DE MOTV AQVAWM 



hanc (hh-mm) zdx-\-(hhb-\- hma-\-hhx-\-mmx) 

 dzzz(hha-hmx)dx. Vtraque autem aequatio inte- 

 grari poteft per lemma fupra promifliim, quod nune 

 demonftro. 



Lemma. 



§. 14. Sit aequatio integranda (ct quidem fine ne- 

 ceftitate feparandi indeterminatas ) azdx-\-(%-\- yx)dz 

 zzz{e-\-^x)dx\ fcribendo y pro £ -f- y x , vnde dx ~ 

 ^, aequatio mutatur in hanc ^zdy-\-ydzzz (e-\- Qx) 

 dx\ qua multiplicata perj^"" 1 habebtfnr^s/f-T 1 ^ 

 ^y^dzzz(e-\-Qx)dxxy^~*zz(e-^Qx)x^-hyx%- 1 

 ydx\ integrando prodibit y~zzzf(e -\-Qx)x^(%-\-yx) 

 '^ydxzz^-^yx)^(e-{-^)--J^^yx)^ydx-^ 

 (%-\-yx)^*(e-\-to)-zzz^(%-\-yx) *-y- - £ ^07 4- ^l^y 

 E— 1 ^. Notetur hic, duos poftremos terminos adiectos 

 efTe more folito ad re&ificandam aequationem , vt ni- 

 mirum euanefcente x , etiam euanefcat z. Diuidatur nunc 



aequatio per y~ hoc eft per (§+yi)*, vt emergat 

 valor verus ipfius z , nempe z zz * (e-\-$x) - zzj^z(%-\-yx) 



\aa-t-ya 7 a 7 / 



*) — ■ 



§. 15. Vt igitur huius applicatio fiat ad priorem 

 aequationem (hh-mm) zdx -\- (hhb-\- hma-\- hhx) 

 dzzzhhadx , erit hic a zz h h — m m , %zzhhb-\-hma, 

 yzzhh, ezz hha y et Qzzo, quibus furrogatis obtine- 



bitur 



