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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 99, page id 845634801:0115
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.86
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# After the first blank line: the recognised lines in reading order, one per line.

15.
in D
pla
Bint
radiet
lano
int.
15
N
adib
qua
eod
ad.
Ea
AE OY A LLO H VM
 2L XII.
Deductiva potestarum allquors ales planas solidasve haben-
tium, a porestacibus smplicium radicum.
L A E O R E M A I.
A quad. - + B in A XGHEtUE Z planO. B in A etto L quadeatum
Cquad. quad. DGudet. Ut L. Iuaet decab B quad. in L planum.
Duoniam enim A quad. F B in A, aquatuE Z plano: est aurem B in A aequale F
quadraro, igieur omo. xquabicur A. ica que quadcarum abs equac. adjunctum plano sut
B d Egundcac. id est Eoa. quad. + F quad. Xquabicur Z plano. Omnia ducaneur in B
quadearum, ergo F. quad. quad. + B quad. in E quad, aequabirur B quad. in Z planum.
uc estenunciacum. Ouum aurem iplum P. quad. radix Cacuecur plana, haec crie aequa-
cionis enunciario. E plari quadrarum ; Bquadraro in E planum, aquabicue B quad.
in Z planum.
T E EOR E M A TI.
EF A quad. - B in A aequetur Z. plano. B in A esto E quadratum, pla-
numve. F quad. quad. = B quad. in P quad, aequabicur B quad. in Z.
PlaHUML.
A E Y F B R.
B plati quad. = Bquad. in F planum, aequabitur B quad. in Z planUM.
Nec dissimilis est ab ea quae in ancecedenre Theoremare expolica est demon-
Atrario.
TH B O R E M A TTI.
ETB in A = A quad. XQuCTuT Z plano. Bin A esto F quadratum, pla-
numre. Bq. in F. g.  E quad. quad, aequabitur B g. in L planum.
A L L Z B R.
B quad in E planum - F plani quad, aequabitur B quad. in Z planum.
Nec distimitis est ab ea quae in primo hujus capiris Theoremare exposica est de-
monstracio.
T A EOR E M A IV.
SF A quad + B in A equetur Z plano. B quad. in A esto E cubus, (0-
lidumre. P cubo cubus F B cubo in P cubum, a quabitur B quad. quad.
in Z planum.
Ouoniam enim A qu2d. + B in A, aqUaTUE Z planO: eA aurem B quad. in A
aequale Ecubo, ixitur  xequabitur A. itaque quadearum abs Leobo, plys Binrcubum id est
= Ecv xquabitur Z plano. Omnia ducanrur in B quad. quad. ergo F cu-
b0. cubus + B cubo in E cubum, aequabitue B quad. quad. in Z. planum. uE est enuN-
ciacum.
TH E OR E M A V.
EA quad. = BIn A XqUETF Z. plano. B quad. in A eAto F cubus, 1OH-
dumre. E cubo cubus = B cubo in E cubum, aequabitur B quad. quad.
Dec distimins elt ab ea quae in ancecedence Theoremate expolia eA demonstrario.
T H E OR B M A VI.
EB in A = A quad Xguetur L plano. Bquad. in A etto L cubus, (oli-
dumve. B cubas in E cubum P cubo. cubo, aequabitur B quad.
ilt L planum.
Quadt. In L PTacum.