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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 107, page id 845634801:0123
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A OV A Y LO N VM
Placeat extibere Formulam aequarionis cubinegari de homogeneo adfectionis subla
cere, ue sic radix de Pvel C explicabilis. dixero rquad. -L. C quad. - + F in C in A = A c1b0, C
quari F in C quad. F C in P quad. de Heri A, F vel C.
Sit F 2O. G 2. AL N. formula aequacionis erit Y24 N - LC, aequabitur 240. explicabilis de
10, vel 3
In concradicencibus, coefsicientes sub graduales proficiscunur ex applicarione ditte-
cencie poreltarum, ad aexcegatum corum quos sustinen coetticientes gractuum.
Hlomogeneavero dae menture, ex applicatione asgregaifactorum reciproce, dpo
duum aggregarum: id aurem quoque obicer est demonstrandum.
L O B L E M a TI.
Vacum Conradicentium equationum consticutionem ex Cyncrili 18.
HOlCCTC.
PEOPONAEUEA pOtestaS L B coëtticienre in A gradum, equari Z homogeneo. EcrursuS
E porestas = eadem B coëtticienre in E oradum, eguari eidem Z homodeneo.
Vnde par existic gradus et par porectas. Oporret ex synerili carum equationum con-
cicurionem agnolcere.
Ouoniamisieur que uni equantur equalia suntinter se, manifestum eR. A porestarem
L B coësticience in A gradum, equari L porestari = B coetsicience in P gradum. de per
ancirhelin E porectarem =A porestare, equari B coetlcienei in F gradum = B coetE.
cience in A gcadum. leaque omnibus per L gradum + A gradu divi(Is. = poccM.. - A B
aquabicur B coëthciedci.
Eractus F a Bradtu
Mu eso Dedehicets suboradualis, ex applicarione difterencia porestarum, ad
SBregarum eorum quos sustiner coetlciens graduum: uc est contticurum.
Porroquum A porestAS L B coetfciente in R Gradum, XGuCTE Z homosenco.
In locum B coëtsciemis, Subrogecurjam agnicus ejus raloc, videlicer ro
adus + a Er actu
_ CA (UBEOBALIONE RGUATIOLCFOTMETUIT. CrBOA POrCstAS L E vocnn a poreaue in ABcadtum,
aequ. Z. homogeneo, hoc est omnibusrire ordinacis avocelur in e ea  e soeluie in a eradi X qu. L
homogeneo.
N Scadus t a Pracu
Oricur ergo Z homogenea, ex applicatione aspresari factorum reciproce d porectate
radicis unius, in gradum alcerius, ad pradictum cui alcera applicario facta eAt graduum 20.
Fregacum: ur es secundo loco enunciatum.
In inversis plane negatis, coethciences suberaduales prosicilcuntur ex applicarione ae-
sresati poceltarum, ad agcresacum eorum in quos coëfticiens est oraduum.
Hlomocenea vero datx mensurae, ex applicarione differencix Factorum reciproce a
poreltare radicis unius, in gradum alcerius, ad praedictum cui alcera applicario facta est
Seaduum in quos coetliciens luberadualis eAt, agBregRTUM.
Idem quoque obirer est demonstrandum.
R O B L E M A TTI.
Varum inverlarum aequationum consticutionem, ex syncrili agno-
PropONAIuE A pOrectaS =B coetscience in A gradum, aquari Z HOMOGCNCO. LFTUI
lus eadem B coitticiensin E. gradum = P poreltare, aequari eidem Z homogeneo.
Vnde incellIBAnEUE A eC F pares gradus, acque adeO parES POTCNATES, OpOTLCAEAEeM
equalicarum harum consticrionem agnolcere. Duoniam iBitIEGUX UnI LGUAnEEX qua
la sune incer se, manitestum HICCx IIS QUA PTOPONNEUIT. A porestarem =B coelticien
in Agradtum, aequari B coetlcieni in gradum = P. porestare, de per anrichelin A pOrC
atem + E poreltare, equari B coetlicienri in Apcadum  Bcoelsicienre in L gc2.
dum.
ciene.
   equabitur B coithi.