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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 404v, page id 00068196:0804
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(2
aa XAx + 2ydus + a’ydx = 2aa xdy cX = 2)ly + a ydx: 2 du -dx uende
aaAx = 2 dy- dx, 2y ddy + 2.3y y + ayaax F a dydx = 2y dy + a ydx. 2ddy - dax 8: 44y. a dylxt de
t
seu  a dxdd-aadr Bdydx + acax dx =(2y ddy adu + Syus 2dys + a ydax edys  a dydx 2did
2y ady dx-6 is di ax ( ayd dxax (C, ae dy dx ax (= 21y dy 2day - a ydx rally + 21y ayaex ta y 2x lex
(5)
Hil
Jam omnes termini quos ingreditur a ponantur aequales nihlo, fiet: 2 dxdi - 3 cx dus 3 dx - Bydus dilx
2ydx ddus
seu y EC AX B = 3 dx dy + 2dX dty,: 2 dydax dedau. Unde ex reliquo aequationis 4 denta
eq 5. fit  12 4y3 = 2y dxddu = 6 dx dus 42y dys ddx 20 seu y= Cy. 3dxay:, dis dix- dx dius
sed hos duos valors y aequanto tollerentur differentio differentiales et res ad solus
Aliter ergo ex aeg. ) est aa = 2y dyse:, 2xdy - xdx- ydx. Unde differentiando
differentiates rediret. et linea fieret recta
fiet : 2X dy = xdx - y dx 29 day + 23y dydy.= 2y dy 2Xdayt rdy - xaty- ex dx -yaax C apax = 0
adeoque (2Xdus Lp dldy t exdus L yay -xdx 2y ddy -xaxby dys - yex 2y ddus  yax biy dyt idus el au u his dus splrdus
ydyxdax- 2y dy ax- 2ydys yddx 
jam omnes terminos quibus in est x ponamus
aequales nihilo, fiet (y d ydais + 12ay - 2) x day - 6 dx dis =  dydau 2y dy ddx
et reliqui in aeq. T termini eruntu 1y ax dius  Bydx d- 2ydx ay - 27 dy dax. Unde ex
aeg.  fiet y- 6ds.  dyadu  x 6dis - 3 exdu, : dx days - dyadx. sed ita ex aeque.
sit  alius rursus habetur valor ipsius y, cujusidem denominatnam
Resummus aequationem 1. et differitum aa xdp +27dy taydx=raaxdus hanc differen
iacidimus in d absurdum, mauto ante occurrens
tiemus, fit ea pdda iect tollamus y differentiando quod si tunc, vel a vel X movasan-
derent, nisi ad unum guodumveme  non darentur nisi pure seu uno gradu; posset
simuliter es gradus poni aequalis nihilo, sed puto altius ascensuros.
in aeq. 1. ponatur  dy: a quantilus ostans seu y ady + 3y dy = 0 seu, yddys + 3itus = 0
et fiot  rddx + cx + y dax (t dxdus = 2X ddus +3 Axdus. sed nilil hnc