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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 84r, page id 00068197:0167
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=167
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
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e
si sit dx.x= adX: X Ellatutum etirvae, adeoque
d shydy + ax ax )Y fart s: et aa. (X dx = XXaXdX + XXdydy. Et dydy= aa
u
as
et
e
Axie
aa XX ex: X quaemtur per avaeratur per quadraturas rationars. Fial ((aa XX) = )aa - XV): aa
teu (a) = aaXX) = a)- 2aaX V + XXBB. Et a X = ZaaV:, aa + vD et (aa - XX) = a a - XV, : a = aa a + =44AVY+ aaV
a
4L WD). 2+244V
en
+y
: ergo aa =XX) = , aa - vv,: ac+ vV e dx = 20
ex = raaro, tael aa - vD,:, quauror
sit ) (aa- X∞) dx. X a e
et pro We ponendo
potusse imrostatim te
mlap
ast
aa -vVI .C
Ergo Y(aa-XX) ex = 29u
Udo l ua tvo)
adv Du (aa - vo:; aa+ vn): V
fiet I(aa =XX) dx: X = a Z qui
aquationem
sa
2
: a4
v+ 2aaDvav. 2440,q (an tvn
(EICD +vv). 20a0: aa+
a vdvqu (aa- vD, aa tvn): vi
. 
Et videorem
Nam proponitur a saa reddi simpliciorem. Nam
i
e
fiet Haa-at at: t
(aa -XX) Xdx: XX, Eet XX = aI
inon poterat him praevideri. Hinc sial da - at = WW fint + = aa-wv. et et -- 2Wat
pproponims ssaa =XX) ap: X ut
lat
et habebimus Haa at) et: f = L
1
v. WddW: da - WW
ergo
d
 seu curva cujus eos
cissiee sinc
e
rreus sint pproporvuriales adsersis loganitimis si lonsfoitha
numenis, pender
ex quaoq tura syperdic
quavalieras elem quibus summartum
ementa
ou a: aa Wii pendere a
progivistonatu
Paet etiam hanc divitia
Olumenta a susa
e cavicem.
., a f7). 7
.2
mti