# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0321
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0321?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 109, page id 824573315:0321
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=321
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000321.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.88
# 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.

P. 136.
arithmetica insinitorum.
dratum Diametri. (Ft quidem mediae proportionales e
runt in subduplicata ratione ordinatim- applicatarum in
Circulo vel F. Uipsc.)
Sic eadem parabola AFO sicu directo, _ PRa sieu inverlo DO
Fica: erune isieur
(ex nacura Parabo.
IX) Oandeaca or-
dinacim applicata-
rum (nempe recta-
FAn DO, DO, _C.
delcendendo; vel
Doo, Da, _c. alcen
dendo,) infinita se-
ries Primanorum;
DUTa a, 2a, 3a _C.
vel. eorum loco, a3 b, c, _c. quorum maximum dicacur D
nempe quadracum Ba(IsFO vel A∞:) EF proprerca, cadem
INVerCO AIEU CrUnE D = a3 D = Z a3 D = 3 a, _C. vel criam
D in a, D  b, D un C,_C. Aquale enim cA singulorum incre.
mencum. si a minimo ordiamur, acque decre-
mencum, E ordiamur a MaximO.) EC conseguenter ixlae ordi
nacim applicacae (quippe in quadratorum Tuorum rarione sub.
duplicacas) illic quidem V a, V 2 a3 V 3 a, _c. vel V a- V b,
a c, _C. hicaUTeM V: D = a. V : D = 2a. V: D = 3a_C.
vel (corum loco) V: D La. V: D m. b. V: D = c. _C. Ductio
igicur his in illas, emersunt rectansula OD a. Nempe
Ductis V: D - 2.
In V2.
PienE V: aD - a
V: D = b
b.
V: D = C
V c.
_C.
_C.
V: bD - b 2. Y: CD = C.2. eC.
Horum aucem rectaneulorum omnium secrepium, ad
rectaneulum V: D = O. in V: D = O, hOc CA V D = =D CO.
ties poliemm: Hoc cR, Colidum ex illa mulciplicarione orrum,
ad dicrum Parallelepivedum: eA ut lermicirculus ad quadracum
Dametri per praecedencem.
et proxierea etiam medixe proxortionales incer concieuas re-
CtaS