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# Catalogue record: 1111 — Tentamen reducendi dimensiones curvarum conicarum ad arcus circuli et Logarithmos
# Incipit: ∫[Sonne] = (1) ∫dx√[[11+10x]/[21+20x]] datur ex Conicis. Sit x = (2)
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1111&katnr=58661
# Work: https://leibnizlegible.com/work/00068070
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 25
# Folios: Bl. 4 (from the shelfmark LH 35, 6, 25 Bl. 4): 2 pages, canvases 7–8, page ids 00068070:0007 to 00068070:0008
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068070&page=7
# Lines: 284 recognised on 2 of 2 pages, mean confidence 0.74
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 4r — 00068070:0007
# Source image: https://digitale-sammlungen.gwlb.de/content/00068070/jpgs/default/00000007.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 169 lines, status machine
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

## Folio 4v — 00068070:0008
# Source image: https://digitale-sammlungen.gwlb.de/content/00068070/jpgs/default/00000008.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 115 lines, status machine
eca ei
iutamen eib reducendi dimensiones curvarum nicaum
darcus circuli et Logarithmos.
1+10X latur  ex Conicis. sit X = ZZ. a se ax=
1+20X
filt 124
1 + 10X  C.
21+207
S. sit g 1 Ex 4 fiet 1 aa
Et
Ld
( = Suxt s 11+ OX
re
21 + 20X
1107
fiat X a a. vr seu ex -- 2a
La d
+a
XN. +1dZ2
 2142075
2e
sit, X = 43: a dx= X = Z: a dx = 2713: a et ex 1 fet
C2
seu  
e
(6
VM
(dus greti (1a + 1022
fiet e siz
Ca 2a + 20Z
C11
Si ergo ( = sade s 11 + ioX
() = (a2749
1 a x. a
21+ 20X
 31 = 20X
en
sen ret1 0 seu e- 2
fir O= utrX, X
xx
et fiat X = ZZ: a et dx = 22dz: a fiet
14 +10ZZ,
21a +20p
(2)
(4
seu O = 2as_
ua tioZZ= 2a saZV
 21a +2572.
torro Datur fBtque datur ergo svaqu. ex quadraturis rationalilus
porro
AB, Z
DE- v
BE cd = a2
VZ dZe BC= f~7 43
ad
2a +2022
sit (d dZ = DE et BC - s18 dZ
fit Zscodque - Pa = ((eodZdZ. Ergo fit
aa
Gu .  f0l  Sez s = feotque 1Z. sed hic me
a
s
a a r2aa
difcinaes.
ZC A B CGA. + BAG =
1oZd3
dia
c
te
e
coqu = saque scon
quae est dentica et per se patet
Aliter sit ne
dZ
Habetur BC -f codZ+ = p a e
oit s.D E = Cd,  (t (Z potest summari ex Conicis 
et fit
1d
Co2dZ= BBCGH= ga, nam datur ratonalite
ABCBBAG = + ABC (3 - G(B3CG = EA BC
codque + dque scod
Alite
in
 o
a LL, 2Ia + 202Z culiogtem esse
Ergo ut sit 20+ 1 = - 1. fiet e = = 1. si ergo O = sed j11 4 10X
c
C
2 Salte ex quara
turis rationalibus
sit DE = Codq  datur (per lalionalem quachatirum (co dZ = 2 = BD
Seodue = Gβ3CG1_ jam GBCG = ABC (3 = GABC
fiet
(codz =
Scodx =
 
E-az- n si potu
taque dimenso curvae sonicae, et id genus problematum reducta
st ad summam summarum conitarum. seu cu pendet
ex quadratura curvo, cujus ordinata et quadratura Caniea pendet
eamqus sed quia quod timmem licet viicatur difficilius quaesito, videm
tamen analysi salis faceere, quia sic res. ad meras ratio nalium summas
et summarum summas, redacta est quarramus ergo V per raliomes
Minio nondum
a usu
Non successitesse
glerimhic nnven
x surio ax =  s
2420 a  E
posito esse
 1 noux (.
aa 21A. aX)
ea ii fit
ex ses
1z: a