42 DE INTEGKATIONE 



•vnde fit 



dx( x -±-ccxyy-yV(i-c*))"\-dy(y-\-ccxxy-xV(i -c 4 )) zof 

 Ex eadem vcro aequnione refoluta colligitur : 



XV(r— C 4 ) + ^'(- — X*) 



J i -f- CC XX 



etV - t ^l-j^yy 



S\ enim ibi radicali V (i — x*) tribuitur fignum -j-, hic 

 radicali V ( i —f 4 ) (ignum — tribui debet • vt pofito 

 x— o\ vtrinque idem valor prodeat y—c. Erit ergo 



x -\- c c xyy - y V(i - ^ 4 ) — — c V{ 1 -y ) 

 y-\-ccxxy- xV(i — O — cV(i-x*) 

 quibus valoribus in aequatione difFerentiali fubftitutis, 

 prodit 



-cdxV(i -y) -\-cdyV(i -x*) 3+ o t 



- dx _ dy 



liue vd— **) — vii— 7*) 

 Huius ergo aequationis differentialis integrale eft 

 xx -\-yy -4- ccxxyy ~. cc -\- 2xy V( i - c*) 



et quia conftantem c ab arbitrio noftro pendentem con- 

 tinet, erit fimul integrale completum. Q. E. D. 



d x 



§. io Si igitur habeatur haec aequatio ' ^zzs^ 

 ^v(7— ^J valbr integralis completus ipfius x eft : 



__v(_— c*) ■+: c v(<—y*) 



X — — t _)_, ccyy 



vnde fi conftans arbitraria c euauefcat fit x zzy ; fin 

 aatem ponatur c~i, habemns x--±_~^^— ^[^y 

 qui funt ambo illi valores parciculares iam iupra exhi- 



biti. 



