pfp_-2iiLj habemus 



codemque modo 



d y ' . 



Praeterea eft 



MFzz:/(PM2-f-PF2)z=i/(j2_4.x«-2/x-i-/*), ct 



MG=z>/(r-l-x^— 2gx-i-§2). 



Aequatio itaque propofita eft 



yd X — xd y -+-/ d y — — yd x — x^ y-^g 3 y ' 



quae eft integranda. Quem in finem reddatur ea homoge-^ 

 nea, ponendo x — f—u, et x — g — v, atque in parte 

 aequationis priore ftibftituatur dx^du, in pofteriore dx~dv, 

 eritque 



y dv- — u B y — ydv — V d y 



~V [f'^ -i- u^) yij^-t-o^S) 



Pofito inftiper u — py, v z= qy, ut ftt du — p "dy -{-yd pj 

 'bvzizqdy-hydq, erit 



du — pdy — dv — qdy Y\ e —lH— — y^'^ 



ideoque _±L_^ — ^^,-i^ , cuius integrale eft: ^ 



Z [/3 ~f- / (i -^ p-)] := U + / [qf + / (i •+• qf2)], five 

 p -I- / (i -I- p2) — c qf -f- c / (i -}- 9") . 

 Quodfi nunc reftituantur valores p — -, q — '^, fiet 



u -h ]/ (y^ -h u^) ~ c V -\- c ■/ (y^ -^ 'i^') 9 

 quare cum fit u — x — f, V — X — g, habemus 



Vif-^ {^~fn - c yiy--i- (x^gf] - (c-i)xH-/-cg. 

 Sumtis quadratis fit 



y 3 (c^-+-0 



