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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 375r, page id 00068196:0745
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et si sit aequalio differentialis addx + yddus  dx, cum absit X
possimus faere y faciamus Xydx an de, adydx de et differentiando
fiet: Xdy da Lx a dydex +adxadus Z dx det et rursus fiet
X dydx ade fietque  dydx + Xdydex + Xaxddus = 0 et rursus
d xdax + dx a ddude: dys seu fre
du a dy Xddx + dx dyt = a adu de puto tollendo
ddx et ddy ope aeq. 1, 3, 5 redituram esse ag. 2
sit. sit aeq. xdu +ade= ady et differentiando fiet
Xddy + dydx + addx = addus + et ursus differentiando
aliter fiet dus X+ adx: dy = a seu dx + a: dydux = a dxddy: dus
sexifier axdus +adyddx a dxddy, fiet adu = dntus raty nexias
A(per 2), dydx + add X3: a -X. Ergo fit a dxdy + aa clyddx - Xdxds
= ax dydax = a dx du + aa dxddx ubi si ponas dax =0 redit
aeq. 1. Hinc ex aequ. 8 est adu - x du - adx. addx - dydx
sed addx- dus ax non est necesse quia sufficit quod scimus adu-Xdus ado
simile quid contrnget quoerescanque rem volemus reducere ad
unam differentio differentialem, vel ad quantitatem
uni aequivalentem. Nam et ibi eam posseum
ponere aequale nibilo, unde omnia destrmioportet salioqi
nova aequatio differentralis primi gradus haberetur
Hinc etiam Jhnc non licet Hinc etlam non licet
assumere valorem constantis de tatem, ut certum sit
posse folli simul X, ey et a. Quod habeceram in
mente sic procedendo, ut ex aeq. differentiali datu data differem
tialis differentietur, et ope ipsius et novae tollatur au restabunt
Adx et ddy
i
 aberinasem
eadem multinta
psu adx + ddy. ququoi non liet. Nam evanescent auxilia,
.0. eranescunt, elgo oportet aequavem pugnositi
 Equidem possumus obtinere x per du, X,, a
si vellemus
possent simul bolli X, y
quia sed si ponatur
posse dividi per datam
 Hinc si sit tatis differentio differenti
Equidem possemus habere dax +ddus per X, y, a, dx, dux, et ita
aequationem pro de, possumus tollere  XY, a
quod lollere difficile
et ita poree
simul, sed tunc vatorem de inpredibur ddx