16 AIETHODrS AEQl^ATIONES DIFFERENT, 

 Qiio diffcrcntiiito habcbitur : 



Comparatione crgo flida fictB' — C: A'=:B— aC ct 

 A==:aB — a*C, debet crgo efle a radix huiiis aequatio- 

 nis o~A — aB^-a*C, quae cum habeat duas radices 

 vtrnmlibct afliimcrc licet • critquc A' — B — aC cr B^ — C. 

 Penicntum eft ergo ad haiK acquationem difTcrentialem 

 primi gradus : 



^-axy.^x^.rrrAO'^-^. 

 Ad quam denuo intcgrandam multiplicetiir pcr e^^^dx vt 

 habeatur. 



tf i«-«>^.v/^*'X </Ar =r A ^f «*>' ^.v -H B ^i?^'^^ 

 quae vt fit integrabilis , debet efle §— fv— -^*^ Ccw a 



H-SziZc, vnde patet § cffc nltcram radicem aequatio- 

 dIs ozhA — aB-i-a'C, eritque intcgralc : 



f(e-aVc 



Eft vero/tf ^^'^^dxJe^^Xdx—-^- Je<^XdX' ji-fe ^'X fl^v 



g-ax g-ex 



Ergo Cjzrz-^ Je^^X dx -\-~ -^Je^^^X dx. 



In hac acquatione intcgrali ambae radiccs a ct S aequatio- 

 nis quadraticae o — A — B 2 -f- C 2 3 acqualitcr infiiiit, 

 et hanc ob rcm fi iflius aequationis radiccs fint cognitac cx 

 iis ibtim acquatio intcgralis f()rmatur. Ifla autcni acqua- 

 tio o ~ A — B 5: H- C ;C2 cx jpCi acquationc propofita 



^cilli- 



