C A P V T II.

349

Secundum §. 440. ponatur xzzf et ob dx~~f- nnostra forrnula erit dy— y -j~- 4- a tt dt , in quaPorro statuatur y-t-ttz, et prodibit -tt[dz-\-zzdt-adi) %quae per t t[zz—a) diuisa separatur, ergo et no-stra aequatio diuila per tt{ zz — a)

^(1— xjf— 3- fiet integrabilis, ex quo multiplica-tor erit — et aequatio per fe integra-

bilis x^ —xyf—^T —°* b pectetur tam x vcconstans eritqus ex dy natum integrale:r x i 1 — x y)-*- ^ a

— / - -

- V a V-r —-c( i

- xy

Jct-X,

pro quo vt valor ipsius X obtineatur, differentieturdenuo , ac prodibit

1 xy dx — d x | dX y4 t v d x — a d x

xx(i — xyj 1

\

x* ( 1 — xy ) z — a x x

vnde

jv_ x*yydx—adx —2 x *ydx-i-xxdx _dx , _

M-A.— jc*(i— x~y)^ — a xx — xx 1 Ct

quare aequatio integralis completa erit

- 4 - C.

Scholion.

; v g-*~x{ > — x y )* V« — *( * — *y)

tVo

X

4yL. En ergo plures casus aequationum dis-terenti alium pro quibus multiplicatores nouimus ,Cx quorum contemplatione haec insign s inuestigationon parum adiuuari videtur. Quanquam autem ad-huc longe absumus a certa methodo pro quouis casumultiplicatores idoneos inueniendi; hinc tamen for-

Xx 3 mas

\

-

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