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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 239, page id 845634801:0245
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=245
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 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.

la rituai
traii, a
Epers
1a10
ecta
Ond
es
uneid
5
B20
FeN
C A N ON FCA R E C F N SZO.
P R OPOSFFFO XX.
Daca hyporenuila crianguli rectanguli, de mediaproportionali inter ba-
ur sc perpendiculum, datur criangulum.
lI.
III.
Enimvero proporiionales sunt ex antecedente propositione,
Ayporenusae seementum unum,
Fatiendo quam facie mediae quadratum adolicatum ad Bs poriasa
Typotenusae seementum alterum.
Dua in ferie datur media es aderecarum extremarum. Ac quadratum quidem latitudin pla
lrcta adjuncdum quadraco unius e seemensis hypotenusae, efficit quadrarum uinius e lateribus circa
lectum. Adjectum vero quadrato seementi alterius, efficit quadracum quo que lateris reliqui.
Est aurem stechanice plano. plani sub quadratonesati de quadraco-quadrato. Itaque in canoni-
earum numerum adseribitur. Dua de causa opus ipsum inceerum consentaneum est exhibere. Pro-
posirum igicur esto.
Data hyporenula crianguli, de media proportionali inter latera circa
rectum, exhibere iplum eriangulum.
Sic daca A B hyporenula trianguli. e data quoque AC media proporrionali incer
latera circa rectum. Oporrec extribere ipsum eriansulum. Ad daras A B, AC inveniatur
terria proxortionalis AD, dt
Aar a B diamerer circuli, in
quam ad rectos angulos de-
miceatur e circumferentia re-
Cta F F ipE AD aequalis, et
Subrendaneur AF, FB. Dico
IpCA AF FB esse latera circ~
rectum quaelica, acque adc0
criangulum, de quo quaeritur
CNE A FB, cujus quidem hy-
Porenula est AB daca. Similia
mamquerriangula rectangula
CUnEAFE, A PB. leaquo est
OEFE adt AE, ica FB ad A B Scd ex constructione es F F id est AD ad A C, ita AC adt AB.
Luare AC proportionalis eCInEEF AF. FB.
Ad dacam itaque AB hiypotenilam. dt A C mediam proporrionalem incer lavera cir-
2 rectum, extribirum est iplum eriangulum A F B. Ouod Facete op OrICBAE.
valet rectanoulum CB in AC. Ergo eadem media eA incer A B d BF, quae inter A B
ECD. Ideoque BF _ C. D sunt aequales. Acque adeo rata est proposirio.
Idem aurem Problema ita poruit concipi.
Oacamedia erium proporcionalium, ee ca cujus quadratum xequale est
agresatO quadratorum ab eXtremIS, InVeNIEC CXETCMAS.
chie dacis A C. media, et A Bpotente extremas quadcaco. inveniuneur ipse exrrema
B
FR AN.