# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/845634801:0051
# Permalink to this reading: https://leibnizlegible.com/page/845634801:0051?run=74
# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 35, page id 845634801:0051
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=51
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000051.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

VOF X P R1O
A E O R E M
F S.
a
Si Fuerine duo criangula rectangula: quadrarum plani quod sic sub hyporenuns
cur quadraro differentia Factorum e balibus in perpendicula reciproce, plus quadrato
adoregarifacti sub balibus, e Facti sub perpendiculis.
dracis hypocenura pruni, de hiypocenulae secundi.
A. balIS M. Alcerum, CosasPocaD.
perpendiculum consequenrer AIB, basis
min o. Oporreat ab illis aHOVAS FCFEIUM ETIan-
EQUATUE QUAdTaTO AOSICZAI LACLOTMIBC BINIBUS IM PETDEHOICMIA LCLIDIOCC, PIOS qua
draro differentia inter factum sub basibus de Factum lub perpendiculis. Vel eriam, aequa-
A duobustriangulis rectangulis similibus, cerrium eriangulum rectansu-
lum ita deducere, ut hyporenulx certii quenal, aae Gua-
P RODOSTFTO XLVTI.
Sine duo similia criangula LCCtat Ota. P FI-
mum, cujus hyporenula B, perpendiculum
sulum rectansi cdlucere, ita uc hypo-
cenula illius guadracum a Guetut B quaaralo,
 D quadeaeo. Ouoniam isicur hiypocett.
Ca quadearun Constac B quadraco, + D qua-
deaco. Taneulm erir quadratum pelpendien-
li adjunctum quadraco baHS Aaecendi cri-
anguli. AE A B quadrarum, Y D qua dralo
ducatur in Ml. quadc.  NI quadraco, et dI
vilio fiat pel B quadearum, nihil quadraro hyporenulae diducti accedir rel deperie, quo-
minus M quadeatum, +. N quadrato aequetur exhyporheli B quadcaro. Piacigitur du-
Ctio, Factum cerre constabit quaruor plano planis, nempe B quadrato in M quadratum.
F D Guadraco in N quadrarum, et B quadraro in N quadratum, + D quadrato in M
quadcarum. Binis primis acdatur plano. planum duplum quod sr concinue absB, D. H,
NI. _ auteratur binis postremis. vel conversim, auferarur binisprimis, et addacur binis
POstrenIs. Nihil Factis accreseir aut deperir quominus facta plano. plana, plaHO. PIaIIO
abs Bquadrara, + D quadraco in B quadratum equentur. Bina porro illa Prateprata,
adsciro rel dempro bis communi illo plano. Plao3 1, L13 pLtaS
habeneradices, quarum
Primo calu, prima est Bin MI, + D in N. AIcera B in N, = = D in M. Secundorero
Bin N = 1- D ires
B in M
adplicacio, et urriulris calus, prima adlimilabieur perpendiculo, leCunad ball.
casu, prima estBinMI, = D in HI. AILeraBin NI, F D in MI. Fiar igitur communis ad B
dItuetimE duo limilia eriansula rectansula, adseam quactatorum ab hspolen
T H E O R E M A.