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# Catalogue record: 764 — Tentata impossibilitas quadraturae
# Incipit: Sit aequatio ax ⊓ b. vel similis
# Date: 1679-11 (79-11)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=764&katnr=58342
# Work: https://leibnizlegible.com/work/00068033
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folios: Bl. 19–20 (from the shelfmark LH 35, 5, 15 Bl. 19-20): 4 pages, canvases 37–40, page ids 00068033:0037 to 00068033:0040
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068033&page=37
# Lines: 239 recognised on 4 of 4 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.
# 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 19r — 00068033:0037
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 50 lines, status machine
Novembr. 1679.
imo pihit
hinc ductum
centala mpossibilitas quadraturae.
quae hic de Ayuibolae quadratum ea dempossumt applicari quadra
turam methodo mea
Sit aequatio
X
a p b. vel simalis
ajo si  X non sit quantitas rationalis
algebraicam
nec fore quantitatem analyticam. Nam
si sit irrationalis, substituatur ejus valor
alytica non est in exponente,
a
quas
unq
aequatio autem ljus exponens est irrationalis
alytica non est
numeri et sit b
sont a et b
Hinc si appareat
a et b tatem habere relationem, ut una
quomodocunque secundum exponentem rationalem in
se ducta non possit producere ulteram, tunc
quod statim apparet, tuto concludi potest
X non esse quantitatem unalyticam algebraicar
pono Cogarithinus. Inventio pendet
a resolutione exponentis aequationis in
qua incognita est in exponente. Et quadratur
Hyperbolae portionis hyperbolae pendet
a logarichmo et unius praeterea portionis
Hyperbolae Quadratura, exemplia gratia ejus
Lex
quinquelinei ACBDE
quadrilinci cujus altitudo
sit 1. et basis CB sit 2
cujus artam
cujus area n sibene memini est 
1
e
+L - 1 Ac. quae est ad aljam aream
quamcunque
ut
rithinum CB.
quaemaq
ACFGE. ut loganthmus CF ad loga
si jam figura coganthint
seu aescisra
cujus numeri sunt algebraici

## Folio 19v — 00068033:0038
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000038.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 39 lines, status machine
habet unum logarithmum algebraicum
itque is erit ad loganthiuum a 2 hujus ipsius
figurae, ut area Hyperbolae H loganthm
algebraico respondentis ad - 1 + 1 et
sa
ll
log alque Ar.Hyp log. alq.
log. 2
L
+ l
vocemus logarichmos illos 3 Tabulares
sit q logarilhmus algebraicus og Tabcularis
logandimus ab a. fiet:
log. tab. a 1
log. tab. 2.
log. Kyperbolicu ab a C
1-  +  erc
e
ponatur logarichuus Tabularis ipsius 2 haberi
potest enim assumi pro arbitrio  ev
ponatur aequalis Y
log. Fab. a, 1- = 1L et
fiet.
log. Hyp. a
quadrari non posset. Si vero non sit
algebraicus. Tunc videndum an sit iti
log.y tab a
et fiet
1- 1 + 1ek.
log. Hyp. ab a p
 seu habebitur
Caeterum omnis
area Hyperbolae
logarithimus labularis hebet esse rationalis
-  + L. etc.. tuna seu ansibere
2
algebraicus. ni hilominus area Hyperbolee LkMF
forte quantitas algebraica divisa per 
quodsi ergo cogarthimus ille Tabularis esset ot

## Folio 20r — 00068033:0039
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000039.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
ce X
 2
si est Algebraicus. sit ABR1. cujus logaretamus
Ia
3
da
s
22
e
logaritimque
ipsi FG
nempe FG
sit es AGB FEBC
et AE⊓ n.
erit GF proportionalis ad
Hd in ratione multiplicata serundum
rationem numeri AG ad numerum
AH. seu erit GF
L 
E.k +
e
b
a. Il a
positoqu a 1. et
et Cp 1- = +L ek. fret
le
pl e
est 0. sit AC2. cujus loganchmus rC
quaritur
11D A
AB AC
e seu sumi AB pro unitate et fiet.
de
 Tocarichius hyperbolicas seu area Hyperbos
F
s
 11
sit AB a et AC ⊓ b Hd et B
a
de
AB
 posito ipsius AB logarithmum esse
cb a e+Cx
et DC sit logaritimque arbitrarius assumtus ipsius b.
i
2
aquatio
+
et
12
posito n numoro, et 
logarithmo Hyperbolico, seu area
1t
cujus basis est n
Haei aequatio ut sit algebraica, debet necessario

## Folio 20v — 00068033:0040
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000040.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 95 lines, status machine
cllens
1- 2t L etc
esse quantitas rationalis
 si lut t et non esse quantibarem ratio
nam 2- + e erc demonstrari potest non est
dequantitatem rationalem. nempe ex natura
don dipeogresionis decadicae neque enim servare
potest periodum. Sed me sed melius idem
E.  demonstrabitur ex m mea mechodo differen
d
an deberet enim alia series dari dlfereu
Htim athibendae et series in quibus suntindeterminati
numeri terminorum in exponente.
e2
e
e
= 47
C
3
d
e
4a
L = + L = L BC
laq
X - X + X - A
X- X +
vantitas
2
etc.
porro
et
quae quantita
es
non est rationalis
non est rationalis debet Al aequari
C maltiplicato pr numerum catio nalem
ratio aequatio algebinica. esse debet.
quantitas algebraica esse debet. Imo sic agendum
facile constare potest L non esse quan
fitatem rationacem prando n non est aliqua
potentia spationalis vel trrationalis) a 2. Sed
si iluue in fiicerto manet sitne penebr l. Algebraica
eta est
vel non sed si n sit talis potentia debete
numero rationali ilagrvidendum an
possit divia
C1
e
si punuu pertum est meliq saso
ee
eam
X
2
entral
etc nunquam esse
Bun
3
Ga
el
Cogein rl
e
hyperbolicam sporedentes esse
e+ de
algebraicam. idem probabisu
5
ecaet
Wbn
as montus
ud ir
iseu posse quantitatem latio
mabe
tsese si X incom
ex tesse
Bs
a
i suen
Esse panc pobatu facititr
sinabiles
evice
t
a
 a
p+
rs
s
d
Leeu
EC
1X
es
e
epse
leu
le a
demonstran poete