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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 128, page id 845634801:0134
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8
DE E M E N D A YFO N
ordine: Guoa aeecoes sub eo oradu, protciscuntur à cremento, de
crementore, quo intelligitur adfecta radix de qua, cujutre potestate, purs
vel adFecta, primumproponebatur requatio.
Tlujus aucem crementi decrementire duplum, est cocfficiens (ub latere
in quadratis; e triplum, coefficiens lib quadraro in cubis; e quadeuplum,
coefticiens sub cubo in quadrato- quadrarisi ex quincuplum coetticiens lub
quadcaco-quadrato, in quadraco-cubis; _ lextuplum denigue, Coctciens
lub quadrato- cubo, in cubo- cubis, ee co in intinitum ordinc.
Teague ad delendum plasina, contraria retrosradaque via Cumuntur
uncixe conditionariae coeficientium radici homogenearum; in quadratis
videlicet, semis; in cubistriens; in quadrato. Quadratis quadrans; in qua-
deaco. cubis guintans; in cubo- cubis (extans; _ eo continuo ordinc: acque
illisunciis conditionariis ad fcitur radix, acque adeo arte Actransinuratio.
lociusitaque operis structura, tres caluum differentias admittit.
Primo, siE A porectas adtecta per adjunctionem homogenei subB coest-
ciente, e A parodico extremo gradu: quoniam isitur ea adfectio attirmata
CA, adticietur radix afirmare a condicionariis Bcoefticientis unciis, e ita
adtecta, Caruetur E, un de L minus conditionariis B coefficientis unciis,
requabitur A. Sub quanora specie, aequatio primum proposita dirigetur,
ec ordinabicurnora, quae ommino eveniec immunis ab adtectione (ub or2.
du extremo: ucopus comprobabic.
Sccundo, sic A porestas adlectapermulcam homogenei subB coesiciente,
ee A extremo parodico gradu: quoniamigitur ea adfectio negata est, adh-
CietuT AncgatC a conditionariis B coefficientisunciis, dc itaadtecta statuc-
cur escE, unde F plus conditionariis illis B coefficientisunciis, aquabi-
tur A. Sub qua nora specie, aequatio primum propolita dirisetur, ec Or-
dinabitur nora, quae omnino erenice immunis ab adfectione sub gradu
extremo: ut opus comprobabit.
Postremo, sic homoreneum (ub B CoeFiciente, _ A extremo oradu, 2d-
Fectum per multam A porestatis: quoniam igitur porestas porius adhcie
quam adticitur, uc pore qua negatur de homogeneo adfectionis, condi-
tionarix B coefticientis uncix multabuntur A porestate, de Statuentur esse
E, un de exdem B coefticientisuncixminus radice E, XquabUNEE A. Sub
qua nora specie, aequatio primum propolica dirisetur, ex ordinabitur nova,
guxe omnino creniet immunis ab adfectione sub BraduI CXIFCO: UE ODUS
comprobabit.
Exemplum in quadrato.
DROPOnAEuE A quad. F B in K L, LGHaC L plano: quoniam igitur in climacticarum
magnicudinum ordine, lacus qua drato proxime luccedie, proxonitur aurem hic qua-
dracum adfectum lublarere, omnino aequalitas plasmarica est, aliundeve etticta. eA au
tem affectio illa adtrmata, itaque plalna Fuic per addicionem semistis coetticientis sub la-
tere, prour condiciognadrati; quae porestas est rarionis duplicarx expolcit.
Ad collendum isirmr plalma, Hac expureario diahemisy: _ idcirco A + B eAoF; eroo
C, = BCriEA, e consequenter quadracum abs E = B adjunctum plano sub B2 in E =B
aequa bitE Z plano, per ea que proponuntur. A. qualicas igitur de P secundum gerem ordi-
necur, omnibus rice peractis. deprehendetur E. quad, aequari Z. plano + B quad: GuX
quidem nova aequatio, pura est ab adfectione sub larere, qua primum proxolira equario
Obruebatur: quum aurem innote(Cet F, non porerir A ignorati, propier datam inter en5
radices disterenriam: praltac liquidem F. ipsi A per longicudinem B. Ouare factum est
F XCMM.
quod oporcuir.