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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 228, page id 845634801:0234
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228 DE N VMEROSA POTESTAFVM RESOFVF
Si de relolurione quadraro. cubi, latus se cundum ducatur in mulcip lex quadrato. qua-
dearum primi, in aliaque dividentia plano. plana; quadrarum ejuldem in Colida; cubus in
plana; quadraro quadrarum in longitudines.
Si de resolutione cnbo. cubi, lacus secundum ducetur in mulciplex quadraro- cubum
primi, in aliaque dividentia plano. Colida; quadratum ejusdem in plano. plana; cubus in
Colida; quadraco. quadrarum in plana; quadeaco. cubus in longicudines.
Erica in infinieum.
Adoresabuntur aurem facta hujusmodi homogenea, cum fuerine ejusdem adfectio
nis. Ouod H diversx, quae fene d coefficiente negante una, vel pluribus, et suis incerme
diis expletionum scanloriis, parrem unam Faciunco, Reliqua homogenea reliquam.
ExE lumma homogenearum primo casu; vel differentia se cundo; magnicudinisresol-
vendae reliquo fuerir requalis, opus erix absolurum. Sin minus, e luperhc punctum porc
stari addictum, duo jam elicira larera Funsentur vice unius, et deinceps subcunda exic
Terria Cura, _ reliquae exPOSiEX, donec ad Anem opus perduCatuT.
Praeceptum Sexeum.
Ad cliciendum radices proximas veris, alioguin irrationales.
Si aurem singularia latera omnia jam sinc elicica, id est, nullum supersir punctum po.
cestariaddictum; neque camen primo calu summa homogeneorum; vel secundo ditte
rencia, sicipu reliquo magnicudinis relolucioni expolrx equalis: argumentum erix lacus
ese irracionale. Ouo itaque proximum eliciacur majus minus- ve. summae elicicorum 12
cerum lingularium adjungerur Fragmenrum, cujus numerator erie reliquum magnicudi
nis resolvenda. Ad denominarorem vero lumeneur divilores iidem, qui esene, si aliquod
punctum porestari addictum supere ser denuo relolvendum. Quo d et in analy (i purarum
Poreltarum poruie observari.
Vel, relolvendae magnicudini adfectae addentur, ur in puris, conditionarii secundum
genera magnicudinum numerales circuli, id est bini in quadearis, rerni in cubis, quater-
ni inquadraro quadraris, ex eo deinceps ordine. Ouin coethcientibus magniemdinibus
ioouore, nus addi intelligentur ror quoque numerales circuli, quot exposcerpraduum iplis
homoeeneorum condicio, singuli si lonsicudo, bini si planum, terni (i Colidum, de eoi
inAnicum progressu. Enivero
PFOPONAEHEKC I 6N, aequari 8. Ouoniam 6 est magnitudo plana: 2 C.- + 6001
aquabitur 8, 000. dc eric haecradix ad illam decupla. FFL C = 6, 00, 00N, aequabieut
8,000,000. _ crirradix haec ad primam centuola.
Exsiproponatur C +. 6Q, aequari 8. Ouoniam hic 6 est longirudo: 1C. F 609, Xqua
bitur 8, 000. e crichaecradix ad illam decupla. EFrurtuSZ C = 600 9, aquabirur 8, 000
000. _ erir haecradix ad primam propolicam cenrupla.
EFEI PEOPONatUEI 9O. F 6C, aequari 8. Duoniam s est longicudo: r99 + 60
aequabitur 8, 0000. et haec radix erir ad primam decupla. Vel 2 9 9 F 600C, aquabicu
8,0000,0000. e haec radix erir ad primam propostam cencup la. LF ita de reliquis, ped
ea quae de ilomaria in cractaru de Emendarione A quarionum cradica lunt.
Ouid verohrN est explicabilis sub noca alymmetrix, quaeratur aurem sub ea spect
exhriberi: X id per arrem non denegabitur, sicur exiis quae superius citato rractatu expo
sica sune, manifettum Eic. Hlic aurem eHto
ExPLLCLEYS DE AVHBROSA POTESTAENH RESOLr