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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 40, page id 845634801:0056
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radiccuna, et Burradice altera, ettingatut aliud criangulum rectangulum. Fichypore
nuta, similis quadraro abs F  D, == B gtaetatO. BaSS, quadraco abS F ] D, = B qua
quadraco, ica D ad batin, qua ideDexie F = D quadtr.
quadraco. Perpendiculum idem ae lupra in priore triangulo
adc. FxUEF  D in B bis ad qua
Coeanc igitur in unum duo illacriangulare.
ctangula, hyporenula videlicet Hane crura al-
cerius crianguli, adoregacum balium in dire
cum positarum, balis. Alcirudo igitur manet
cadem: Caererum, uc basis primi ad alcirudi
nem, ita alcirudo ad majorem base secundi. Est
enim
EEB in F L D in B 2 ad D in F , D in
B2, ica D in F f D in B2 adD cabum 2, D
quadrato in F2. Balisaurem secundi similis est
D in F + D quadraro = B quadraco. hoc
CA F quadratum in D, + D quadraco in F2.
+ D cubo, = B quadraco in D. Ilcrinque
abdicatur F in D quadrarum 2, _ addatuE
B quadrarum in D. Reliqua denique Colida
dividantur per D. Illicremanet D quadracum, = Z quadraro, hic D quadrarum, L F
quadrato. Ceamdutem perhypochenti, I quadrarum ip(Z quadraro. FA igirur alcicu-
do proporrionalisincer balinprimi, de majorem bale le cun di. Duare angulus quem sub.
rendir balis secundi, minor est eo quem subcen dic perpendiculum primi. Angulus ita-
que effectus ab hyporenulis seu cruribus est acurs. Igitur d eriangulo rectangulo de
ducta lunc duo criansula rectangula xeque alca, a quorum coirione quod componirur eri
angulum aeque altum, succedencibus videlicechyporenulis in vicem crurum, adoreonto
vero balium in balin, habebir angulum verricis acurum. Appareraurem talem F qsu
mioportere. ul quadrarum absf. F D praecter iphi B quadraco, ur ad consticurionem ba.
Duoniam enim uE B in F L D, ad D in F = D, ita esse B in F F D ad D in
F. + D, luce clarius est. Tam pitna quam secunda proporrionalis maonirudo, duca-
tur in B L. TerrIA VeEO _ quarFa AHCaTuT in D 2. Frir iraque ut B in P  D in B2 20
D in F = D in B 2, ica B in F =F D in D 2 ad D quadraTI 2 in F  D. Sec
B in P + D in D 2, RGUATUE D in F + D in B2. Aque D quadratuM 2 in F +
D, non difere a D cubo2, F D quadraco in F 2. Ouamobrem ut B in F = D in B2 ac
O in F = D in B2, ita D IH F = D in B2 ad D cubum Z, Y D quadraco in F2
PROPOSTTTO LVI
Friangulo rectangulo deducere duo alia erian
sula rectansula aeque alta, ex quorum coitione
quod constatur triansulum ae que altum, succedenti
bus videlicet hyporenusis in vicem crurum, adore
sato rero balium in balin, habebir angulum verticis
obculum.
Exponacurcriangulum rectangulum cujustyeorenusa Z. ba
E
LOCTS TZCE N SPEC
Exponatur eriangulum rectangulum, cujus hyporenula Z, balis B, perpendiculum
D. OpOrECAEFacere quod imperatur. Sumatur quaedam Fminor ip (a Z, e absF j. D uI
teou
draco. Perpendiculum F ; D in Bbis. Cui secundo criangulo aliud constirmacur simile
habensperpendiculum D, Faciendour F- L. D in B bis ad quadracum absF L D, -
dratum abs F F D, = B quadraco, ita D ad hyporenulam, quae ideo erie DinE= Bgunot
c. Facera denique cum iltius cum expolrianguli rectanguli, ducanrur in F. L Did
B2. Duoisirur Cuneeriangula rectangula. Primum cujus similis hyporenula, Z in F L L
in B2. baHSBin F F D in B2. PErpCHAM D in F F D in B2. Alcerum criangulum
cujus similis hyporenula, D in F F D quadearo F B quadraco. ba(Is, D in F. F Dg. - L
sissecundi, B quadearum ex quadrato abs F. + D possir auterri.
Duod quidem d riro claristimo adlumprum exar