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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 254, page id 845634801:0260
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=260
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 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.
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# After the first blank line: the recognised lines in reading order, one per line.

Y E P L E M B N F i M
PROPOSETTO ZX
rerum e cruribus ad balins licut quadratum cruris ad quadracun compon
Ex exerure _ bale: quae a termino balis ducetur ad crus linea recta ip (I CFU
riaequali, secabir bitariam angulum ad balirio
Repetatur ancecedens con-
Rructio, actaque D F sccet
quoque circulum in F, de jun-
Sacur AF. Dico AF secare bita-
riam angulum E AD
Duoniam enim exhypoche.
E cs ur DB ad D A, ita quadra
cum ex AB ad quadeacum ex
 DC: ideo eAt urD B ad AB
ica quod AE (uBD A, AB 2d
quadratum ex D C. sed D B ad
D E Seu A B, CAUED F ad DC
Ouare est D F ad D C, Sicur id
quod hctub DA, AB ad qua-
drarum exDC. Ecconlequen
rer eAt D Fad AB CCuD F, SicuF
D A ad D C; ex sub ducendo est
DF ad FE, HCuED A 2d AC. OHarE CONHeKA F. C RripSuS F A parallel2. Traque AH
sulus F. C D angulo F AD est aequalis. Sed angulus E. A D duplus est anOMMIL. C D, Ct
ille GE Ecenro, hic c circumferentia. Angulus igitur P. AD sectus est bitariam a recta
AF. Ouod erac ostendendum.
PROPOSTTTO ZXTI
ad cruslinea recta ipsi crurixequalis, secerbitariam angulum ad balin: an
sulusad verticem requicruri, se (quialter est utriu sque angulorum ad balin.
Sic eriangulum A B C habens A B, A C crura xqualia, à cujus termino C cum duci
cur ad crus ei oppolicum recta linea C. D cruri aequalis, qua iplum AC B angulum bita
riam secet. Dicoangulum B A C esse sesguialcerum
anguli ABC CCU AC B
Ouoniam enim a C cermino balis crianouli aequi-
cruri AB C, ducicur recta C D ips cruri A B vel
C A xqualis, ideo exterior angulus D C F. rriplus
estanguli AC B vel A B C. Oualium iraque angulus
ABC. CCu AC B partium est duarum, calium exre-
rioranguli DCB eAt parrium (ex, anguluSverODC A
qui dimidius est anguli A C B corundem estuna, VE
eriam angulus DC B. Constancisitur angulus DCF P
 luus exterior talibus seprem partibus, valene aurem
duos rectos, sicuceres anguli irianguli. Cum sincigitur anguli ABC, AC B quilibe
duarum parrium, angulus B A C relinquitur carundem erium. Est ivitur B A C anGV
lus sesquialcer urriulris anguli AB C. seu A C B. Ouod erat ostendendum.
Sifuerittriangu lum XQUICFUTUII, HC AIILCMLMMICLCHCT LICCLDA e 21
Si fuerie criangulum aequicrurum, quae aurem e termino balis ducetu