3 



merator hanc induet formam: dx^{i-hppY, deinde vero 

 denominator euadet —qdx'^, ficque ifta quantitas erit 



^_{i-]-ppf 



§. 2. Quodii nunc talis fun^io Z differentietur^' eius 

 differentiale ex tot conftabit partibus, quot in ea infunt 

 litterarum x, y, p, q, r, s, etc, ideoque tali forma ex- 

 primetur : 



dZ =:Mdx -i-^f^^dy -^Vdp ■+- Q_dq H-Rdr -h Sds -^ etc. 



Hic autem, ne multitudo litterarum M, N, P, Q., R, etc. 

 in calculo moleftiam creet, eas, quoniam omnes pendent a 

 natura funCtionis Z, per fequentes charaQeres vfu iam fa- 

 tis receptos repraefentabo : M — (|-?); N z= (|^); P = (|-?); 



Q.= (||); R=:(||); S = (|^^); etc. hocque modo, nullas 

 litteras peregrinas introducendo , erit 



9 Z = 3 X (II) -4- dy (f|) + S p (||) + 3 g (||) + etc. 



ac fi porro loco differentialium dy, dp, dq, dr, etc. va- 

 lores fupra affignatos adhibeamus, prodibit 



aZ = aa:(||) + pax(f-|) + qax(||)+»-9*(||) + etc. 



f. 3. Hinc ergo fi ftatuamus: 



V = (||) + p(||)-)-q(||) + r(||) + etc. 



quae erit quantitas fmita, pariterque certa fun6lio ipfaram 

 X, y, p, q, r, etc. ab indole funSionis Z pendens, erit 

 BZ = V5x, ideoque integrando Z=/V^x, in qua in- 

 tegratione omnes litterae x, /, p, q, r, etc. tanquam va- 

 liabiles infunt. Vbi probe notetur, fi V fuerit talis fun- 



aio. 



