512 L. EULERl OPERA POSTHUMA. Anaiysis. 



.11111 , . 



± i- ± jl J_ 



32 ^ 52 ~*~ 72 ^ 92 ~*" 112 



2-»-^-^i^-»-^-^ TTz -^ ®^^' — 2 ^??- 



j i __L J_ L 



33 "^53 73-^93 11 = 



>• * 111 1 , 1/^1 



1— o3-»-F3 -^-*-^3—I73-^ etC. =4^92 



^"*"P"^5^-^7^"*"9^-^ir*-*" ^*^ =8D?* 



' ,'^ _. j \ ^;rir j etc. 



coefficieiites ita a se invicem pendent, ut sit 



„ ^AB ^ '2AC-*-BB ^ <^AD-^'iBC „ ^AE-k-^BD-i-CC 

 ^ = 1,, B=\, C=——i D = — -^^ > E= , F= — , etc. 



unde colligunlur isti valores 



A = t, B=l, C^l, D = {, £ = 1, f=l. C = ^^, H = ^S etc, 



ubi insuper litterae seorsim per 1, 2, 4, 8, 16, 32 etc. multiplicari debent. Hinc istos numeros ulterius con- 

 tinuavi, quos ergo cum potestatibus ipsius q sequenti modo repraesento. Prior columna valet pro potestatibus 

 imparibus, posterior vero pro paribus: 



Aq =i.q Bq' =i.2q'^ 



Cq' =|--V Dq' =T-89* - 



etc. ' ' etc. 



Quodsi litterae posterioris columnae ordine dividantur per hos numeros 2.3, 2.15, 2.63, etc. prodeunt meae 



fractiones — , ss' dT^' 57^» ^^^- 



Supra habuimus haec duo producta 



.,ir, ^r--*, 4' §. 12^ 12 , , . n: 2 6 6 10 14 , , 



4^^ S 7 11 13 ^^^- —^ ^^ 2 3 5 7 11 13 ^^^" " *' 



horum prius per posterius divisum dat: 1 • -rr • -x- • rr • t7 • 77; • ;^ • etc. =1. Hae fractiones invertanliir 

 * * 6 6 10 14 18 22 



et sumantur Jogaritjjjimi^ ^^i;;i(qije . 



('-r-B-^>H-(,'p,|^,io^,u^ ,,„. ^, 



/T. 0[,^.:} :. »1^ ^^ 



^ ^ V 1 

 6 -*'T 6 ~T 

 Cura igitur sit / — = i -., l—=l L., elc. evolutis logarithmis semissis dabit hanc aeqnatioii^rh : 



