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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 232, page id 845634801:0238
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=238
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.87
# 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.

RFFF CL IOAYM AEOME EECAEY M
PROPOSTTTO LL.
Si fyerineeres linex rectxe proportionales: QuadFRLUM MINOLS CXHLCMa
adjunctum rectansulo sub differentia extremarum ex ipsa minore extreman
quatur medix quadrato.
Exponatur canonicum diagramma
erium lincarum rectarum proporriona-
lium, _ incelligicor F C minor exrrema,
cui aequalis ponatur BC, unde differen-
tia inter B Fmajorem extremam _ BC,
id estF C MInOREI EXEreMAM, (IE FC.
Dicoguadrarum ex C F adjunctum re-
ctangulo (ub C F, F C, aequari quadraro
ex D F. Nam quadracum cx C F aliter est
Factum ex C F in GB. Leaque duo HXC
Facta ex C F in GB, e C F in F C valene
FaCtUm ex C F in FB. C ui Facto (UB ex-
cremis consequenrer aequale est quadra-
tum ex D Emedia inTCTCxETeMI2S.
C ON SEC Y A H
quadrari adfecti adjunctor plarii subtarere
Itaque cum proponetur A quadrarum, plus B in A, aequar D quadrato: intelli-
rerur D media inter extremas, B differentia earum dem. Et ex media es differen
tia extremarum quarentur extrema, quarum minor erit A, de qua quaritut.
Elchic ex datis O P, FD contruentur proporrionales BF, FD, F C. FF erix F C minot
quaesira. VE ex Zerericis porerararsui, de jam Rgura Ceomerrica per synche lin demonstrat.
PROBOSEETO X.
Si Fuerine eres linex rectX proportionaleS: GUadFALUI Ma) OFIS CXEKCMa
mulcatum rectansulo sub difterentia extremarum, _ ipLL MaiOFC CXTCMa
requatur medixe quadrato.
Repetatur proxime anrecedens con-
Aructio. Dico quadeatum ex BF, mi-
nus rectangulo Tub BF, CF, aequari
QuadracO exDF.
Ouadratum enim exBF, valer tactum
ex BF in CF, e insuper ex BF in BC. A
quadratoisirur ex B F auteracur Factum
ex BF in LG, relinquirur factum ex B L
in BC, id est ex constructione in FC
Cui facto lub exrremis consequenter xe-
quale est quadratum ex D Pmedia intex
exTTemAS.
E V
N
It
fetu
Mextr
lit