# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0252
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0252?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 40, page id 824573315:0252
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=252
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000252.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.92
# 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.

Ariihmetica Insinitorum.
ProP. 49, 50.
cundanOTum) cR L ad 3; erso Ceriei planorum conreniet ra-
eio 2ad5: Quia nEMPC X, 3, 5, Cunc Rcichmetice proportio
nales: (ProucUlnicas, Radix, e ouadracum lunc Geometrice.
proportionaies) Er quidem, li rectae TO, TO, _C. tint Ceries
Sccundanorum; carum quadraca (rel plana quadratis pro-
Porcionalia) erune Cerieo auarcanorum; cui in l’abella conre-
nic ratio 1ad 5.
P R O P. ZLIZ. Corollarium.
Cmiliter; si complemento semiparaboloidis ex
bicalis aptetur (circa ipstus Diametrum) Conoi-
des vel erramidoides; erit hoc ad Cylindrum vel
erisma (super eadem vel aequali base aeque altum,) ut L
ad 7.
Nam, cum rectae TO, TO, _C. (in complemento Semipa.
raboloidis Cubicalis,) sinc series Tercianorum, guibus in Y2.
bella convenicrario rad 4; horum. quadeatorum C vel pld
norum quadraris proporcionalium) Periei conreniee racio s ad
n: quia i 4. 7, sunc Arichmetice proportionales. Velcciam,
quia plana lunc series Sexcanorum, quibus in Tabella alligna
cur racio 1ad7.
PROP. L. Corollarium.
sI Pariter; si semiparaboloidum aliorum (puta Bi-
Lquadraticalium, Surdesolidalium, G c.) complemen-
tis aptetur (circa eorum diametros) Conoides vel egra
midoides aliquod: habebit illud ad Cplindrum vel eri sma
CImper aegualibase equealtum) rationem notam (puta L
ad 9, Tad TI, ∞ C. 3
Cum enim complementorum illorum rectae sinc Ceries quar-
eanorum, anincanorum, ec. adeoque raciones in Tabella astis
nacas habeane, ad5, Iad 6, Rc. series quadratorum (vel pla
norum quadracis proxortionalium) cationem habebune
xad 9, LadEF, _C. Guia L, 5, 9, rel 1, 6, IF, _C. Tunc acich.
metice