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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 138, page id 845634801:0144
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# Lines: 50 recognised, mean confidence 0.90
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88
DE E N E N D A Y FON
Ouibus Theorematis finirima Tuncea, quibus ex daca una ambiguariim
radicum, habetur alcerius comicis nocitia: nCMiPC
T E E O R E M A VTY
CBplanum in A = A cubo, xequetur Z Colido; _ rursus B planum in L
D = Fcubo, aequetur Z. Solido. Innorelcatautem P eNC D: A quad. F V
in A, ae quabitur B plano =D quadrato.
Ouoniamenim B planum in A = A cubo, aequarur Z Colido. de rursus B planum in
D = D cubo, aequatur Z. Colido. Tgirur B planum in A - A cubo, equabitur B plano in
D = D cubO, _ permerathesin, A cubuS -D cubo, aequabitur B plano in A = B pl2
noin D, d urraque aequarionis parre per A - D dirila, Hc A quad. F D quad. +. D in A,
equale Bplano. Oua aequatione secundum arrem concepta, A quadr. f D in A, XGUAEUE
Bplano --D quadraco.
SiBN = TC, aequerur 7. Potest 1 N esse F.
fit 2N V. 25-
duare 2 8 F LN, aquarur 7. e rursus
F E E O R E M A VIII.
ETB in A quad. = A cubo, aequetur Z Colido, _ rursus Bin F quad. - F
cubo, aequetur Z Colido. Innorescat autem P. CNCD. A quad. =D = Bin A,
aequabitur B in D - D quad.
Ouoniam enim B in A quadr. = A cubo, equatur Z Solido, ex rursus B in D guadr.
DCabo, aequatur Z Colido: isirur B in A quad. = A cubo, aequatur B in D quad. - D
cubo, de permerathesin, A cubus =D cubo, aequabitur B in A quade. - D quadr. Ver 2
que pars aequarionis dividiror per A = D, sir A quad. F D quad. F D in A, aequale B in
A. + B in D. Dua aequarionerire concepra, A quad. F D in A - B in A, aequabitur B in D
D quadraco. uc est ordinacum.
Sig 9 - 1C, aequecur d. Porest 1 N esse X. Ouare+ O = 8 N, aequabicur 8. et rursus fit L N
24. + 4.
 A P Y Y IV
DeTsomaeria adversus vitium fractionis.
Somceria est species transmurationis per mulciplicationem, ita institutas
uc xqualitates a Fractis numeris quibus laborane liberentur.
Reducuntur videlicetFractiones ad candem denominationem, ex legc
Logictices.
Deinde Ac ductio homogenei communis denominatoris, vel Orrorum
ab cograduum, in datas coefficientes; datumque homogeneum compa-
rationis.
Radices ducantur in coesficientes lonpitudines, quadrata in coefficien-
tes planas homosencare datae mensurx plana, cubi in parabolas solidas
homogeneare darx menlurae lolida, e coconstanti ordinc.
Duodque tic ex denominatore communi, et radice aqualitatis propO-
SEx, estradix aequalitatisita praeparatx.
Incerdum cxaleneme, Mlpcatione ilomaerica non opus lic, led
dirisione: applicantur videlicet coetfcientes longitudines adradices coet.
Sicientis planx, homogenex que datxe mensurx lolida ad cubos, d eocOn
Sanci ordine, quodque oritur ex applicatione radicis ad communem de-
nominatorem, est radix aequalitatis ita prxeparatX: Findameneum autem
luum habet de demonstrationem, ex symbolo x qualitatum, quo cavetus,
SI X Gu a-