Neperios 2009_arithmos e

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Neper

Transcript of Neperios 2009_arithmos e

e . 1617 . , (Gerhard Mercator 1596). , , . . , . John Napier (1550-1617) of Merchistoun8 Merchistoun , , , . 1-10-7 =107(1-10-7)L

:L=Nap log. --- 111 --- 20 --- 222 --- MMMiiirrriiifffiiiccciii LLLooogggaaarrriiittthhhmmmooorrruuummm CCCaaannnooonnniiisss DDDeeessscccrrriiippptttiiiooo... : 11 , . 17 , , . : : % . 1 : 11100 = + 2 :221100 = + : 1100 = +

: . 1005% . 1 :105,00 100 5% (2) 2,5%. 1 :105,06 (3) 1,66%. 1 :105,09 (12) 0,416%. 1 :105,12 (365) 0,0137 %. 1 :105,19 . %. --- 333 --- --- 444 --- : .. 11000000 , 110000000 2,72 . 1 + e. 1 + e. 111 : :: ===111000000 1 1 = + 111 2 222 2.25 333 2.37037 444 2.44141 555 2.48832 111000 2.59374 555000 2.69159 111000000 2.70481 111000000000 2.71692 111000000000000 2.71815 111000000000000000 2.71827 111000000000000000000 2.71828 111000000000000000000000 2.71828 e 1 + . . 1 + ( ) 1 0. 1 1 1, e=1. 1 + 1, 1 , 1 + , . . . . 1 + , ( ) C C C C C1 2 2 11 2 3 1+ = + + + + + C --- 555 --- (+1) . C Pascal Blaise Pascal(1623 -1662) 111 111 111 111 222 111

111 333 333 111 111 444 666 444 111 111 555 11--- 666 --- 1000 111000 555 111 111 666 111555 222000 111555 666 111 ... Pascal , . : ! ( 1)( 2)...( 1)!( )! !C += = 21(1 )1 1 ( 1) 1 11 1 ... 1 1 ...2! 2! + = + + + + = + + + + 1 : 1 1 1(1 ) 1 1 ...2! 3!+ + + + +1 1 12 ...2! 3! 4!e = + + + +

Gregorius de Saint Vincent (1584 1667) , . x > 0 r 1> > 0 x,xr ,2xr , 3xr 1=1 r , 1+E2=2(1 r), 1+E2+E3=3(1 r) , . : =1 --- 777 --- e JakobBernoulli(16541705) spiramirabilis , . ( ) . . ( ) . . --- 888 --- --- 999 --- : Weber-Fechner : S(), K ( Weber), R ( ), S=KlnR : , : m=2,5lnl+c, (m: *, l: , c () ). : pH. E : pH=-log[H+]. ([H+] + ). : [+]>10-7 (pH