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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 97, page id 845634801:0113
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Ard.
1161
b1S
31
et
AE OV A XTONV M.
Ouoniam enim B quad. 3 in A - A cubo, aequatur Z solido, est aurem B + A radici
E aequalis, igirur F. =B aequabicur A: quare Colidum abs B quad. 3 in F -B, minus cub0 ab5
E= B, aquabirur Z Colido. Solidum aurem illud afectum constac, B quad. in F 3 - B cubo 3.
Cubus reronesacus de solidoillo, - F. cub. L B in F quad. 3.  B quad. in F Z -] B cnb0
Ouare omnibus bene ordinaris, B in E quad. 3 = F cubo, aequabitur B cubo2 + Z Colido.
A P V X ZI.
Deductiva adfectorum cuborum tam sub quadrato quam sub la-
reres a cubis adfectis sub latere.
E E E O R E M A 1.
A cubuS + D plano in A, xquetur Z Colido. A = B eAtOF. F CU-
bus = B in F quad. 3 = B quad. 3 - D plano iN P, Xquabitur Z Colido + L
Ouoniam enim A cubus.  D plano in A, proponitur aequari Z Colido: est aurem A + B
radici L aqualIS, IBITUIE L = B aequabITUE A. Ieaque cubus absE =B, adjunctus solido
abs D planOIM S - B, 3quabML Z Colido. Cubus aurem absE =B COnSAE, F. cubo - B in
E quad. 3. F B quad. in L. 3 =B cubo. Solidum vero aftectionis, 1 D plano in F. -
Dplano in B. Ouare omnibus bene ordinaris, L. cubus =B in L. quad. 3 F B quad. 5
D plno in E, aquabicur Z Colido + D plano in B. F B cubo. ur eA enunciacum.
T H E OR E M A TI.
A cubus F D plano in A, eequetur Z Colido. A = B CAtOF. P CU-
Dbus F B in F quadL. 3 F B quad. 3 + D plano In F, xquabitur Z. Colido = D
Ouoniam enim A cabus.  Oplano in A, aequatur Z Colido: est aurem A = B radici
E. aequalis, igirur F. + B, aequabitur A. Itaque cubus absF Badjunctus solido abs D pla-
nO in E + B, aequabicur Z Colido. CubuS aurem abSE  B contaE, F cubo + B in F quad.
3. + B quad. in F. 3 F B cubo. Solidum vero affectionis, + D planO In F, + D plano
in B. Ouare omnibus bene ordinatis, P cubus + B in F. quad. 3 +B quad. 3. + D pl. IB F,
aequabitur Z Colido - D planoin B = B cubo. ur est enunciarum.
T I EOR E M A TII.
EF A cubuS = D plano in A, aquetur Z Tolido. B = A XGLCTIFF. P Cu.
Dbus =B in F quad. 3 + B quad. 5.  Dplano II F, a quabieur B cubo -  D planO
in B = Z. Coliao.
Ouoniam enim A cubus Y. D plano in A, aequatur Z Colido: est aurem B = A FadiCL
E xqualis, igirur B = F aequabitur A. leaque cubus abs B = e adjunctus solido abs D pla-
no in D =E, aequabitur Z Colido. Cubus aurem abs p = F constar, B cubO = P. in B quadr
3, + F quad. in B3 = F cubo. Solidum vero affectionis, f D plano in B, = D plano
in F. Ouare omnibus bene ordinaris, E cubus = B in F quad. 3. =X B quac. 3 = Dplano In L.,
aequabitur B cubo + D plavo in B - Z Colido. ur est enunciatuI.
Y E E O R E M A IV.
A cubus = D plaHO in A, aequetur Z Solido. A F B CAOF. F cubuS
B in E quad. 3 gud. 3 - Dplano iM F, a quabitur Z solido = B cubo -
E aqualis, igitur E. -B aquabitur A. Leaque cubus abs F = B mulcarus (olido abs D plano
IMF =B, aquatur Z Colido. Cubus aurem absE -B COnAAE. F cubo - B in E quad. 3 ] L
quaet. H C. 3 = Bcubo. Soc vero affectionis, = D plano in F. + D plano in B. Ou2
re omnibus bene McaC, C. CuDUS = B in C. quad. 3 = B quad. 5 = D planO In F, a quabituE L
Colido. F B cubo = D plano in B. uE est enUnCIAEUM.
L HBO.
Plan. in B + BC4b0.
Planio in B = B cubO.
plano in B.
Duoniam enim A cubus. = D plaHOMI A, aquatur Z Colido: est aurem A F B LaaICI