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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 245, page id 845634801:0251
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=251
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.82
# 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.

emde
HB
1aH)
auE
ca7
BC.
F d
e
EFF ONF F R T A
aurem BE. Composra est ex BA, A F. prima e ICCAIA. IpIa Velo C LCoIPOILA ex
Dara icaque A B prima erium proporrionalium _ LCCLA DC, CajuS GI CTaTUI Xqu2
CO, GE secunda Xrerria. Ouadrarum denique ex C. F. ditteri d quadcatO ex BF. PCF
quadratum exC B.
le cst ei quo ditterr quaatatu ex L. C Compolica ex secunda _ reriia a guadTATO Ex E. D
Propoctonales. Ouod taciendum fuIt.
Atque hinc licet compendiose
Delcritere quatuor lineasrectas m PopaeS, quarum ex
trema linc in Fatione dupIa
Ostensum est enim in Porilticis. Ouod Si Fuerineeres linex rectae proporrionales; qua-
aratum aurem compolirx ex secunda L lel ditterat a quadraro compolirx ex lecunde
ld continue proporrionalis.
compolita ex prima e secunda, inventae luncF A, Peu GC, _ F. C secunda de cerrix
 prima per rriplum primae quadrarum: sux dupla est ad primam, exic ea in serie quar-
aveniencur secunda de lertta. Vua in serie dupla ad primam exir quarra.
leaque adsumpea quacum que prima e Caiua Porcu Guadtalo eriplum iphius prima
PROPOSFTIO VIII.
Si Fuerie crianoulum xequiceurum, et a balis cermino ducatur ad crus
linea recta ipsi cruri aqualis. asulus excerior factus a bale _c ea guxe du-
Citur Cbalis termino, iriplus est urriusque angulorum qui sunt ad BasIn
XeGuICtCHI.
Si trianculum ABC habens AB, A C crura aequalia, d 2b anoUIO A C B aUCaEUK
Acrus AB (idcirco h opus est concinuandum) recta C D, ip h cruri A B vel AC. aequa
lis, ex producatur BC in E. Dico anoulum D C F esse criplum anguli A C B, Peu ABC.
Duoniam enim aequicrura crianeula sune B A C, D C A, ideo angus A C. B angulo
LBC est aequalis, _ angulus AD C aequalis angulo D A C. Icaque qualium parrium an.
sulus AC B vel AB C est una, calibus duabus parribus excedune duo recti angulun
AC, cujus exteriori xquatur angulus BD C. LAMM ISMUE parrium est duarum angU
us BD C. F. X angulo aurem DB C et angulo BDC compolitus ett angulus D C F-
Duare anoutusD C F. est eacundem parrium e. LlL igicur angulus D C L. criplus an.
Buli AC B seu AB C. OuoctCrat Mccndenaum.
PR OPOSFF70 IX.
Sic darus atte co A, Gue OPOIICaV
ecare critariam.
Datum angutun lecare tritariam.
HErC