X78 DE AEQVATIONIBVS 



C O r O 1 I. I. 



20. Si fuerit «zzi , prodibit ifta aequatlo difFe- 

 rentialis fecnndi gr dus : 



j , mady^ . y d x '^ 



, . ,. (^~hyx)dv ia+zQx^y XX) dy 

 quae ergo multiphcata per ' 



,2 m 



fit integrabilis, eius integrali exiflente : 

 ayyydx^^-^-iim-i )a{^-\-yx) ydxdy-\-{m-i Y-a{aL-\- 1 ^x-\y xx^dy^ 



2.[m—iyy^™' 

 yydx- 



— Qdx^. 



C o r o I L 2. 



21. Pofito «i-i^fjL, fi ftatuamus yzze^^^^ y 

 aequatio noftra fiet difFerentialis primi ordinis : 



adv—\Lavvdx~\-' {^^,i^Tz^y^ — o 

 cuius ergo integralis erit 

 ayyydx^-{-i jx a {^-Vyx) ydx dy-\~p. ^a(a.-i- 2px-\-yxx)dy 



(eu pro y valore ibo fubftituto 

 (iy'{-2iJ.a'p-\-yx)v+iJ^^a{c(.-^2px-\-yxx)'VV- ^^~:fy^^ 



Coroll. 2- 



2 2. Statim ergo aequationis difFerentialis pro- 

 poritae : 



adv—ikavvdx^^^^^^yxx)* — ° 



pofito 



