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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 152, page id 845634801:0158
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752
D E E M E N D A Y ION F
Proponatur LC L 86OH, aquari 1728. 2C + 215H, aequa bitur 216. 8 est L N I. Vnde fit r4
dixprimum quaesita 2.
C A P V F IX.
anomala aequationum aliquot cubicarum ad quadraticas aut
etiam simpliciores reductio.
DRxparandarum igicuraequationum Colennes modi ita se habent. Deir-
reoularibus autem non Pcaruuntur praecepta, quoniam anomaliaillanon
magisfinita est quam artificis in indagando ris et Polertia. ad excitandum
camen cam vim ex Colerriam, oportunum est singularia aliquor aequatio-
num consticutira ex reductira Theoremata adnocasse, insignem aliquam
emphalin vel elegantiam prae se ferentia; qualia jaM (CGLUINTIT.
T H R O R E M A L.
EtAcubus = B quad. 2 in A, xguecur B cubo. A quad. - B in A, xqua
bitur B quadrato.
Ex iisenim quae proxonuntur manifestum Exper ancithesn: A cubum, equari B cnb0
+. B quad. 2 in A, X addendourrique parci B cubum: A cubum Y B cubo, aequari B cU-
b02 -F B quad. 2 in A. Omnia applicentur ad A +- B; illIC OrIEUE, A quad B in A , L B
quad; hic B quad 2. e consequenter abjecto urrinque B quadrato. A quad. B in A, 2.
guabirur B quadrato.
Si 1C -- 181, aquetur 27. igieur 2D - 3 N, aquabitur 9.
T H B O R E M A II.
S+Bquad. 2 in A - A cubo, aequerur B cubo. A quad. - + B in A, equabi-
tur B quadeato.
Ex iis enim quae proxonuntur manifectum hcperantithesn: A cubum, aguari B quad.
2 in A - B cubo, ex auterendo urique parri B cubum. A cubum = Bcubo, aequari B
quad. 2 in A - B cubo 2. Omnia applicentur ad A - B; illic oritur A quad. Y B in A
L b quad; hic B quad. 2 et consequenrer abje cto vrrinque B quadrato. A quad. + B in
A, aeguabicur B quadraco.
Si 1BN - 2C, aquetur 27. igitur 1D. F 3N, aequabitur 9.
H E O R E i A TII.
CT A cubus = B quad. 3 in A, aequetur B cubo 2. B dup la est ip (a A de qua
quaeritur.
Ouoniam enim B dupla, est. ip Ca A de qua GuAeFItUE, CrBO CX IIS GUX PTOPONUNEUE B
cubus 8 -B quad. in B6, sequabirur B cubo 2. quod quidem ira se habet.
1C- 22N, aequetur 26, fit ZN 4.
E H F O R E M A IV.
S+B quad. 3 in A - A cubo, aquetur B cubo2. B est ip Ca A de qua quaeri-
CUT.
Ouoniamenim B est ip (a A de qua quaeritur, ergo ex iis qua PrOPOnUTUEB quad.
in B3 =B cubo, aquabitur B cubo2. quod quidem ita se haber.
6H = rC, aequatur N 32. fit LN N 2.
T H E O R E M A V.
SFA cubus =B in Aquad. = D plano in A, aequetur B in D planum. Ipta
Best A de qua quaritur.
sa
II
Dira