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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 281, page id 845634801:0287
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=287
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 76 lines, status machine
# Lines: 76 recognised, mean confidence 0.83
# 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.

nod S
uodH
rectaet
quall
90ni
10.
iras, 11)
rC
1oniaM
ales, e
AEPACd
Eonve
piaM 
ulo ab
bb15te
CHM
BocuE
101 
l
diftes
AB.
A
1
Vel ex D eacat in EB
perpendicularis DL. Ouo-
niam criangulum F. DC da-
eorum est lacerum, ex data
quoque ipsa C B, dabuneur
segenEAFC, CL, LB, aF-
que adeo ipsa alcirudo DL.
cujus quadrarum una cum
Quadraro L B, aequabitur
quadraco diagonix DB.
quae quidem rectum (ab-
cendic augulum in criangu-
lo rectangulo DL.B. FX C
aurem cadat in F D perpen-
dicularis C K. Ouoniam
criangulum FDC datorum
estlaterum, et data quoque
ipta F A, dabuntur (egmen-
TAEK, KD, IEA, aeque adeo
ipla alricudoKC, cujus qua-
drarum una cum quadiato
ER, aequabicur quadraro
diagoniae C A, quaequidem
rectum subcendic angulum
in eriangulo rectangulo
CKA,
Primo casu sit AB65, BC
25. CD65, D A9. Fit AC. vel
DB70, altitudo 60, diame-
ter BI
Opus aurem secundo ca
Cu insticuendum in hanere-
cidiranalogiam.
Sit latus primum cerrio oppositum idemque majus, ex secundum majus quareo.
Erit ut rectanculum sub primo ex secundo, una cum rectansulo subtertio ex quar-
 ad aderecarum quadratorum primi es secundi minus aderecato quadrato-
um secundi ex terrii, ita rectanculum sub primo es secundo ad adereeacumi qua-
tratorum primi ex secundi minus quadraro diaconiae, quae anzulo qui fit à pri-
Mo e secundo, vel terrio ex quario subtenditur. ex ita rectanculum sub tertio
quarro ad quadrarum diasoniae ejusdem minus adere caro quadrarorum teriii
e quarri.
Exhaec ex Analycicis suam habene demonstracionem. Sic enim quadcilacecum ABCD
eculo inscriprum. acprimum quidem lacus AB hemajusipso CD, es C B majus iploDA
Lagatur diagonia C A. Circumterentia ixirur ABC major erit circum terentia CDA.
angulus iraque CD A eric obrulus, angulus reco CB A acurus, et aequalis CD F. exteriori
neuli CDA. Cadanevero in AB, AD perpendiculares CP, C Q. illa ixirur caderincea
plangulum C AB, haec extra criangulum CDA. Iraque quod Ec lub BP, ABbis, aequale
equadeatis ex AB, CB, minus quadraco ex AC. Ec quod sirsub OD, Dabis, aequale
Equadeaco ex AC, minus quadratis ex CD, D A. EF per aqualium cum aequalibus ad-
ationem, quod sictub BP. ABbis, una cum eo quod tic sub OD, AD bis, eric aequale
ladraris ex AB, C Bminus quadcatis ex CD, D A. Porro similia sunerriangula CDe.
CBP
e