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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 36, page id 845634801:0052
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OCFS T TCF N S PE C
li5. aequarur quadraro adete sat ex bale primi, e Pelpencelo secundi, plus quadrato
differentia incer perpendiculum primi, de balin secundi, vel ctlam, aequarur quadta
coaderegari ex perpendiculo primi et bale secundi, plus quadrato difterentix inret
balm primi de perpendiculum secundi.
PR OP OSTFTO XLVIII
Duobus erars us rectangulis aequalibus e xequiangulis, cerrium
Lcriangulum rectangulum, constitere.
Suneo duorriangula rectangula, quorum communia latera hyporenula quidem A,
perpendiculum B, balis D. Oporrear ab illis duobus cerrium criangulum rectangulum
constiruere. Fiar de ductio licur docuic Propolicio 46. caluprimo. Deduci enim cantum
Porest synareleosvia, non aurem dixreseos. Fir hyporenula similis A quadegto. BalS, D
quadraco ==B quadraro. P erpendiculum B in D 2. Perrium aurem illud, vocetur erian gu-
lum anguli dupli, de ejusrelpectu primum ret secundum dicerur anguli simpli ob cau-
la5 F suo ponendas loco.
Caussa est quod angulus acurus trianguli re-
ctanguli a duobus triangulis via synareseos effecti a-
quetur angulis acutis horum trianculorum simul
adorepatis, cujus theorematis conversum demon-
stravit andersonus theoremate secundo sectionum
angularium. Porro acuri voce intellisitor is angulus. Dins
cui perpendiculum subtenditur.
pli, erlarsulum seclatigulum eftinsere. Vocetur aurem cerrium illud,
criangulum anguli eripli.
Sunco duo criangula rectangula, unum anouli simpli, cujus trporenula A, pervendicu.
Ium B, ba(isD. Alcerum anguli dupli, cujus consequenter hyporenula sic similis A qua-
drato, batis D quadraro = =B quadcaro, perpendiculum limile plano duplo, ex D in
B. Oporreat ab illis duobus criangulis rectangulis, terrium eriangulum rectangulum et
Angere. Fiar deductio, ur docuir Propohrio 46. primo calu. LFingi enim tantum po-
rest Cynaereleos via, non aurem dixreleos. Fir hyporenula, A cubus. BalIS, D cubus
D in B quadratum 3. Perpendiculum, D quad. in B 3 B cubo.
P R OBOSTF1O,
Friangulo rectangulo anguli simplis
extriansulo rectansulo anguli eripl
tertium criangulum rectangulum consti.
FICTC. Vocetur aurem illud, criangulum
anguli quadrupli.
Sunco duo rriangula rectangula. Vnum an-
buli simpli, cujus hypocenula a, perpendicu
tuns B, balisD. Alcerum anguli eripli, cujus tY
potenua Conlequenter tcsimts, a c00. BlI3
Friangulum ariguli dupli.
ROPOSTFTO LLLZ
Triangulo rectangillo simpli, e
Claslo rectansulo anguli du-
Triangulum anguli eripli.
DC, D in B9. 3. Perpendiculum, livisse D 4. I 63, =Bc. Oporceae ab illiscertium
triangulum rectangulum constiruere. Etat decuelto, de docuir Propolicio 46. casu pri
lum BIHDC 4, = BCIBB
mo. Fic hyporenuta similis, A 99. BaISD99. -Dq. in B9. 6, -+ B99. Perpendict
PRC