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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 377r, page id 00068196:0749
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Aequatio differentialis (1) differentietur (2)
Et ope egg. 1 et 2. sollatur dus fiat aequ. (3)
Exinde si liceat aeq. 3. sic disponere, ut pars in qua
comnia cuembra in qua sunt X, y, a, fiant (4) aequ. de
et constanti, restabit aeq. (5) in qua erunt dx, dax 
de, ddy. quae pendet a quadraturis. Si coti-gat vel
esemel, ut duo memba haa ex ax, ddy, du com-
 posita habeant coem multiplicatorem compositum
utcunque CX X, y, a, possunt ognia per commn
inem ille verbigo si sit Xxrac, _: gy do: dxd
NX+a: gi ddd rodx nadx daus e
 = X. y. a, dx
3
 XX+ aa: y dax + nddu = dx X. y. a
fint, ddx + nddus, : dx- X. y. ay: xetaa
at de et si et s fiet
dax ddy =- d dx + dx de seny = dx+ X
tade +bde. ubi cessat ubi nec impedit violati
E segis homogeneorum, ve hoc  casu posset
tacu alio ipedire, at si fui qu
fiet de quid s pro ddx + huldus fut) (et
cddu +nadlus nddu: dax,: de = de
efiet andays = de dura de dxdix 
dax dxa sed ita turbatur summatio
Ed si esset Xx raa: gu dx + nddu dx-
E. addX X. y. a + a ddu X. 9. a + dx X. 9. a
= de. fiet dx + nadus: dax ex = de. seu
dx ddx et nddydx = de ddx. seu fret
n ndy + de + bdc - de dux: x
pc
vite.
hubrae tamen adhuc an hinc exilus
aady + Xydy +Xydx + aydx axdx. seu y - axax = ady,:,
seu X seu y y = axdx = aadque): Xdu + Xdx + adx
du = axdx + a . paus + xax + adx
qa
dus = axdax + adx =aa daus Xdy + Xox + adx + axax - acdus rdlily , dndyt relix ralx tadaus
(2t xdy +xax +aax
si faceremus ddus = o fic et haberetur dg: dx per a  et  a ix per a ddx: dx
(6
si facionus Xdy + Xdx radx = ade frerbt ex aeg. 3
adedu= Axdax + adx -ddu et ex 4 difperentiando fiet X ddys + dxdys + xddx + dx Taddx =0
tolle  fiet X ex X = ade - adx,:, dy+dx = dedy- ex +addu = - dx- addx dxdu
dd X
daus + ddx
fit  adedax = adX ddx dectus - dx du + a ddydus + deaxdus-dx tadxadus. si
si opi aegus s et 9 tollatur du habebitur aequatio in qua daus: dux, et du: de, et addx: de
Ex consit ax L aadaus ady racx= dx radux duX _: dxcdx + de ddy + dax du Ex 10 et 11 sit aequ. (12) in qua
verte eago
extibunt dibe ddy: ddx per dx: de, et a ddx: de sendas. ddna