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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 153, page id 845634801:0159
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

le fit 11
Deir.
lato
ndun
ratio
quat
Qua
cob
BCt
A, 2
10b
q
euE
1XrI
qua
spid
Oud
AE OV A X +O N V M.
Duoniam enim B est A de Gua quaerituE: erBO ex IIS QUX PFOPOHUITEEBCNDUS = BTR
BGllad.. F D plano in B, aequtabirur B in D planum. quod quidem manitesto ira se habet.
+Q FSN, aequatur 20. facto ex 4 in 5. ergo + N est 4.
T H E O R E M A VI.
TA cubis F B in A glad. = D quadr. in A, aquetur B in D quadeatuM.
IPla D est A de qua quaTItIE.
Ouoniam enim ipla D es A de qua quaxitIE, erBO CxiIS quX PEoPOnunEuE, D cubus
F B in D quad. = D quadc. in D, xquabicur Bin D quadrarum. Ouod quidem mani-
Fecto ira se haber.
2C + 52- 4 N, aequatur 20. facto ex 5 in 4. ergo XN fit V 4 vel 2.
T H E OR P M A VII.
FB in A quadr. F D quad. in A = A cubO, aquCtIF D quadratO in B.
Ipta B rel D, est A de qua quaritur.
Ouoniam enimipla B est A de qua quaeritur ergo ex iis quxe proponuneur B cubus
+ D quad. in B =B cubo, aequabitur B in D quadrarum. Ouod quidem ica manifesto
sehrabet.
Rurtus quoniam ip (a D est A de qua quaeritur, ergo ex iis quae proponuntur, Bit D
quad. + D cubo =D cubo, aequabirur D quadraro in B. Ouod quidem ira quoquema-
nifesto se haber.
68 Y 4N - 2 C, aquatur 24. fil L N 6 vel 2.
F H E OR E N A VITI.
GFD in A quad. - + B in D in A = A cubo, Xequetur B cubO: St D in A - A
Quad. aequabitur B quadrato.
Ex iis enim qux propOnuntur, manifestum sEper ancichesin. B cubum L A cub0;
aequari D in A quad. + D in B in A. Veraque pars applicetur ad A Y B, erBo A quades
B in A + B quad reguabitur D in A.
EEPCFAnLitheGBD, Bin A= A quad, aquabituF B quadraTO.
SiTOB, L ZON = ZC, aequecur 8. quia lacus cubicum ex 8 ductum in 10, facit 20. Jpitur 12
N = +9, aequabieur 4. ex fit ZN 6 = V 32, vel 6 + N 32.
T H E O R E M A IZ
SFAcubuS =D in A quadr. + D in Bin A, Xguetur B cubo: D = B in A
A quad. ae quabitur B quadrato.
Ex iis enim quae proponuncur manifectum Arper ancichetin; quum A incelligitur ma-
TOr quam B, A cubum -B cubo, aequari D in A quadr. = D in A in B. VIragUC PArS
aequalicaris applicetur ad A = B. IBitur A quad. = B in A = B quad., aquabItUE D in As
Ex perantichetinD = B in A - A quad., aequabirur B quadrato. AEqui quum B intelli-
sicur major quam A, B cubus = A cubo, aequabitur D in A in B - D in A quad. Veraque
pars aequalicaris applicetur ad B. - A, iraque B quad. F A quadr. + B in A, XquaBIEUIE
D in A. UE anEC.
SirC = 109 F 2ON, aquetur 8. quia V C. 8 ductumin 10, facit 20. I8ituT BN - 1 0.
equabitur 4. 87 fit L N 4 = N 12, vel 4 = N 12.
L E E O R F M A X.
eas =DPL. MA, equetur VB plano- plano. Planiz, v vo3 + v D run.
AE A de quaquariEE.
Ouo.