# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0255
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0255?run=74
# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 43, page id 824573315:0255
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=255
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000255.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.87
# 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
PrOD. 54.
Drithmetica insinitorum.
numerorum sire quanticatum arithmetice- proportio
nalium, a punctorel o inchoatarum; (puta vor VI,
V29 Y3, _C. VCO, VCI NC2, NC3, _EC. V990, V99E
V442, V943.ec.) Ouas appello series Sublecunda-
norum, Subtertianorum, Subguartanorum; _C.
Exlempli gracia. Si exponantur ejulmodi infinica cnadra-
ea Rrichmecice proporcionalia, sive juxta Ceriem Primanorum;
quibus in Pabella astionacur rario + ad 3: Forum L aceribus.
hoc est, seriei Tablecundanorum) convenier racio 1 ad 12 20 ne quidom
lire 3 2d 3;) quia 2, 12, 2. Cune Arichmenice PEODOE P. Y inductiono
eionalia.
Tcem, E suxponancur ejusmodi infiniri Cubi Arichmerici
proporeionales, sire juxca Ccriem Primanorum; quibus conret
nic in Tabella, racio x ad 2. IIlorum radicibus cubicis, (hoC nâ haec inducho
eR Terici (ubcercianorum) convenice racio 1ad 1 Z (vel 3 ac quod 1, 1Z, 2 sut
43) _ harum radicum quadraris, rario 1 ad 1 3 (vel 3 2d5:)
Ouia CciliceEx, 13, 23, 2. Tune Arichmecice proxorcionalia;
sicur Ulnitas, radix, quadracum, _ Cubus, sunc Geometrice ortionalor, non
proportionalia.
PC parimodo, Gintinica Beguadeaca, Surdelolida, &c. con- AHtanin 1 mu
Rituca incelliganeur juxca Ceriem Primanorum, quibus conve- istud dechuplu
nic racio 1ad2; corum radicibus Biquadracicie, Surdetolida-
libus, _c. conreniene rationes 4 2d5, 52d6, ec. vel 5ad 14
1ad 23_C. quia nemDe 1, 1 =, 143 18, 2; ICM 2, 25, 1 53
a3, 24, 2; 8c. lunc arichmerice proporriona lia. Adc09, -.
PROP. LIV. Theorema
Lincellisatur series infinita guancitatum a PIN. sione univit salt
etoseuo inchootarum. et continue crescemium, guir. duor
pro ratione Radicum quadraticarum, cubica- igitum alca in
rum, biguadraricarum, exc, numerorum Arithrieriée ductono opus
proportionalium; (quam appello seriem Subsecunda non fuuis.
norum; Subtertianorum, Subquartanorum, e c.) Prit 1o-
tius ratio ad Periem toridem maxime aegualium, ca
TIR Z
qua
demonitrare
autor Bohuta;
arithmotico pra
datu ividiat ot
ex quadratura
parabola rera
visi conitat,
similitique ec
cquadratum r
Ecquam parabo
cordum conclu