# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 291, page id 845634801:0297
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=297
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 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.
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# After the first blank line: the recognised lines in reading order, one per line.

icium late
subject
gi1Bj
11b.
3cub. 1184
Din B
pd a1
diaeo
115
unce
Inquarto, ut guinta minus cercia lexies, plus prima, ad guartam quater,
minus sccunda quater.
In quinto, uc lexta, minus quarta decies, plus lecunda quinquies, ad
quintam quinquies, minus cercia decies, plus prima.
In sexco, ucsepcima, minus quinea quindecies, plus tertia quindecies,
inus prima, ad sextam (exies, minus quarca vicies, plus secunda lexies.
In sexrimo, ut octaraminus sexta vicies semel, plus quarta tricies quin-
Guies, minus secunda sepries, ad seprimam sepries, minus quinca tricies
quinquies, pluscerria vicies lemet, minus prima.
Ecita in infinicum, distriburis cuccesire in duas parces proportionalibus,
lecundum carum lexiem, urrobique primum adtrmatis deinde nesaris, et
C lumprismuleplicibus, uc ordo graduum in arriticiola geneli porestatum,
gubus ex addicuntur exigit.
Ouxe quidem omnia, superius expolicam cabellam in spicienti, clara (unE.
E H E O R E M A IV.
Si a puncto in peripheria circuli, SuIAHEUE SESIENEA GUOTCUNGUC XQUa-
da et ab eodem ad lingula sectionum punctarecta educantur: exit urmi-
nuna ab libi proximam, ita reliquarum quaevis a minima deinceps, ad sum-
Enam duaruI SIBI VEFINGUC PTOXIIAFUIM.
Sic circuli circumferentia quantalibet AE, secta in parces quorcunque aequales, quibus
abrendancur rectae AB, BC, CD, DE, e educanur recta AC, AD, AF: ducancurque
rectae CF, DC ip (ISC A, D A aequales.
ExicigitUEUE ABad AC, ita AC ad
AE, _ AD ad AG, ob similicudinem
eriangulorum iloscelium ABC, ACF,
ADC. CA aurem recta AF aequalis
iplis AD, AB: nam in eriangulo aequi-
CTUTE ACF, est angulus C FA aqualis
angulo CAF, id est anguloBAC, an-
sulus vero CDA anguti BAC duplus
A
(Equidem dupIx circumterencia
insic.) est isicur CD A angulus du-
plus anguli CFD, acqui aequalis est
duobuSCFD, FCD. Cunc icaque an-
suli CFD, FCD aequales, latetaque
D, DF aqualia: aE latuS CD aqua-
le ost ipk AB, erBO_ FD ipH AB~-
qualis eric; _ recta AF aequalis com-
POTIIX ex AD AB. Similicer in erian
blloisosceli ADC, suncanguli DAC, DCA ad basin aquales, est icaque angulusDCA,
auasis angulo CAD, de angulaS DEA externus criangulIDCF, aequaliscriplo ejuldem
meuli C AD vel DCE: liquidem eriplae circum terencia in Cltic, qualium igicur parrium
angulus DCE unius, calium est angulaSFD C duarum. est ica que criang ulum F.DC
aquiangulum ccrangulo ACD, et lacus D E aequale lateri CD; exirigicur et laruS L. C. aequa-
Claceri C. A, re ctaque AC aequalis compOlIIX ex AC, AE. Ecigicur AB ad AC, ica AC
 Compolitam ex AB, AD; ec ica AD ad ComBOlIcam ex AC, AF, acque ira deinceps l
lura Tuerine legmenra. Quo derac demonstrandum. acque hine
AD ANOVE A R ES SECFTONES.
29)