# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0054
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0054?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 34, page id 824573315:0054
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=54
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000054.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 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.

CAP. 10.
supponamus rectam AB (quancum opus cAt prolensacam)
DunCTO A manencc, circum-
duci; aceoq: peripheriam
secare in variis succestire
punctio B, B, B, _C. FC ab
tiis punctis lectionum rectas
BC, BC, BC. _C. duci, ad
idem punccum C. Manise-
cum cR, Prouc punctum B
ad punctum C. propiiis acce
dicu rectam e B longiorem
tieri ( modo legmencum
prepoticum non excedat le-
micirculum) eBC brevio-
rem, (angulo incerim ABC
NOM MaEaTO,) ulq; dum recta AB ad iptam AC accedentE,
idem trac punctum B _ C, hoc cR, recta B C in unicum peria
Pheria punctum degeneret, adeoq; recta BC (quanca quanca
HC) Jacere supponicur im ipla peripheria; adeoq; recta AB, ad
licum a C delata eoldem nunc angulos cum peripheria Facie
quos prius fecerat cum recta BC producta, nempe angulum
A B C, ejulq: reciduum ad duos rectos; hoc cA, angulum inte-
riorem Cqui est opposci lesmenci anculus) cundem cum an-
sulo A B C, acq; (eadem ratione) angulum superiorem cun-
dem cum ipsius complemento ad duos rectos. Scd _ idem pror-
sus ereniret in simili Ecgmento a By, adcoq; _ illic a B, ad Au
cum a 2 delaca, ealdem ansulos tacic ad peripheriom quos pri
uS Ecceratad q B Culera punctum B productam) hoc cA, c0s
quos A B ad rectam B C (productam) fccic. Adcoq; similium
lEGMenEOrUMI A B C, aB 3, licce inaqualium, ( quod cciam
oppolicis eorum Ceymentis accidie,) angulilune aquales. Ouod
er ac demonstrandu.
Acqseciam eadem opera demonstracum eA, E segmenta illa
similia sine Cemicirculi, eorum angulos aequales esse rectis recti-
lincis; eric enim in semicirculo, cam aneulus ABC, quam ip-
us reliduum ad duos rectos, ansulus rectus.
lcem, in univerlum, angulus in Ccgmenro, aquadis cA ansu-
Drorius ese ubicunq; in ea peripheria Cumatur punctum B, cun
De angulo contactus.
dem nempe cum eo qui est in simili legmento a B7. His poltis