FORIVIVL. DIFFERENTIALIVM. 135 



(ij) = (^j) ' (^) = ('->) "^- ^:^) = ^rp "c. 



HLirum vero aequalitatum ope , valor.es quantitatum 

 M, N, P, Q ctc. in (equente^i transformantur : 



M := (^^^) 4- p (^^JJ.) + q (^_i) _i- ,. ('l_t) etc. 



N = (l^) -h p i'^) -^ q ^ + r li^) ctc. 



P = C^s^?-) + P ('if ) + q (^f ) -t- ? (if ) etc. + ^ 



0.= (ly + /. (^f ) + q [^) 4- r (f-^) + etc. +7t 

 etc. 

 Tnde deducitiir : 

 . ^dx=dx(^-^) + dy{y^)-\-dp(y!^) + dq(^/^) etc. 



N^x = <f^-(^^)-+-</j'C-f) + ^p(^j^)+</-?(if) etc.' 

 (P-FW^-rfA-CJ-f^ + ^/j^li^+^/pi^^ + ^/^fif) etc. 

 {q-^)dx^dx{y^)+dy(y^)-V-dp('^)-^dq{'^)tic.- 



Sumtis igitur integralibus confequimur : 

 \k-fMdx; v-fNdx; n-fiV-v^dx-fFdx-fdxf^dx 

 yi-f{(^-T:)dxzzf(^dx -JdxlVdx^fdxfdxf^dx 

 f -fK d X -fdxfQjtx -\-fdxfdxf? d x -fdxJdxfdxfNdx etc. 



Si itaque iam compendii.cauflli , integrale /^a/N^r, 

 indigitctur per p^^Kdx-, fdxfdxf^dx per 1^'^^dx 

 et in genere huiusmodi integrale , quod poft m iti- 

 tegrsitiones oritur per / ^"'^N^a;, fiec 



