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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 25
# Folio 4r, page id 00068070:0007
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068070&page=7
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 169 lines, status machine
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sua= Z1b- sdZ posito)
Sitiu
(2V2 codu co- 2t iea eot sit
cs
6
21a+ 20C
e
(iiq a dZZ
214 + 2622
(4)
Ergo 2 - 2a saZ s siXtio
Soz 2((+207
Nai Sit ZZ = ax fiet: H2zd  - adx et ea seu 2dz- o  adx: Z Ergo 2adz. q ( adX: 4Z = ) dx: X
lodq - 24B + 11Z. 142
eda
Ergo V(odx siponx. Quam vucamus quadia
tau
1)
_ 1 f1CX: 21+28+ = vv: aa ( t  +10 x = 21 ∞V + 20V seu fiet
X= EevD -iiaa, : 10a - 2VV et dX  10c  - 2opp. 2. 2 vdv - 2, v - 1aa - rn
(13) + 262. 10.2ia4 vav (= 2202 du
eu dx =
et dxiX
=2. 11.208
e
(2 10a ( - 2eav
+ 2 24 PP ap dg: 1 lidaam bvo
=11. 20, 2aa vav 21VB -1 a: (3500a - 20∞7... Ergo per 8 et9 fit
(14) 4202
du () +co 2 avav.
X, 1olona 2dvv. Eervlcaa D
265) 10. 21 2VA. 2FvV - 11aa. P3I vaa - 20 V et 22
= - 11.20
 1ona -0u. 2dvv - 1iaa
simil alare Reperi cognata ratione Ya- vel simlia summari. sit pro curva
Ilochiona acalcu paracentulo, in curva alibi posita reperi. at: t = dm:  aX
potito am esse elementu arcus circuli _t radium exs centio circuli ad curvam; et
intero allum curvae abscissam seu intervallum a condirectrice per centrum ducta
sit A sinus veru rom coplementi arcui M respondens fiet du = ad2: taa-
jam X = tA: a. Ergo dt: t = dn; 1tX seu at: vat = dm  San
jam  habetur per M  ex quadraturae circuli recipioco. Ergo set
summam summarum habetur re latio inter t et  quo et ipsa rusus
ex circuli quadratura pendet
Cum Hurgenius mihi quadraturam hius curva proponeret cujus aequatio sit
X + B = RXy. Posui, y = Xv: n sit x = n3B: H + B sit 1 + V = aco fit et
fet (ydx = nb  n. 240 + 2n: 3aco ads es sumta ab ut adjectione summationis
nempe yax = n vVdo - 2n v dv,: (3(V+n si restituamus X et y
fit sylr = nb = p. 199 + 2nXX: 39 se, X inerpit a 0. est b =0
2025)
mn
mm
=,1= 202. 21
Sen v1 est, 20 10
20
20 21 20
V - 18a, - 2.10 - 1 11, 10 + 19.
IL.Ao
20
oexetto ui 2o matro a
V+ Va, H- 10 11 +10 _2. 11, a
12
20
e
20 21 20 21
 p
v a, 2a, E 20. 22
t
Le
 20) 21
  2u a
ra, 13 + Lu. 1 - 1ero p Bori d) seu v- na -11 al 2 +10 0 1 +tromnu
n um -mm
2.20. 2 a
10a + 20Y, 10a +2OV, 21V + na, t1V- 11a, VF ea, V. rea, v+ a, V- H a
vrea LD  1 1 0 ua
 seu ve a, + 10. 18 
M
m nin nmn
en
X 25+20aX
quam summationem ut reducamus ad Quadraturas ationates, frat:
(11
102- 208, 21V-W a resa
(18)
A
ser
seu
21
Ergs A
213
2 212 202021 2a 20. 2)
20, 20.21
2 213
21 2 2021 21  20. 20. 21
Seu r -  a, 20, - 11 + (10. 10. 1
+2, 101 - 18. 1= 18,1 B. + 101 V
Seu 210. 115 + 2. 1011 =4. 18. 153
Ca(1 -V, p= v2, 103- 10 112, 1 - 1. 10l sen 183. 153 - 1 85. 114) seu
viea, 18- 1B. H v. iea, -1 + 101
203 20. 4
20 202
+ 1 10. 1P 10. 15
vtra, 111. 10 v- La, - 13 + 1. 10
213 21. 20
21
 2B 2128
(et 2.20. 2, 18 -W a (.9) 20.10 20: 10 21:1   21: 11 (2(2, 10 21 - 11. 20
2
10a 20, 21V- 11a
oies
vert 15 - V, 102 D, B 1 10 41i -v, 10∞ 1. 11.8 +10-V, 11LV) 162 10. 1 + 18 - V, 1 AV, 18- 10. 1 
16. 10a30 Seu, 2, 10. n - 183. 1 L 10. 1 B +1 8 V 
Ergo  =
2(18) 10d- 20v, 21V- il a
10. a 2V, 21V- 18
n
vrea v. lea vFa v- a 10a 20 v) 2v- 1ia
22
20.10 20.10 W.n 21. 1. jam Bvv
Ergo ap (uBdo, vrs v ea vita viua
v+ b
+b
 ubi b est  a vel- 10 a vel t a vel - 7 a
vib
Ero alp rv. 20  ro 2- ion 2 +: vr. 2) b) (.1) o  20 1 aV r2or a ru nav. . naB) + G
per isit 1Z.
+ 20 10 aa (av
poro savsto = vrbs.
1020 vea = i   ta
1
 na seu  p 10 fdo - 10 (dx 1 pdie nsdo
de
a 20) vrea 20 v ea 2) vita a va
v. EnBi va  io  4 verum hic haeremus nam quaeritur siet
non vero spdo. Sed dZ per v rarsus est rrationalis, cujus reductio ad rationales quaeritur
vtb
Redeundo ergo ad initium, paginae quae quer sit O= (dx. xe  siet .. explicanda est e sic ut sit ax = 23
X, 4 +28 ax
etaex= 2ZZ et C = p22a2 27. a, N 4o . un
nsasta
22 +202Z
e si
(112 41022
Aqq X tro
ergo ex equat. sit B- sax si+1o ax. quarum ergo   finsur s compentii caursa serioque
i i tro ax
2+20
 e129, seu e- 2
ago aefiat 
vocemus D
X= Ddu
o aln ttu venus
ae shero
X Dax et
no deripi dxomnes tenmini habentur dento srimo quarenda ergo lex serier
n eo ZZ
qu
M -Hn
+e
n
+MM
mur
a
si
seu restituendo 
ad- D, v. H a
10 seu 2. 202s
10a 105 a B. La
sit desidevabatu