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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 6
# Folio 10r, page id 00068130:0019
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ngura quaesita est simnl acivu propectionis in 1bdeo liquido xens rnoni
pouioram oepanturs rice antris ese quadratis velocibit so plbconales qua crtva
eaporum le
ut A
eissse sima
setibdatu
cn duplicata eatione temporum positis temporibs
e
litalist
in progresione Mtritnetrea epunt arcas in pro-
es
l
egmetrica. san si abscissae sant
lpsarum ase arcus sint ut numeri
uare
d
s
adias quadraticae (quo
s
punt abscissarum
temporibus proportionales sunt) ut logaret rmi
e
rax: a = log. Sastad a=
a
sax +d
Sidx tan
L
ga
Et L log. h: a = 2X. fiet RAadx. Sax = van ray: (. C +ct
e
en 0g. 1.a
daxia
e pltaxia
ax2 + dys. seu N NX:
fit fsaux Aia. o
voa
du dy- axs
a
2.a
etrata
vaxia
htriaa.
de
dy ex fe
e
l.
s
u
2.
=ix odtus
pro x none C da nin
 es
atia
a
+= q
rursque arh:a
a t = n4
= na+ maina et 2t- mn-nqu, et
i M - nq
fiet 2ah. a
ira minanq. seu fiet:
ea ton lon 2at tn-n4ra ogh: a = logi n 4 loqm
ex
una
A Z M am + 2gulg.. M  + 44
fit: A loghra, tn = qcd FCM nd- 2B 9dq = Za dn: n + 2m d +3qdy: M r4
seu
t dn: A + C Eam.
e
sit ma si hoc aequalio posset reddi trinalo obtimnissemu situm ia simplilicnt
emoltis si faciamus
2
d.y = et Y nB: 14
e
asit ex ratia et e fit
aa
1
seque
fuius opus est quadratura