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# Title: [Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica (shelfmark Leibn. Marg. 101)
# Folio 9, page id 845634801:0025
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9Rcqueidcirco si accidat homogeneum tub datamentura immilceriho-
ogeneoluboradu, al ntichelis.
Antichelis eA cum acteetes attectaere maonitudines ex una equatio.
aqualicas nonimmuratur. Ld autem obiter elt demonstranaum.
PR OP05Y+ 10
nis parre in alceram trantem luD Contraria adtectosnoca. io ope
Antichest aequalicarem  at.
quadrarum plus B in A equari C quadrato plus D plano, neque per ictam eranspolitionem
lab concraria adFectionis noca equalicarem immutari. Ouoniam enim A guadratum m
nusD plano equatur C quadcaro minus B in A addatur ucrobique D planum plus B in
A. Froo ex communinorione A quadratum, minus D plano plus D plano plus B in A c.
quatur C quadraro, minus B in A, plus D plano: plus B in A. Jam adfectio negata in cadem
Equationis parre elidat adtrmaram: illic cranelcer adFectio D plani, hic adFectio B in A,
e Supereric a quadrarum plus B in A equale C quadraro plus D Plano.
20 Ecli accidat omnes datas magnicudines duci in oraduin, de idcirco ho-
mogeneum lub data omnino mentura non Catim ofterri, hac EIspobi-
balinus.
FErpobibalinus est aequa depressio porestaris ex parodicorum graduum
oblerrato (cala ordine, donechomogeneum lib deprestiore oradu cadac
in datum omnino homogeneum cui comparantur reliqua. OuO OperC X
qualitasnon imutatur. Id aucem obiter est demonstrandum.
Hypobibasmiopus a Parabolismo differe in eo cancum. quod per Hypobibasmum utraque aequalitatis
pars ad quantitatem ienotam adplicatur: per Parabolismum vero ad quantitatem certant, ut ex exem.
plis ab auihore allatis perspicuum est.
PEOPONntUT A quadratum minus D plano equari G quadearo minus B in A. Dico A
P R O P OS FFFO II.
Lodmo aequalitarem non immutari.
basinum A guadratum, plus B in A; equari Z plano.
Illud enim est omnia Colida dirisisse per communem dirilorem, à quo non immutari
equalicarem determinatum est.
HI EFS accidat gradum altiorem, ad quem adscender quae sita magnitido;
non ex se sublictere, se din aliquam daram magnitudinem duci, tac Parabo-
lius.
Parabolismus est homogeneorum, quibus constat aquatio, ad datam
marnitudinem, qua in altiorem quaelicitix gradum ducicur, communis 2d-
Plicatio; utis gradus porestatis nomen libi vendicet, _ ex ca tandema qua
rio lublictat. Ouo opere aequalicas non immuraem. Id aurem obiter ell
demonstrandum.
+LbF05tF1b TII.
PEoponatur A cubus, plusB in A quadeatum; equari Z plano in A. Dico per hypobi
PEOVONALIE B IN A qUAdTALLIIM PHIS L PTAHES M A EGHAIT LIOHAS. DACD Per L aL4DO
lilmum A quadratum plus  olne in A equari Z caia Iludenim: est omnia Colida divi-
Eisseper B communem divilorem, a quo non immutari equalicarem determinatum est.
12 Fcrunc diserte exprimi aequalitas censecor d dicicor ordinata: 2d AN2-
losilinum, si placet, rerocanda, tali praeserrim caucione; ur liib extremis
Facta, cum porestari rum adfectionum homoseneis relpondeant; submediis
vero, homogeneo lub datammensiira.
13 Vndc etiam Analogilimus ordinatus detiniatur Ceries erium quatuorre
magni
Lataboldo aqualllateM AOn Mistulabo