i) M C F Richter : ) km 2800) A µm) M L = log 0 A ) ii) ph ph mol/l [H + ] ph = log 0 [H + ] = log 0 [H + ] 909 Søren Pete

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1 Pierre Simon Laplace : ) 2 Christopher Columbus : 45506) Vasco da Gama : ) ) ) log ) 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)}

2 i) M C F Richter : ) km 2800) A µm) M L = log 0 A ) ii) ph ph mol/l [H + ] ph = log 0 [H + ] = log 0 [H + ] 909 Søren Peter Lauritz Sørensen : ) 25 C ph 7 ph 7 ph 7 ph 7 ) ph iii) db 2 ) A B n db) B n = 0 log 0 A A mw 0 2 W 2

3 ) John Napier : 55067) Merchiston Castle) Mirici logarithmorum canonis constructio : 69 ) 3 pp78 92) 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

4 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

5 ) n n [ ) n ] n Nog = ) y y = Nog ) e = lim n + n = n=0 = log n! e = ) y = ) y log e = log e ) y = y log e ) log e t) = t t2 2 t3 3 log e ) = 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 log e log e log e ) log e 5

6 = ) 0 Nog = 0 = ) Nog ) = Nog L = Nog M = y Nog N = z L = ) M = ) y N = MN L = 07 ) y ) z = 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

7 Mirici logarithmorum canonis descriptio : 64 ) 4 ) Gr Gr Gr

8 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 = = ) = Nog log e sin sin = sin = ) = Nog log e sin sin = sin = ) = Nog log e sin O α P H log Nog = e log e log e ) log e Nog 8

9 2) Henry Briggs : 556?630) Sir Henry Savile : ) ) Logarithmorum chilias prima) 624 Arithmetica logarithmica) 5 p) ,28 A A B C D B C D logarithmus lìgoc ) Ćrijmìc ) Log Log Nog Log = Nog Nog Nog Nog 0 = log 0 Nog Nog = Nog ) = k = 07 ) k 9

10 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, , ,3002,99956, ,99997,82847, ,2590, , ,4772,2547, ,99998,26278, ,87366, , ,60205,9993, ,99998,69709,70 969,0030, , ,69897,00043, ,99999,340, ,2460, , ,7785,2503, ,99999,56570, ,67896, , ,00000,00000, ,) 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

11 3) Jost Bürgi : ) Arithmetische und geometrische Progress-Tabulen) Bog = ) y = ) y 0 4 y = Bog 0 0y ) 0y 7 ) = 0y ) = Bog = ) 02 = e =

12 0y = Boge 0 8 ) 0 4 log e e = + ) y ) n lim + ) n = e n n n Bog = 52 Bog = 296 Bog = = Bog MN 0 8 = Bog M + Bog N a r n N N = a + r) n a = 0 8 r = 0 4 n N ) 5 = % 00 5,00,50 D E Smithed) A Source Book in Mathematics Dover D J Struiked) A Source Book in Mathematics, Princeton U P J Napiertransl by W R Macdonald) The Construction of the Wonderful Canon of Logarithms William Blackwood and Sons 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 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 ) ) 0 348) ) 34) 999 ) ) ) 9 7 2

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