 70462 500 0050227 0004966 230 45299 6790 80869 020 = 0y 000 20 3 3 ) 002568 = Bog 002568 = 02 0 8 +0 4 ) 02 = 00256822579 002568 e 278288284590452354 = 2784593 0 8
0y = 00000 0 5 Boge 0 8 ) 0 4 log e e = + ) y 0 4 + ) n lim + ) n = e n n n Bog 0052328 = 52 Bog 0300409 = 296 Bog 0354080 = 348 0052328 0300409 = 03540806752848 Bog MN 0 8 = Bog M + Bog N a r n N N = a + r) n a = 0 8 r = 0 4 n N 50 005005 005005 0 4 5 005005 + 0 4 ) 5 = 0050050455 00% 00 5,00,50 D E Smithed) A Source Book in Mathematics Dover 959 2 D J Struiked) A Source Book in Mathematics, 200 800 Princeton U P 969 3 J Napiertransl by W R Macdonald) The Construction of the Wonderful Canon of Logarithms William Blackwood and Sons 889 4 D Roegel A reconstruction of the tables of Napier's descriptio 64) The LOCOMAT projecthttp://locomatloriafr) January 20 5 H Briggs Arithmetica Logarithmica Gulielmus Iones 624 6 D Roegel A reconstruction of Briggs' Logarithmorum chilias proma 67) The LOCOMAT projecthttp://locomatloriafr) January 20 7 D Roegel Bürgi's Progress Tabulen 620) : logarithmic tables without logarithms The LOCOMAT projecthttp://locomatloriafr) 26 November 20 8 948 23) 9 999 ) 0 348) 2000 2) 34) 999 ) 2 2 2004 6) 3 52003) 9 7 2