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# Catalogue record: 37167 — Impossibilitas quadraturae circuli universalis. Transmutatio figurae analyticae simplicis. 1: Impossibilitas quadraturae circuli universalis
# Incipit: Quadratura duplex est, universalis et particularis: Universalis, quae
# Date: 1676-04
# Akademie-Ausgabe: AA VII,6 N. 018
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=37167&katnr=Cc2+1245%2FA
# AA VII,6: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-6
# In the Akademie-Ausgabe: AA VII,6, p. 201 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII6.pdf#page=201
# Work: https://leibnizlegible.com/work/00068024
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 6
# Folios: Bl. 5 (from the shelfmark LH 35, 5, 6 Bl. 5 (v°=Cc2_1245B)): 2 pages, canvases 9–10, page ids 00068024:0009 to 00068024:0010
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068024&page=9
# Lines: 94 recognised on 2 of 2 pages, mean confidence 0.80
# 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.
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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 5r — 00068024:0009
# Source image: https://digitale-sammlungen.gwlb.de/content/00068024/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 58 lines, status machine
Duadr. Circ. generalis
impostibilis
Quadratura duplex
est Universalis, et particularis.
Universalis, quae regulam exhibet cujus ope quaelibet circuli portio
possit mensmari, seu cujus ope ex data tangente (vel sinu) possit inveniri arcqu sive angulus particularis quae certam tantum
c
vivincte
si quis totum circulum totamve circumferentrum
exhiberet, non vero nisi eas partes quarum ad cucumferentia nota jam tum ratio est, is quadraturam qualis desideratur, universalem
tenerulis
non dedisset. Itaque quadratura perfecta et muveralis incliit dectionem anguli universplem, sive Trigonometrtam accurate
Geometricam, age quae longe majoris sunt momenti quam ipsa quadraturcirculi
particulariis per se spectata. His intelligentiae
causa positis, ajo quadraburam Uinversalem, seu relationem generalem inter tangentem svel sinum)
ala
ef arcum
lm dari non posse, nisi qualis a me exhibita est per senem aequationem terminissum
alnuiter
etalibus infinitor Inveni enim radio AB posito ∞)
tunc fore
3
2
3
9
tangente A
+1
1
etc.
4
Hoc ergo demonstrabo +heorema: impossibile
Arcussu
∞
C
axpeltato
seu C fore
est Telationem
generalem inter tangentem (vel sinum) et arcum exhibere, nisi
per Analysin transscendentem. Quare et sectionem anguli univer salem
a
seu in data ratione, et generalem, cujus libet circuli portionis quadraturam alia
sequesur
quam qualem dixi ratione analyfice exhibere impossibile esse demonstrabo
Analysin autem transcendentem voco quae non sit per aequationes ordnatas finitas tum vator incognitae
rexerimiber
non per aequationes ordinarias certarum demensionum exhibetur, sed per infinitas aut m
Tac. Gregorius neque particularis neque universalis Quadraturae impossibi litatem
deqobgalias,
evicit porro Theoremate isto semel a me deponst rato infinitis laboribus, inutilibus imposterum
finitas in effabile.
a specem pliue hodum center ad eeem sacene plan bies.
supersed ebunt Geometrae. NNam plereea Methori quibus hactemus in qvadraturam circuli inquisitum
su
tc possem
est, ita comparatae sunt, ut si unus sectoris aut segmenti darem quadraturam, omnium darent, una quadam
vel
relatione sue aequatione generale Quas methodes ad unum omnes mutiles esse jam nunc praedicere possum
ut enm qui nimium probat nihil probat ita qui plus facturus est quam fien possit nihil agit. quar

## Folio 5v — 00068024:0010
# Source image: https://digitale-sammlungen.gwlb.de/content/00068024/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 36 lines, status machine
eodum planamodo ostenimpossibilitate
non
quicunque imposterum in Anal quadiaturam circuli inquirere coolat,, circumspiciet an methodus qua usum
eA ea tantum methodos quaerere deberh,, quae ad certas tantum circuli portiones vel etiam totam dirigument, non
nam
aeque a estadleris ap
Nc
b si deprehendett generalem etfcat fores
perfanti
debrere
vera esset utilis esset, fiustra progredietur.Certas aulla portiones
vel etiam totum circulum, (sed non quamsibet ejqus partem) applytice inveniri pose
e
anatusi ordinana genespti de
non dum despero. Qvemad
erahibese metis codum vcauo gene slirul ndiature  et
dum lucto erdis quamlibet portionem melato generai auaste
eadem velae modo simposribile esseta ment
eodemplene moda ossendi spossit ex venemli arcyli quadracurae enopibilitele sugpositn, uta vgo hihito mines tahnendin
e
et
segmerta hyctoerdatia absolute quadravimus, quou
a
uo
silgemus alterum c d celeberimo Hugemio
ab anitios
hltum e alterum mihi fortuna obtulit. Artem autem dispernendi Methodum universalem a particular
plerumq non codmodum afficitem arbitior excogitandi methodos pure particulares, et
invenm
discernendi ab a generalibus alterius loci est explicare
et ses. 
Rursus Y e Differentia inter figuram novam et prinam aequatur diffenentiae interprima
v
et e+
 rectangulum circumscrisitum adeoque
XXXV veC V NB