AFQVlTlOMS DIFFERENTUUS. 4 f 



diius propterea aeqnatio* integ^lis eompleta erit : 



x x -\-yy —/-+- b x xyy -+- 2xyV( i -hg -+-/£) 

 quae etfi nouim conttaiitem inuoluere non videtur, ta- 

 men efl: completa , cum in differentiali tancum ratio 

 quantitatum /, g y et h fpectatur, ita vt- pro /, g, et h 

 fcribere Mccatfcc, gcc et hcc , vnde aequatio in~ 

 tegralis manifefto completa prodit: 



x x + vy-fc c ~{- hc c x xy y + 2 x y V (i+gcc+fbc*)' 



vel / (x x +yy) -fe e + hee x xyy + 2 xy V/(/ •+-£ e £ ~+ fo*) 

 pbfuo cc~j,- 



§. 20. Quodfi ergo propofita fit haec aequatio' 

 difFerentiahV 



d_x_. d^y - 



V(/-+- g xx -h fe * + ) — • V (/-+- g y y +• &.? 4 ) 



valor ' ipfnis y per fundionem algebraicam ipfius x ex« 

 primi poterit, ita vt fit: 



. KV(i4-gc c + /fcc^ + cV (f-f-gxx+h x+ ) ' 



V — ' 1 — h c c x x 



■ 1 ' - '- * V /(/-+- g e e -+~_ he±) ± e Vf( f -+- g x jc -+-&jc+> 



Vei J' — ." j - hee x x 



Quodfi ergo fit g=ro , vt habeatur haec aequa"» 

 tfo>' differentialis 



dx __jL2L 



V(/ + fcx4) V(/-+- W 



valor integralis completus ipfius y erit 

 „ ?E^iMf^|^«//r/j4^c^J 



*/ ■ — / — h e e x x 



vnde cohrtantem e pro lubitu determinando,' innumeri 

 valores particulares - prb^ deduci' portunt. 



§V 21. 



