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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 251v, page id 00068196:0498
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sed videamus si aequotionis E rursus quaeratur differentialis an res procedat aempe ady = Xdy+ ydx+ fax
sen dy: dx = y+f a - X sed hoc est falsum nam ay: dx = 1: D et y+ f = 2a e1 a =x = 2a
ergo y+f,: ax = 1 itaque non licet aequationis differentaliternivestigatae
iterum absoluto ex5, ex dis
Idem aliter tentemus
=rax +raC=fF1fy + yy
differentialus prioris est: = fadx = +f dy + p y du de seu py: dx  =a: y
videtur eum
diobeo
aveeder
em tentemus
et XX+ yy = ph
qu
y Xy+XF, cujus aequationis ope poterimus toblere
et 2. et valoreet y lotsendo ex 4q. 2 prodibiti vator ipsius h desideratus nec opus est calculume
in quadratricibus
P. a = y faadx aatu San axspax:ax  y: a et vytx = ee
fit dx: a +X = dy: a et dy: dx :: - x: y = a: a +X, et fit
quC + ax + XX, adeoque y   ax XC: a =
adtoque X Laa - ay -  a Sec- 7 atue ita haberi p
X et Y y ex data e, adeoque et X, verum ipsa , seu radius circli
non datur. Videtur autem dari posse, si novam ex aeq. 5 ducamus disferentialem, quae erit
=ady adx F2xdx. Hanc enim aequando cum 4 prodibit nova aequatious inter x et y quam
cum ipsis 2 et 5 conjungendo tollemus tam x quam ty et inveniemus c. Neerum, quia id mihi
suspectum tentavi, in ca exemplo praecedente in curvarum notarum . Veripe ubi
seq. 5. erat ay = Xyt XF et differentialis inde ducta fiet ady = Xdys tyax + fdx, seta
dy: dx y+f, a- x Sed hoc est salsum Nam in numeris propositis cum assumitemus f- 4a et a= e
fiebat d: du: AX:  1: 2, nam =a: y+ F (in aeg. 3. ibi) est = - 1: 2 verum y+5 = 2a et a - x = 2a
ergo fit y+fj. a X = 1. nquod est falsum, non licet ergo aequationes ob differentialitale
inventas. a rursus disperentialiter tractare ad hovum aliquid deter minandum
Et sane non est necesse ay = xy + xf sit aequatio ad curvam quae corva parabolam
et circulum, Tangat Si tamen circul circulus et carvam propositam 
oscularetur, seu duco contactus coinciderent inter se tunc utique nova pess aquali
es valores aequando, sit 
etita inveniri e
ex differentialibus inventa rursus posset tractari differentialiter
dplerumque coincident tunc x et e, seu y fiet in finite parva. Sumatur tamen
assoa santurs opelerer, resaretis sai duatirr eo use p aatuer velrquata
Non tamen video quid prohibeat dami aliquam, quam rirculus cujus centrum in axe ipso