# Leibniz Legible — https://leibnizlegible.com
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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 287, page id 845634801:0293
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=293
# Source image: https://digitale-sammlungen.gwlb.de/content/845634801/jpgs/default/00000293.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.89
# 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.

M.
(F V L +LLLS
L
SECTTOVI
PHTEOREMA LA LLOOAIRODTEDA
DEMONSTR ATA
D E R
AL FX ANDR ITMI ANDF RSOA Et M.
T H E O R E M A I.
og ltuerine eria criangula rectangula, quorum primi an-
 Sulusacurus, differat ab acuro secundi, per acutum cerriis
(S Lsic excestus penes primum, lacera certiirecipiunt hanc
olimilicudinem.
FErpocenula, Ec limilis rectanisulo sub hypotenulis pri-
midlccundi.
Perpendiculum, smile rectanoulo sub perpendiculo
erimi eebale secundi, minus rectangulo sub perpendiculo secundi, et bale
Primi.
Balis, rectangulo, sub basibus primi ec secundi, plus rectangulo Cub per-
Pendiculis corundem.
Lanculus acurus incelligicor, cui lacus perpendiculi voce designarum subtendicur. reliquuse recto, cui
hasis. hypocenusa vero, latus recto subtensum.
Siperria crianguIA AEB, ADB, ACB, quOrUM BALES CINEAE, AD, AC, perpendicula
Lb, OB, CB. SCCCCF Bbalin AC in spuncto: de demirtatur perpendiculatis DC in se-
ctam AB
ErirguenE AD ad DB, ita AE ad FF, id
eICF. B minus IB. _ rectangulum DBInAF,
equale erirrectangulo AD in FB minus AD
in LB, addiroque communi AD in IB: DBin
AE plus AD in IB, aequabitue AD in F B. est
Quogueur AD ad AB, ita CB ad IB, dre-
cangula AB in CB, AD in IB aequalia: Cr 30
OB in AE plus AB in BC, aqualia erune ip (I
AD in EB. ec ablaro communi (AF in DB,)
ABin BC aequabicue AD in F B minus AF. in
B. quibus ip( AB applicaris orierur larieu.
oDC, erirque AB quadeatum ad AD in
LBminuS AE in DB, uc AB ad BC. Ouoderatdemonstrandum.
LLUECUSUEAG ad AD, iFA AE ad AI, _ AD in AF, aquale erir ipl AC in AI; est au-
A ABinAC, aequale AC in AL plus AC in 1C plus CB in AC: e C B in AC, aequale
ACB in AIplus CB in 1C. est quoque AC in 1C plus CB in lC, aequale AB in IC. et
Loinde AC in AI plus AB in 1C plus CB in AI, aequalia erunc AB in AC: Sed CB in AI,
Mm 3
aequale
o