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# Catalogue record: 1147 — De impossibilitatibus quadraturarum et summarum generalium analyticarum facile dijudicandis
# Incipit: Sit Terminus seriei vel ordinata figurae quaecunque y. quae y sit
# Date: 1679-04-18 (79-04-08)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1147&katnr=58685
# Work: https://leibnizlegible.com/work/00068073
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folios: Bl. 3 (from the shelfmark LH 35, 7, 1 Bl. 3): 2 pages, canvases 5–6, page ids 00068073:0005 to 00068073:0006
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068073&page=5
# Lines: 100 recognised on 2 of 2 pages, mean confidence 0.87
# 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 3r — 00068073:0005
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 45 lines, status machine
8 April 1679
De impossibilitatibus
Et summarum
Quadtaligarum
generalium analyti
carum faule dijudicandis
st sedes Terminus seriei vel ordinata
is
quae y sit expressa
per formulam fractam ex litera X. formatam.
quaeritur  dis in figuris.
quaeritur
CL ax
seu
posito 2 aequa y
sit eat equantites cintegra quaecunqa
site et ponatur
L dx aequ. 1
et siet  aequ. b b + C+ d erc. ponendo
ja
e esse A b. c. d. esse formulas integras ex data 
datas fiet: rationales vel cirrationales, et
rrationales simplices vel compositas, neque
tani 
β. 1ec A
enim id refert, fiet:
de aequ.  dx aequ. ∞b db + βC dc + ete
ponatur primum b. et c, etc esse rationales in tegros
eo casu facile ostendi potest non procedere cm
pontunem comparationeq nisi aliquam
-
1a-1 vel  Ce vel similes
Vet quidem saepius
sit quantitas rrationalis quod nempe cum est a
aequ. 2. vel X aequ. 1. vel a aequ. 01 sed cum
x-
et ideo
non servit. cum X est 1. tunc 4 - 1. est o. es deo
ideo fit quantitas constans, jam tunc ab etio
erit quantitas constans non ergo compa
lis uum 2. Restat t a sit aequ2
db autem post esse inconstans sed cum b sit
st
b
integra etiam ab erit integra non ejus

## Folio 3v — 00068073:0006
# Source image: https://digitale-sammlungen.gwlb.de/content/00068073/jpgs/default/00000006.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
comparabilis cum L
ce V
rationaliss
simple
qu. 2.
At
a
denique
s
quantitas intergra
catrogam
ab etiam est quantitas integua rationalis
srgo nunquam prodit fracta. Cumi
quod in singulis locum habeat et in
C
toto locum habeat patet quantitate ratio
natem fractam, non posse dodum
differentialem integrae c. Eodem modo videtu
oitendi erationalem, non esse differentivnt
irrationalis Nam omnis virationalis
simplex aut differentialem irrationatem
composita. fac
iu
s
Ergo multo magis
methodo facillime piri potest an data
aliqua figura sit quadvabilis universaliter
Nam hinc ponro intinifestum est si exponentes
summatricis sint nmeri irrationales, seu ipsa
formula sit plus quam virationalis. adharce minus
rem procedere.
Nac methodo etiam
investigari potest
Ain figura aliqua ex
altenus datae quadratura possit quadlati, c9.
an figura proposita quadruri possit ex quadratura
etc. Ecogitari forte
Hyperbolae
elaam ratio poterit e quadrandi omnes
figuias per paucas certas et determinatas
convenientisssina ratione.
Eadem applicari
possunt et ad series summatrices, exempli
causa hac methodoscire possum an de tur senes
-
summatuix huous
 1 + L = 1 etc
si daretur, daretur et tetragonismus. Nonlamenta
verum non datur esset enim sob decta) rrationalis
mnatu
qualem nullam esse posse demonstravi alias. Sed
etsi serres summatrix non detur, seu regula communis
pro qualo quo quibus libet serici termunis hinc tamen
non sequitur nondari specialem casus aliquando.
e