mWEHEKTlO-LlFr^RmTIAL. 



T2f 



fuiffet, fi poruifremr:=:c^'^?-'^^^^™^^, ety—cn. 

 Ell autem «-f-/»— I numerus dimenfionum , quasj^ 

 conltituit 'j et m-\-p quas x. Facile ergo in quoui* 

 cafu particulari a determinatur (latimque debitafub- 

 ftitutio habebitur. In aequatione inuenta, cumab- 

 fit f, pomtm- dv—z(ff, erit dd-vzzzzddt-i-tlzdt , fed 

 ddv—— a^i;^— i=5=^$ ;s^ dt^. Hinc inuenitur ddtzn 



m-Hf> 



zi^^—\-ls:^zdt^. His fubftitutis emergit aC^±^-L)P 



z m-i-p ^ ^ m-+-p J 



z^dtP—t\dt-^tzdt)P-- r-^^fzdt~-^^-\- 'i.zdt--^ 

 "^-^' tzzdt^). Quae diuifi per dtP-' dai3itrt("±i-±Ai> 



ZPdt^i\ I -\-tzT\ ■ ^im-n^p ^j_i^_^^m^-^ ^ z^^. ^ 

 ^ ' ' '^ fn.-+-p a m-t-|j > 



p. Reduda ergo efl: aequatio generalis pro- 

 pofita rt-.v"*^.;^— j^rtjf^^t/^' ad hanc difFerentialem 

 primi gradus ^(!^-ii)f 2?-+-' dt—tz^i-^-z^f^^ 



( ' •^''^-^■^P z^^dt-^-^^^i^^^tz'^ dt-dz) , multiplicataae- 

 quatione inuenta per 2. Haec aequatio A^nico adii 

 ex ea inueniri poteft, pofito in prima fubftitutione 

 loco V hoc jzdt. Ficri ergo debet 



^__^(7i-+-p_ . ];«df tm-i-f.) gt Iqcq ^ pQj^l ^jgj^g^ ^/zdt^ f-jyg 



quod eodem redit , ponatur .rzif^"-+-^— '^^«*t 

 et jzzc^'^^^^'*^/. Si ex aequatione difFerentiali in- 

 venta iterum propofita difFerentialis fecundi gradus 

 inueniri debeat , videamus qoales loco z et Z' fub- 

 flitutiones adhiberi debeant. Cum fit .r— ^Ci-t-i'— 1 ]/*« 

 tt\tt^''^^—x'-^'^^-'^: quare.r— .r('"-+-f>-^"-^-^'V. Vn- 

 de habetur /— j^t— ('n-+-j>;{i-*-i>— 1\ Deinde quia 

 ^/zdt__-,^i.(n-j-f.-i) erit ^zdt — ^^—^Jx ; ergo zdt:=: 

 J:^ .. Sed eft <// — .r-t"'-^^^^"-*-^"' Vr— i^^tL 



(n-f-p- 1 )x ^' n-tt-p— i 



^^.-(m-»i-2f>-hi)(n-+-f.-i)^^^^. Confequeuter inuenietur 

 Tom. III. a ;s=: 



