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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 40r, page id 00068049:0079
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 67 lines, status machine
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. sit X= yy fiat Ca Cydy Sb hobysus
(A+ bx
dx 
AolX
sihtabyus
rgo ipsius s figurae ad u
pholyu
t hoc ergo habetu
halyi
ratur momentum in verticet audem
satur momentum ex uxe seus 5zzdy. itaque datur reca in quam cadit
centum gravitatis nonspens sepper per cocursum condrrectricium
Z eliam = Y h Ab gy - ab s 9: bh-llyy
1
hat, Z = 15 54 + 9b G yy -ablly : h - ly
tha
a - ly, Z = . . . . . . . . . .. y : h+ ly
halusque + h - ly Z = EhZ
quia datur Jyzdus. Ergo
si daretur S(+ Caus vel sih. du
daretur SZ dy
sit ds ti  abhitix - abl- itq d, h +.. vy B-.. . datur
U
ry.g +nG dus  + 4 = X teq irtqus +hq
y
datur si. yZ y3
h+ly
h+ly, y
y etc. Namdatur Curetu sit
Datur generaliter (ZXC dx Modo e sit integer. Ergo ponendo X = yu
et ex =ryds fret SzX ax = (Z y et
dy
Datur fax Z et f quaeramus seriem talem
XZdx, SX Zx, sx
haberi posset daretur et
X
dx
2t y dx
SX Z dx cuius lex
quia nihil refert sit Z = Saa- Xx haec pendet ex quadratura circuli
sed XZ seu X saa- x redigamus ad rationalitatem. Scribamus potius Z = Trax-XX
= er ca xvia fit  2ax = XXa = XXVV seu X = 2a0) aa + vD
et ax = =4a bdv, pilaator 2 2av: aatve ergo fiet
Qex = 4a vD do, (2) aarvo, sit aarvo-
si tangests, t erit a = = - +3 + f etc. Ergo da = 1 8- t + F etc.
erua
 HH Ergo dar Ergo an = a(dt. sed + seu A T ad BC seu traxXx
=
1+ +F
ut a ad auxseu
+ = a Y2AX XX :j a = X arcisse  arr. A. perK per La = sect A e
et sect = segm ABC + = Frax -XX a =X. Ergo E segm. ABC = arc. A per a = rax = XX (X)
ergo Lt seu 25 Srax-XX dx =aa5 dl = at (a. X)
ad est cum v crescit, X decrescit
ax = XX _ sit Z = VX: a si et ZaX - XX = fOVXX: aa seu 24 = aax + vVX
seu 2 Co X Ed,: Rat vi et dx = - 4 dv;: 12) aatvo Ergo Zdx = BaVdv: 13) aa +vV
d = 2aa0: aatd. Ergo (3dx jam si v = est  Et et 720
4=20
si 220 tunc vel x 20 vel X= 2a, et
a qpitio cum 20o sit fyex=
quia igitur oportet  esse infinitam, cum X 20 dinc inverso
nit
vonasi 200, pt bd fit xC2a. Hin fit
plane modo est procedemem nempe meipitur ab X = 2a, quia
tunc v20, et tanc inde cum v =1 fit
Redeaum ad 
6