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# Piece: https://leibnizlegible.com/api/records/818/text
# Catalogue record: 818 — De quadraturis rationalibus ad logarithmos reducendis non succedit nisi cum divisores sunt reales.
# Incipit: 2a³∫[dx : [aa-xx]] est logarithmus de [aa-xx]
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=818&katnr=58400
# Work: https://leibnizlegible.com/work/00068041
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 23
# Folios: Bl. 23 (from the shelfmark LH 35, 5, 23 Bl. 23): 2 pages, canvases 45–46, page ids 00068041:0045 to 00068041:0046
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068041&page=45
# Lines: 205 recognised on 2 of 2 pages, mean confidence 0.66
# 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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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 23r — 00068041:0045
# Source image: https://digitale-sammlungen.gwlb.de/content/00068041/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 94 lines, status machine
ZaSAX: aa-xx est  logarithmus de aa- x
a
qua est logarithum de . X + log. de a +X
modo bo a +x aequ a dx: a+X. Ergo) log a. X elque a +X est aequ.
n aequ. 2a ax: aa - XX
et eub n
a
atu
e
AF logacit log. a- 
e
pe
2
2a
aa xx
+ BE, a: a+x
em
aegu
A∞ log a 4 X = DE vel BF, log. aa 
e
Addatur Modus quo invessigam Longitudinem Loxdromiae
AB vel Ad, X.
2
DF, a: a -x
asd
aa
in figur adjecta sit At vel AV a.
Cd, aux d ∞ aZX
vedeam Haec plongius produxi jam olim dideauus quid
m
fintuccum. divises fomlarum sunt imaginarii. ut. quaeritur
e
2
 a
log. aa+ nfera 1 e seleatur e quaeritar
de
Loganthmmner t Cogxilluo sedivscum; fiet uu aequ= XX. seu Xequ. y
er
c
adeoque
a: aa tyy foret log. _u arg
osuqB (
-
ct hae a
an hoc verum sit ut possimus fidere caticulo per
Imaginariasonscilicet 2a fax anirus ergo du equaus
e
i
ft
e
jam si X aequ. ys 1 erit ax aequdus V-1
a’ergo erit : 2
aA
ress ser 
e
23
d 
de
e
argoia
at sieS
s
quadralog aargus test quadrat. de fay taatyus
4au
seu
Ergo
se
m
mnatio log. a -x aequas dx.a x.  et eodem
a dx  4 e ∞ equ  sax
aux atx
Ergo erit 2a si pdy: a  ag.
duplus Logaristd A: aa- xx est logiathmu de a. ax
+
Nam  logarithmys de
di
erquam ae
urgu
e 
seu
1
440
2a
quadr. log. aatyu est quadrat de
 si esser
 aatyus
2
Cay:natyg
si
et
au ejuss logarillinus erit: 2avsy: natrus
sedapt
am de
e

## Folio 23v — 00068041:0046
# Source image: https://digitale-sammlungen.gwlb.de/content/00068041/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 111 lines, status machine
010.
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t
ae n
sa
et (Cx essex. et tunc
eum s 
dxit aqualis santio
tac
x sut a X. junc xa a erit Dee
(d Xa erit = AF. log. de _Xa
eta d
et fdx: X Fa erit Bg. AE.. Ergo AC AF seu log. Ctx
e
 equ X -2
uea
CAsi F.
og nex+
alo
sa
m 
eodem modo fore
ea ade
oafiet: bb+ Xx eego 1o0 codnus log est. 0. 004)
e
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fu
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t aerge
A ek.
p. 20 15 500900 1000
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Da
i
a
a
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emares non
0001 error foret
minor quam
vo
acum tamen differentia inter boni
 et d. 00434
qu
Non ergo
i
e
et10000 +3 sit
longe majorvit
licebit  ungligera
istam quanditatem. +A
moinde non possumtue higc uti satis logarithmis
s cam
igneraliter tameu daista regula succedit. sit mr
ex + 2CX +em
(A)
e
a
n
num
et
lb fiet jumm ex ma  aequal log. ut selvus   ploq
X FLX
en
eum
es
a Ael.  xim
e
xen
formula rationali; haberi potest quadratura
per logarithims, modo divispres ejus formutae sint, reales. In megalivis
ercum 1 m. n.  nonsunt affermativae aliquid est mutandum
 e
xel. XFm X+n quae invicem decta dant X + EX+ Im palmu. et d
5
summm ductarum in  vicem binicuum est +2lX +im
Et proinde data quacunque
a
consonet C pro mistentit, nam si poneres
e
 Ot =00S
noa
s
 f.d X: Xaan, aeq. log. TX a
3+
a = bs-1 dx: XX+ bb aequ log. XX1bB
+ X
ote
ac P. 01333
0001
+
inficito .
.
sed
garichnus de X- a est A(F) posito
sotesse X-a, CA  vel Dxessea
Ergo AE= AF erit log. de a tx 4 log l: X- a et AE+ AErgo
tam paXI. Xta rga R
sit b, 1. et X.
ITXX.
dvo
1
et
t
si quo logarithum aliquis
si
a
quid sic  quaeritur
e
ile
201