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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 341, page id 845634801:0347
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=347
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.87
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# After the first blank line: the recognised lines in reading order, one per line.

ipe llaro
enire
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rii
L aet
et
nat
+
Equales, auctx videlicet lemidiamerri circuli C FD. laque componime data BH ex CtU.
TibusAB, AD. COnNeCtATUE aurem AF. Ouoniam GD secacur bitariam in F ab ea quX
elt ex cenro (constructa est enim CD dupla iphius VY) ideo lecatur CD in Pad angulos
rectos. Cadar igirur in balin BD perpendicularis AC, CTUNEAF, CD aequales e paral-
Cclx, acque adeo aequales X parallela FD, AC. F.I ltaque AC alcirudo erianguli ABD.
Lriangulum igitur ABD constructum est sub data bale BD, habenS AIIIaIe AC X-
qualem darRFD, e crurum AB, AD aderegarum aquale est ip ( BHI, id est BF data.
Ouod Faciendum erat.
P E OB E E M A IV.
Daca bale, alticudine dE diHFCTENLIA CFUTUII EKLAHBIIH, AHIVENIFC ELLAH-
Sulum.
Frianguli de quo quaeritur (c data
batis BD, alcirudo DF, differentia
crurum BF. Oporret invenire crian-
sulii. Cenero B interrallo BF descri-
bacur circolus EH, inclineneur au-
temDE, BD ad angulosrectos, ipla-
que DF dupletur in C, ee per puncta
i, D describatur circulus CFID cir-
culum EIE. concingens in II, _ SIF
circuli OHID cenerum A. IEaque COn-
nectatuE AD. Priangulum igicur COn-
Ctructum est ABD Tub basC daca BD.
ee sunc AD, AHIxquales, uter que vi-
delicer lemidiameter circuli GHD.
leaque crus AD diferE a CruTC AB PeF
BF, id cA per BF datam. Connecta-
EET RuTeM AF. Ouoniam CD secatur bitariam in P ab Ca qUX eAt ex CenrO (constructa est
tum OD dupla iphuSDF) ideo lECatUT CD in F ad angulOSreCtOS. CadaFIBITUE BALIM
D perpendicularis AC, CTuNE AF, C D aequales e parallelae, arque adeox quales e p2-
aleEFD, AC. Estaurem AC aliicudo reianguli ABD. Friangulum isicur ABD Con-
aructum eA sub daca base BD, habens alticudinem AC aequalem datae FD, d ejuscrura
AB, AD diHCrUNEPeF BHL sCu BE. datam. Ouod Faciendum etaE.
P R O B L E M A V.
IDacabale, alcirudine, ec angulo verricis invenire criangulum.
Sic daca criangulibalis AC, alcirudo C F angu-
bsad verricem aequalis angulo Z. Oportet inve-
hirc criangulum. Inclinentur AC, C F ad angulos
ectos. Faciane vero AB, AC angulum aqualem
ei quem relinquir e recto angulusZ, incercipien-
ce ABiplam C F in B punAtO. Ec per Signa A, C, B
delcribatur circulus, quem acta per F ip ( AC P2-
callela secer in C. Dico eriangulum ACC iplum
Elle quod quaericur. Anguli enim sive ABC SvC
AC. C duplam amplicudinem eadem detinieperi-
Pheria AC, quare lune aequales. Sed constructus
angulus ABC daco Z aqualis. Fancus estigi-
Erargulus ACC. Cadat aurem in AC Perpen-
dicularis CHI, cricisicur ipCa erianguli ACC alci-
adoac data CF aequalis, caecerum AC ip(a CAt
halis data. Factum estigitur quod op orcebat.