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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 104, page id 845634801:0120
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107
DE RECOGHEZEONE
bus: F B in A quad., aequabitur B in D in A. Sed ex iis quXPFOPOnuNErin D- 
aequatur A. Ouare ea incerprecatione adscira ad exprimendum valorem solidi B in
in A: A cubus. = B in Aquad., aequabirur B in D quad. - D in A quad. de adhibica col
Erua meracheli. A cubus + B F D in a quad, aequabitur B in D quad. ur est ordinarum.
Si = Q + 16 N, aequatur 80. facto ex 16 in 5. 1C. + 21 9; aequabitur 400.
Y H E O R E N A V.
E A quad. = B in A, Squetur B in D. B - D in A quad. = A cubo, X qua
Nec dissimilis est ab ea quae in anrecedente Theoremate expolira est demonstratio.
Si +9 = 16 N, aquetur 60. facto ex 16 in 5. 21 O = 1 C, aequabitur 400.
T A E O R E M A VI.
EFB in A = A quact. aequetuT B in D. S = Din A quad. = A cubO, _ qud
Nec dissimilis est ab ea quae in quarro hujus capiris FheOremate exposica est demon
Arario.
SigN = + 9, aguerar 18. facto ex 9 in 2. 7Q = LC, aquabitur 36.
C A P V X ZV.
ambisuitates radicum, quarum pocestates dehomoceneis adfectionum
in adae quationibus necantur, demonstratae.
T H E O R E NE A.
Scendendum est quum in xquationibus porestates de homogeneis al
Fectionumnegantur, radices elle ancipites.
Proponarur differentia inter B ec A esse aqualis S: _ siC B major quam S. aur igitur C
cessus estpenes B, vel penes A. Primo calu, B = A aequetuES: itaque B =S AE A. Secu
Aocalu A = B aequetur S: iraque B + S Fr A. Ouoniam aurem primo casuB -- A equ
S, urraque pars aequalicaris ducacur quadrarice, isirur B quad. = B in A2 F A quad, 29
birur S quad. e xequalicare ordinara, B in A2 - A quad, x quale Ar B quad. -59
Ouoniam vero secundo catu, A = B aquarur S, urraque pais aequaliraris ducatur quact
rice, igicur B quad. = B in A2. F A quad. aequabitur S quad. de xequalirare ordinata,
A2 = A quad. rursus aequale AE, B9. - S9. Veroque ixitur casu in candem incien
aequarionis Formulam: est aurem radix duplex; ipsa vero Formula aquarionis est, ut P
num sub larere, ad Aciatur mulea quadeati.
Sit B. 6, 54. AIN. 1ZN = + 9, aquatur 20. e fit L N. 6 - 4 vel + 4.
Ouam amphiboliam in omnibus similibus equarionibus locum habere Caris ince
BituE, UE II pFOPOnatIT D in A - A quad, aequari Z plano: ip (a D dicerur eAeB2, et L P
num eseB quad. - 5. quad.
POrrO, per sextum Theorema ancecedentis capiris, apparer ab ea quadrari ambih
aequatione, derirari cubos negatos de solidis sub paradico gradu, de perterrium, lex
ecnonum capiris duo decimi, ab eadem derivari quadraco. quadraca negata de pluct
plaris sub paro dico gradu, quod ad ulrerioris ordinis aequariones posle extendilact
manifectum.
C APVI LV
De Syncrist.
bitur B in D quad.
bicur B in D quad.
hendendum carum constitutionem collatio.