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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 233, page id 845634801:0239
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.89
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extrema
extret
1II.
ec
H
C A N ON PC A AF CF N SFO.
CONSECT A R LVM AD MIEC H ANICFA EVADRKII
adfecti mulia plani sub larere.
uaque cum proponetur Aquadratum, minus B in A aequari D quadrato: intelli-
setur Dmedia inter extremas, B differentia earum dem. Ft ex media es differen-
lia extremarum quarentur extrema, quarum major erit A, de qua quaritur.
Vehic ex daris GF, F D ConAruentur proporrionales BF, FD, FC. FFeriE BFmajoF
quaelica. Vc ex Zecerieis porerat arpui, et jam tixura Geomerrica per synchelin de-
monstrat.
PROP OSF= FO XI.
Si Fuerinc eres linex rectae proporrionales: rectangulum lub compolita
ex excremis ex harum alcera majore minorere, mulcarum ejuldem alterius
quadraro, a quarur medixe quadrato.
Exponacur canonicum diagramma
erium proportionalium. Dicorectan-
sulum lab BC, FC, minus quadEaTO CX
C, aequari quadratOexDF.
Ex rurtus rectangulum sub BC, BF,
minus quadrato ex BF, aquari quadea-
EDCEDF.
Duoniam enim BC est compolica
Ex BF, FC, ideo factum ex BC in FC
Valec FaCtUI Cx BF IN FC, _LFC in FC,
hocekquadeatum ex FC. Cum itaque
ex Facto BC in FC auterecur quadta.
TUM exFC, relinquetur factum ex BF
in FC. Cui facto sub exrremis conse-
uencer aequale est quadratum ex DF
media inter extremas. Acque id esto
Primum.
AEque quoniam BC composira est ex CF, FB, ideo Factum ex BC in BF valer Factum
ex C F in BF, X BF in BF, hoc est quadracum ex BF. Cum icaque ex Facto BC in BF aute-
retur quadratum ex BF, relinquetur factum ex C. F in BF. Cuifacto sub extremis conse-
qencer aequale eA quadrarum ex DF mediaincer excremas. Ve lecundo loco tuic demon-
Arandum.
C ONSECF A R YVH A D M E CA AAIUEN PEA HF
sublatere necari de quadrato.
Teaque cum preponetur D in A, minus A quadrato aequari D quadrato: intela
igetur D media inter extremas, B aderecarum earumdem. Ft ex media ex ad-
crecato extremarum quaerentur extrema, quarum alterutraerit A, de qua quae-
ritur.
Ic ex Zecericis pocerarargui, de jam figura Geometrica per synchelin demonstrat.
PR OPOSFFTO XTI.
Dacamedia rrium proportionalium ee differencia extremarum, inveni-
C exETCMAS.
Meshanibe