# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068022:0040
# Permalink to this reading: https://leibnizlegible.com/page/00068022:0040?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 20v, page id 00068022:0040
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 21r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068022&page=40
# Source image: https://digitale-sammlungen.gwlb.de/content/00068022/jpgs/default/00000040.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

At sumuna omnum A
quoum
Esto curva ADC. cujus od ordinata ABp, X. EC
BC,  y ⊓ AE.
Erit X, a
d
a quad. Hop +
2
et X p ad
a +y
ay axtyx.
quorum
a + y, H
aequilibrii
Summa est mongutum figurae AECDA ex HE axe _E
aY2 que pendet ex qu ad cunte
a2+y25.
aequlib
est momentum figuiae AECDA ex v Axc AB
jum ut quaram, y, ita procedendum est, ex aequatione figurae
fiet:
y X - a y  - ax sive 3 - a y, - a sive
 a ax, unde +9 + =  a  a -x Unde patet Toliter
y- a y + a
deau figuram a sa=x dm pendere a quad ypervolae. Nam si  ipsae
Y pendent a quad. Hyp. aufer ipde ipsas a
Hyp. etiam a Y a -x pendebit a  quad Hyp. Ejus vero centrum
gravitatis pendet a quad circuli nam si ducatur in X fiei: a Sa-x
quae est homogenea circulo, si  Ducatur in se, fier: a- a x quae
habetur absolute. Habito ergo figurae cintio gravitatis ex datu circuli
quad ratura, quaeramus aliesm ejus alterum ejus indeterminata, fiei
a at - a X B Y X, erit init ordimant X + S X + du  5 4a
unde X +3 Y y+ aua figura paltit ex quad Hyperbolae
plag. 10 Ergo et  yt+ a pendoit ex quad. Hyp. Ergo a X -  ex quad Hyp
sc
sive a = ax = y, CaX + y. Unde  aYa p y. cujus ordinata
ex qu. momentur ergo omnim y ex axc eorum ex quado circuli.
Sed _ sasa X H y. quae tigura pendet ex quad. Hyperbolae
 Sed Xra Sa- pendet ex Quadkaturu circuli )) Invenim
tit ad figura; nostram redeamus
in ea BC, ess momentu
AB
figurae ex AE AB AECDA ex AE pendea ex quad circuli quia
a quia ay Xy a2 
a
momentum i vero
figurae ex ABCDE, ex AE, pendet etiam ex quadratura
circuli, quia X y +a Juae x 4a quia inventa est
YY + a Yae-X
a ideoque cenerum grantatis figurae pro
positae pendet ex gro quad circulii ergo atu
a - a x + 2a2 ae X + a
7
quad circuli pendebit.
aty, 1
et per consequens
x + at
Sed ista exitum
item
24 a a- F ex
parte
Ejus nomentum Hujus figurae  quadrat ordimatar
y habentur absolute, sed y ex X dunt a
et
2
us
fus
X
ias
4 ( 2 + a
1 Laeay, et X, VSaeraega
vide
pag.ul