EXEMPLIS ILI.VSTRATA. 2^1 



itaque qnantitates vt indagentur , capiendum eft 



difFerentiale affumtae aequationis , quo fiet : 



^f^dj -^py^ ~" dy^-^-nqy^^ — ^x^ dy dx -|- n ry"^ x^ ~ ' dx'' 



— sA.x^-^dx^—f^-^^-i-nsj^ix^^^dx^ 



X 



atque duda hac aequatione iny'~'^x"''^ et ordina- 



tis terminis reperietur : 



yx"~^ddy -\-p a,'' "^ dy-\- nqy^^^^x dy dx — sy x~^ dy dx 



Si iam ■vkima haec aequatio , conferatur cum ifta , 

 cuius intcgrale quaerimus , determinantur incognitae 

 hunc in modum , vt fit r——\ , p — h^ q—pi:z\ 

 vel ^— ^-f-i, nq—szzc et n[h-\-\) — c-^s^ eft 

 Vero quoque n{s — r) — ns-^n — a^ proinde (j-H- i). 

 (x4-^)=:a. (^+i)ex quo eruitur j-z:-^i±il^-- V^^' 



^- 1 -H- 2 V('.l=^" -4- fl. (^+ 1) 

 + ^.(£^+1)) et n- — ^, - vel 



a (^-l-i) 



fi ponatur /= 2 V (f^ziT 4- ^. (^ 4- 1 j) , erit s-- (£±^^-^ 



et «=z^^=^;=/. Subftitutis itaque pro p, », ^, f , s 



ipforum valoribus , deprehenduntur binae aequatio- 



nes primi gradus , fcilicet 



y^dy-^-T^^^y^-^^x-^dx^K.x - dx et 

 y''dy^'-=^^^y''-^^x-'dx-'^,^^~ dx, 



ideoque dum fubtrahatur pofterior a priori -^: 



Tom.XIV.Nou.Comm. Hh =* 



