# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068237:0009
# Permalink to this reading: https://leibnizlegible.com/page/00068237:0009?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 24
# Folio 5r, page id 00068237:0009
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068237&page=9
# Source image: https://digitale-sammlungen.gwlb.de/content/00068237/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.84
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

L
Centanda aliqua
Octobe esi 1699
propressio  ehiaracterum in
radicum extractionibus qualis est in ees divisionibus seu reductionibus
fractionum ad decimales. Viden.
Vi Hac ratione sciri potest quaenum progossio sit conveniention
naturae, decimalis an alia, si scilicet progressiones
characterum elegantiores uno alterove modo prodeant
pro irrationalibus, quadraturis, et videndum etiam an diversas progessione
+Ab A + XB d1D
X
648+Y XB
a A  CpHA X AB8
Xa _ NGXAA∞ b44I L 5b4b bA 1
 ∞ ∞ ∞∞6OBa∞∞46BO∞6166
4 1
+ 2
AX A8 Y24674
LxB
4 4
Dx
28 88
Z7
844
inter se comparando constans aliqua
regula progre pnis delis
progrediendi continuationis pro
fractionibus pariter ac irrationalibus
prodeat
Demonstratio quod
problemata alsiora desrimi
non possint; pounntur
posse deprimi, et ab una parte
statuatur et dentur valores duo
unus per numeros et irrationales
inferiores alter per altiores, manifestum
est, tolli posse omnes radices inferiore
salvis superioribus tum scilicet
numeros in superiorum labus transferendi
fit ductus ab una parte virationalis
quantitas, ab alteu compositum ex
superiorit et numero in se pro
modo gradus ducitur atque ita
tandem habebimus ab una parte
radicem irrationalem irredacibilem
ab altera parte numerum quod
est absurdum. Neque enim ullo modo potest
BBossunt heterogeneae llaecrrationales B invicem
d. destruere, eodem modo demonstratur non posse tolli
28
imaginarias apparentes. Hinc jum etiam demonstratur, quod
rigorose, quod non detur generalis relatio sectoris, ad arcum
L - 1 + 1 - 1 + L - -
dividatur in septem partes, dabtur arus heptagoni
2
+ X
a p BA 6 4
X ∞ ∞ 8 P ∞ 6 000000000