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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 237, page id 845634801:0243
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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 0.86
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10gue 
1a deat
ex AD
3C89
deatu.
tionet
(ni
15210.
i
A N O N LC A R ECF H S FO.
X
primum deleripri
quales quoque ex con-
Aructione AD, DB. FF
80 hune quoque aequales
FA, BF; X rursuS aequa
les FB, AF, Facta lubdu-
ctione e addirione equa
lium ab aequalibus. Media
aurem proportionalis in-
TerE B, BF, eABC CXPEX-
dicto canonico diasram
mare. Media quoque in-
Tex E. B ec A F id est ipsam
BE, CsFOF. Ouare ipla
GE eadem est quae BC
Duod octendiste opOr-
ruir.
Ad daram igitur A B
Primam, e BC Poten-
em quadcato duas reliquas, invenix lunerres proporrionales A B, BC, BL. Ouodta-
ciendum CFAE.
Si quadratum medix inter perpen diculum crianguli rectanguli de hypo
enulam adplicetur ad balin: perpendiculum proportionale est inter ba-
uin e cam cujus quadratum a qualc est difterenrix inter quadratum lati-
rudinis oriundx ex ea adplicatione d quadratum perpendiculi.
Sicerianguli rectanguli hyporenusa quidem AB, baliS A C, perpendiculum BC; me-
Aia vero proporrionalis inter AB e BC, SE C D, cujus quadearum cum adplicabitur
ad AC, Faciar lacirudinem C P. Sed d quadrarum ipsius B C. adplicerur ad A C, dt La-
PEOF OSILTO, LVII.
ExBE. DiCOBF ese aequalem iplI C. L. Leaque C’F elle eam cujus quadratum aquale
Ae difterentix inter quadratum ex C F seu B E, Xe quadratum ex B C. EF Con(EqUEnTEF
inter eam et A C proporrionalem eNe B C, ur decernie propolitio.
EK enim uE A C ad C D, ita C D ad C F, ex constructione. F. B quoque, ut AC ad
C, iTa A B ad BE, ex criangulorum AC B, AB E. similicudinc. Ouadtatum autem ex
Daequale est ex hyporheh rectangulo ex B C in AB. Ouare cadem media est inter AC.
RCF, CL InTET A C E BE. Iaque BF. e C. F sune aequales, acque demonctrara cA P c0-
Politio.
PROPOSFTTO XVITI.
Data base criansuli rectanguli, de media proportionali inter hypotenu.
am e perpendiculum, datur criangulum.
Enimvero proportionales sunt ex antecedente propositione
ciar laricudinem C E. cujus quadrarum una cum quadeato ex BC, aequetur quadcaro
Basts
LL. Perpendiculum,
II. Lacus