# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0247
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0247?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 241, page id 845634801:0247
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=247
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000247.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.86
# 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.

in duca
ue
enda 
ionens
iteCo
Ot
natO
1A1d
ipsi
15 qua
OVPPLEM E N TVM GEOMF ZRTX
Citur Per ceneum minor lcproportionali inter alcerius parreminteriore
Itaucincidat circulo, _ ulterius porrecta cum quoque circulum lecet.
circulum sumpro, educta. Vna BC D ETANHIENS PEF A CCHETUI, AIICFL BCP. Vde Palces
exreriores secancium sinE BC, BF; incerIOTeS CD, EF. Sit aurem BC minox Me-
dia proporrionali in-
TETBE, LF. (HIOCaU
rem accider omnino,
E quando FF est ma-
Jor ipla BE: quoniam
BC minima est inci-
denrium circulo ab
eodem Bpuncto, pro-
Portionalis auré me-
dia inter BE, EF major
ericipIa BE.) Dico abSC
Bposse duci eam pro-
porrionalem icaurin-
cidat circulo, ee ulce-
rius porrecta ipsum
quoque circulum se-
cec. Circulum enim
eundem tanGAE BC.
Fric ioicur BG major
proporrionaliinterBE, EF. Ntam et BC PlopOtionalis inter BE _E coram BF. Ouare
acidens cducenda contisterinter puncta C. G. C onuIaC Tahic in IL. P orrecta igicur BF Lul.
cerius secebir eundem circulum, urpore in I. FF conltar propou.
PR 0POStLFO II.
Si dux linex rectae ab eodem puncto extta CCuu Cuucra spute
CCHE, UNaPCF Centrum, altera lecus: est secans prima ad secancem secun-
dam, licut pars exteriox Secunda ad partem exteriorem prime.
Circulum (OB A CCBErO
descriptum, sec ene dux li-
nex rectae ab eodem B pun-
eto exrra circulum (umpTO,
cductae. Vna BC D, altera
BEF. Vnde parres exrerio-
res secantium sInE BC, BF
Dicoese BD ad BF, SICUE
BE adBC. Octensum est e
nim in elemenris, id quod Ar
(ubBD, BC, aequari ei quod
CicTubBF, BF. OHAFE CON-
Narprovolicum.
_ Parrem exteriorem. Potest ab eodem puncto duei illa proportionalis,
Circulum sub A cenrro descriprum, secent dux linex rectae ab eodem B puncto extra