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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 188r, page id 00068195:0375
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Tentamen ad praevidendum quousque ad summum
asurgere possit curvae differentraliter dato aequad
ordinaria si quam habet
Xydx + aa dy + X dy =0 sit aequatio differentialis ad curvam
quaesitam. dif Hoec differentietur, fret Ny dix + xdady +ydx + N pto s
posito ddy 2o. Hunc ope aequs. 1 et 2. tollendo dy set
dy = (ex oy. 1.) = - Xyax:  aatex (ex 2) y vex egxd
rydes
seu 3X x = Xdax + +X aat ubisingular est quod simmil
E
evanescunt dy et y, posita dus constante.
sed si fuisset Xyax + aady + X dx =o fiet
 differenlundo Ny ddx + X. IXdy + ydx f 2dy X 2X dx F XX ddlx = 0
et sit, d ex 1, du = - xydx - x dx, : aa = (ex 1  Fix
et fiet: Xydx + xax  py aa dux +y aac inde habetur
+Ex
alor ipsius y, et hinc videtur sequi in aequatione relaione
ex
exprimente inter Xet y non posse y assurgere ultra a
gradum simplice sed nesclo an fidi huic ratiocimo possit, quia
potest aliquando plane evanescere y, ut paulo ante
signa res inquisitione quid siat cali modo: datur verbi gratia
CP ex AB. Assuntur punctum C pro arbitrio in recta BK
et sumta recta alia quacunque e) cui ex C angulo
pc V recto eduta CV occurgat in V. et ex
quaeratur s, ut P ex AB et ipsarum VH
concursus sit F, est similiter (V) det (F)
usque ad altimum puncta escum () icidit in C linea euius FF.
Quod si aliud prectum sumas C func linea
(C)P) ducta cie concurref priai Cp in puncto  credo f.
est ipsa C