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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 413v, page id 00068196:0822
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si possiomm pat
per curvas quabus quaesita in dato ad horizon
tem angulo occurrit; videor mihi etiam metio
dum pourigere posse ad aequationes differentia
les inferiores. Sit verb. gr. aequatio 2di
2di gradus in qua dentur , y: a, x: a,
addx: dxdx, et dx ddy: dex A sumatur
(3d0) ddy: ddx = Y; a quo in serto in aeq. t. fiet aequa
tio ad curvam datam Aqu ofeent (3) differentialis, mi
gradus ad curvam ordinatim dasam, posito r esse ostantem
in eadem curva, sed ariabuem cum curvis. Haec aequatio
resolvatur, methodo, quam suppono inventam, ut habeatur
a) (4) in qua de detur relatio curvae aequa
tionis 3 pargata a diffecentialibus jam ope aeq. 3 etque
assumendo, si placet X:a = de: de, (5t) seu
posito ipsas x esse progressionis Geometricae, habeti
poterit g Cto) aequ. in qua extabunt tantum
dx, dy, de sine a, x, y. Nam 
xia tolletur per 5tam
ps
si
 y. d habetur
per quadhaturas, etiam y. a diffecenti audo tolletur
sed haec supponuis quadraturas  revocari
ad Logarithmos et similia itaque forte nondum
res per oca in pte est ponamus tamen haberi
a4. 6. Tunc utique consuren habemus equa
tionem ex  du ly de ddx, et day eodem
modo ut alias dxide dy:de, et day: ddxseuia
eodem modo ut alias in disferentinibus primigradus ex,
X: a, et y: e, et do: dx seur: a iaque salte
hinc sequitur perfecto qa analytice, quadgaturam
negotio  seu reductis, unuor n et
quatrotaris ad exponenncra vivar iest
tiales uno gradu difcentiq
absolutos fore omnes
e
ato
juditus