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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 154, page id 845634801:0160
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=845634801&page=160
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.90
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154
DF EM E E D A PTO NP
Ononiam enim veranis+ vertani est ip(a A de qua quaerieur. Ideo exiis guX pFOPO-
BUNEF~ B olanoplano ptani 27. F V B plano plano plavi 81. +. a B plano ptano. plavi 21, + V B plano plano. planit.
W B elno vino vlani 27, = v Bplano. pluo. plani3;, Xquatur a B plano. plano. plani 2. Ouod quidem
ita se habet, subducendo in prima a qualicatis parre ab aequalibus aequalia.
2C- 6N, aequatur4. Isitur a 3 + 2. fit LV.
F H P OR E M A XI.
S1Bplan. 3 in A = A cubo, aequetur V Bplano. plano. planii 2. v a vtem3 - vB ot. 1.
Hc A de quaquaeritur.
Ve apparer, insequendo restigia anrecedentis demonstrationis.
6N - 1 C, aequatur 4. IGituT V 3 - 1. fit L N, eaque minor, altera est 2.
C A P Y F X.
Similium reductionum continuario.
Y H B O R E ut A 1.
; A BuS -+ B in R quadr. 3 -t. D plano in R, Xquetur B cubo2 =L
DolanoMB. A quad. = F B in A2, aequabitur B quad. 2 = D plano.
Ouoniam enim A quadr. F B in A2, aequatur B quadr. 2 =D plano. Ductis ioiruE
omnibus in A. A CuDAS F. B in A quad. 2, aequabitur B quad. in A 2 = D plano in A.
Eriildem ductis in B. B in A quad. = B quadc. in A2, aequabitur B cubO2 --D plano
in B. lungacur ducta aequalia aequalibus. Acubus Y B in A quad. 3. F Bquad. in A2,
aequabicur B quad. in A 2 - D plano in A + BcubO2 - D plano in B.
Et deleta urrinque adfectione Bquad. in A2, & ad aequalicaris ordinarionem, cransta-
caperancicheln D plani in A adfectione. A cubus -, B in Aquadr. 3. + D plano in A,
aequabirur B cubo2- D plano in B. Quod quidem ita se haber.
2C + 308 + 44 N, aquatur 1560. Isiturr C + 20N, aquabitur 156. es fit 1 N 6.
TH E OR E M A II.
SF A cribus- + B in A quad. 3 = D plano in A, a quetur B cubo2 -+ D planO
in B. A quad. -+ B in A 2, aequabitur B quad. 2 + D planO.
Ouoniam enim A quadr. F B in A2, ae quatur B quadr. 2. F D plano. Ductis igicur
omnibus in A. A cubus F B in A quad. 2, aquabicur B quad. in A2 ] D plano in A.
Er ductis iildem in B. B in A quad. Y B quad. in A2, X quabicur B cubo2 + D pla
no in B. lunsaneur ducta aequalia equalibus. A cubus F B in A quadr. 3 +. B quadc. in
A2, aequabitur B quad. in A2 L D plano in A F B cubO2 f D plano in B.
Ec delera urrinque affectione B quadrari in A2, d ad ordinationem aegualicatis, cran
lata perancirhe lin D plani in A adfectione. A cubus = B in A quadr. 3-- D plano in A,
aequabirur B cubo2. Y D plano in B. Ouod quidem ira sc haber.
1C 1. 309 - 24 N, aquetur 2240. Igitur 1O. F. 20 N, aquaFur 224. e5 fit I N 8.
T H E O R EM A ITI.
SFAcubus =B in LLGuad. 3- + D plano in A, xquetur D plano m B-
cubo2. FcsicB quac. 3 majus D plano. B in A2 = A quadi. aequabitut
in B = A. DGllad. in A2 - BIB s G. =B in Aquad. 2 F A cubo2, aequabitur B quad.
Ecordinara aequalicace A cubus - B in A quad. 3. F D plano in A, aequabitur D plane
in B = B cnb02. Quodquidemira se habet.
Oplano = B quad. 2.
Duoniam enim B in A2 = A quad., d GtaCu D PIaHOB quad. 2. Duetis omnibus
in A2 = D planoin A- L D plano in B = B cubo2.
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