

ANALYSIS AEQUATIONUM ALIQUOT FUNCTIONALIUM, 



QUAE 



PARTIM IN THEORIA ELLIPT1CARUM 



PARTIMQUE DILOGARITHMICARUM 



MAGM SCNT USUS, 



ACCTORE 



CAR. J01I. I:SO\ BUM,. 



1. Data aequatione (x -f- y) = (A", X . . ., Y, Y. .) sen <p (z + y) = Z per 



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functiones separatas (X, X, X, . . . . Y, Y, Y fy c) exhibita, invenire indolem 



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harum functionum (X, X . . . Y, Y < c) differentialem. 



Differentiando secundum x, habetur <f> t (x -f y) = d x Z = Z',etse- 

 cundum y, (f> t (x -j- y) = d Z = Z lt ideoque Z' = Z, ipsa aequatio est, 

 quae separando arbitrarias x fyy, aequationes differentiales, & quidem 



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Iprimi ordinis, in X, X, X fy c (ut et inter Y, Y, Yfy} suppeditat. 



Sit Ex. gr. Z = X. Y, eritque Z' = F d X, et Z, = Xd Y, ideoque 

 Y6X=XdY;& separando d -j= d -^=c= const, arb. 



Haec vero aequatio differentialis integrata praebet L X cz+Lb, 

 seu X = $ cx 6=6. r f cx . Sirailiterque altera suppeditat Y= a.$ cy , quare 

 & <p (x -f- y) = a b g (x + y \ & (f) u = a b j> c ". (Scribimus vero g, /J vel 7 

 (L inversum) pro 2,71828 . . == g,^. . .) 



