AEQVATIOxNIS DIFFERENTIALIS. 223 



et y haui dijERculter inuenltur , fequenti tamen 

 ratione idem multo f-ici!ius perfici potefl. Dum ad 

 aequationes in §. 4. addiidrjs regredimur, inuenimus 



a^ddy-ifVi^a^dydx-^jiaydx^-^^^^rf^,. 



Aequationum differentialium tertii gradus ibidem 

 allitarum intcgrctur ea , quae ordine tertia efl: atque 

 ponatur m—i^ eruetur inde a^ ddy -~{^e^f)a^dy dx 

 •^-efaydx^ — —^ , quale^m vero formam quantitas V 

 liabeat , infra oftendam, lam coilatis inter fe hifce ae- 

 quationibus obtinemus : 



a ay laj ax^ (.-^K,-::^-t-(/_o(/-£)+(7^r;Kg^J 

 a^dv — favdx — gd x _ sd^ l_L1^ 



atque ex his demum 



av— 2^ V- ?- \- i^^±!r- is) ^ "L , 



"-^ — (e'v)(e'-g)^^(/-pX/-£)» ^(5 -'-;-(£ -/r-^a(g- o;g-/> 



Nunc itaque redat, vt quantitas V inueftigetur , 

 quoniam autem per hypothefui fit g ziz i , erit 



fN^Sdxzzfdx{C+fl:^~^dx)zzxCC-{-fN « Xdx) 



-^fN^^rxxdx adeoque V — N^(D+/N « Sy^r) 



gx ~gx ~gx 



=:N«[D-i-A;(C+/N « Xdx)-f^f^xXdx^. 



Eadem 



