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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 24, page id 845634801:0040
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A D LOCFS TZC E N SPFC
2b5 A- + B, adtectum adjunctione plani subD _ A. t= B, COMPONCTC. DUCATEA. L B
in A + B) 1 D, ex colligancur effecta singularia plana. Frune illa
A quadracum, + A in Bbis, 1 B quadraco, F. D in A, + D in B. OuX ideo aquIA
buncur quadraco abs A + B, adtecto aejunctione planiex A. + B in D longicudinem. Hinc
aurem ordinatur
T H E O R E M A
geneleos quadrati adfecti aftirmatire sub latere.
Si fuerine duo lacera e praeterea coesticiens sublarera lis longicudo: quadratum late-
ris primi, plusplano à lacere primo in lacus secundum duplum, plus quadraco laceris le-
cundi, plus plano à larere primo in coefticientem longicudinem, plus plano a
lacere lecundo in eandem coellicientem longicudinem, aequacur quadcato adgregati late.
cerum adfecto adjunctione plani sub coefticiente illa, &t dicto adercg2to.
Sic latus unum A, alterum B, coeficiens sub laceralis longirudoD. Dico A quadra
rum, = A in Bbis, F Bquadrato, + D in A, F D in B, aequari A F B quadcaco, +
in A + B. Ex opere mulciplicarionis A + Bpex A + B + D.
AlIBd Y E E O R E M A.
Si ab eadem binomia radice componantur duo quadrata, unum purum, alterum ad
Frmare adfectum sub radice et adscira coetticienre lonsirudine: singularia plana, quae
compolicio adfecta addic compolitioni purae lune
Planum a latere pruno coefficienrem longirudinem
Planum à lacere secundo in eandem iplam coefficiencem lonsicudinem. FX colla-
tione vertulque suppolicionis.
P R OPOSTZEO ZXVI
Cibum adfectum adjunctione solidi sub latere, à binomia radice, ad.
Scito congruenter sublateraliplano cocfciente, componere.
Sic radix binomia A F B, coefticiens sublarerale D planum. Oporreat cubum abs
A i B adFecto adjunctione solidi tub D plano, sc ip (a A Y B COPOHeTC. EFInCREUE
quadrarum abs A F B, de in illud superaddico D plavo ducatur A = B, e collIBAnEUE
effecta lingularia Colida. Frune illa
RcabuS, + A quadeato in BFeC, F A in B quadratum cer, = B cubo, + D planoin A.
= D plano in B. Ouxideo aequabuntur cubo abs A L B, adFecto adjunctione Colidi sub
A I B ec D plano. Isinc ordinarur
F H E OR EM A
Si Fuerint duo lacera de praecerea coesticiens sublaterale planum: cubus laceris primis
plus Colido à quadraro lareris primi in larus se cundum eriplum, plus (olido à Inrere primo
in lateris secundi quadrarum eriplum, plus cabo lateris secundi, plus Coldo à lacere pri-
moincoëtticiens planum, plus solido à larere secundo in idem coësticiens planum, _
guarur cubo adsregai lacerum adtecto adjunctione lolidi sub coefticiente plano ec ad
sregato pruedicto.
P R OP OSFFTO ZXVII.
rbum adtectum adjunctione solidi sub quadrato, aradice binomia, ale
(cica congruenter lubquadratica coefticiente longitudine, componere.
Sicradixbinomia A. F B, coefticiens (obquadrarica D longirudo. Oporreat cubum
abs A -F B adfectum adjunctione ColidisubD, _ quadraro ab5 A. F B COmpOnerC. FF
Angacur quadracum abs A -L B, _ ducatur in A -t B -+ D, e colligantur effecta Cingu-
in D, F AI BBISIn D, - B quadratoin D. Oux propierea aequalia erune cubo abs A
FB, adteco adjunctione solidi sub A + B quadraco ex D longirudine: Fincconci
BicuE
laria Concta. Lrunt illa
A cabus, F Aguadraro in Bcer, = A in B quadrarumter, = B cubo, - = A quadeato
E C