->^% ) 43 ( ^i^- 



f. 31« Hinc igitur colligimiis idud Theorema 

 analyticam: 



Tiieorema. 



Si capiatur s~— ^ — ^ — -,, erit differentia ifta- 



f V(c+-+-(aa— cc)(j7)' 



rum formularum integralium femper algebraica: 



/ dsV(a* -(aa-cc)rs) r d q ^/ (c* + (aa -c c) qq) (n a -ce)<] y/ ( ec- qq) 



* aV^au-ss) J c-Vicc-,iq) c V(c* +[aa-cej ,j ij ) ' 



^.32. Operae igitnr pretium erit per euolutio- 

 nem calculi hanc egregiam reduciionem oftendifle. Primo 

 igitur cum fit 



j— ""'' erit 



V(ct-+_(aa— cc) 717)' 



vnde fit pro prima formulii integnili 



^{a* — { a<l-cc)ss) r 



o V {aa-s s) V(cc-:j.^j* 



Deinde vero repcritur 



a a c* d q 



ds~ 



3 ? 

 (f*-h [aa- c c) qqf 



hinc igitur formukrr.m integralium prior erit 



dsV {^'' — {aa — cc^ss) a a c^ d q 



aV{aa~ss) ' ^{c' •^-{aa-cc^qqjv {^cc- qq^) 

 ab hac igitur fi fubtrahatur alcera /^^^^-^^-^f^^ diffe- 

 rentiam integrabilem cfle oporter. FacT:a autem redui^lio- 

 ne ad communem dcnominatorem hacc diffcrentia fit: 



[a a — c c) d q { c" -- z c^ q q — { a a — c c) (j*) 



J z 



c{c' -{■{aa-Cc)qqfV{c-q]q C 



F 2 cuius 



