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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 105, page id 845634801:0121
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ee
18
AE, OV A Y T O N V M.
Due aurem equationes correlare incelliguntur, quum ambe similes (unE,
apraecerea iildem daris maonitudinibus constane, live adFectionum para-
bolis, sive adfectionum homogeneis. Radices tamen ideo direrla lunE,
quoniam velipia aequarionum Formulx de duabus pluribusre radicibus, ex
lui consticurione sunt explicabiles, rel in iis diverla est adfectionum qua-
licaS, CCu nOTa.
AC de simplicioribus quidem correlaris susticiet doctrina, id estuna tan-
cum adfectione obroluris, ur pore quarum vi, de iisqua pastionibus abun-
dane, plastices peritus ratiocinabitur (CCurC.
Correlatarum igicur simpliciorum xquationum, eres sunt differentix.
Prima est ancipitum, in quarum ueraque porestas nesatur de homoge.
nea adFectionIS.
AIcera est concradicentium, in quarum una porestas adficitur adtiema-
te, in alcera negate.
Tercia est invertarum, in quarum una, porestas adEciturmulta homo-
genex adfectionis, in alterae conera, homogenea adfectionis mIILEaLIII
POcCRaTC.
Sive auremancipitum, sive concradicentium, sire inverlarum xquario-
num constiturio, synerili cognolcetur probe: incundx liquidem Cynerileos
lxecestratio. Ouoniam enim quae uni xequantur inter le aequalia linE:
Proponuneur autem porestares dux adhcientes, adfectara, cidem data om-
mino maonicudini homogenca comparari; ipsum aurem adfectum, 2dh-
ciensre homogeneum, urriris porestati immixtum, Reri lubparodicis i(-
dem gradibus, eademque parabola. Erso porestas radicis una cum homo-
gencolubliio gradu parodico, aquabitur porestati alcerius una cum homo-
geneolubsuo quoque sraduparodico; e transtatis ad unam ica constitEX
quoquexequationis parrem porestatibus; ad alceram vero, iis qua (ub sr2-
dibus hunc adfectionum homogeneis, cricrursum requalicas. Cinde quum
disterentia aut aggregatum porestatum, applicabitur ad difterentiam vel
agErCgacum laterum, (uter verorerminus, opusindicabit.) Facietoririmag.
nicudinem parabola aqualem: cujus ideo cridens erir constiturio:
Duodliposteaucrarispolicarum equationum, Cynerisi exposicarum,
non jam lub iplam et parabola exhibeatur, (eu sub ae quo parabolXe (PFOLLCjUS
consticurio agnita tuic) ralore: quod ordinabitur, crie consequenter dato
comparationis homogenco aquale, cujusideo constitutionon porerit 1s
nocari: quoniam oriecur illud ex Facti ab agoresato vel difterentia radicum,
auc graduum, in planum sub radicibus applicatione ad eundem cui antece-
densapplicacio facta estcerminum, sire disterentiam, sive aggresatum.
Secundum quae, prosicilcuneur parabola adFectionum in ancipitibus, ex
applicatione difterencix porestacum ad difFCreNEIAML COLLI QUOS ICFIEUE
Parabolagraduum.
lomogenearero comparationum, ex applicatione disterentix lacto
rum reciproce, a porestace unius radicis in gradum alcerius, ad peaedictam
cui alcera applicacio facta est, graduum difterentiam.
Id aurem obicer est demonstrandum.
LO BLB M A I.
lalc aepicum aquacionum concicutionem, et lynec a
110
lCeic.