Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ lineæ erunt interſe, vtrectangula ſub partibus baſis ab ei-
ſdem æquidiſtantibus conſtitutis.

Sit ergo parabola, FCH, circa axim, vel diametrum, CG, ad
quam ordinatim applicetur recta linea vtcunq; FH, ducantur dein-
de intra parabolam axi, vel diametro, CG, parallelæ vtcunque, A
N, MO, baſim, FH, in punctis, N, O, diuidentes. Dico igitur re-
ctam, AN, ad rectam, MO, eſſe vt rectangulum, FNH, ad re-
ctangulum, FOH; ducatur per, M, ipſi, FH, parallela, MI; eſt
ergo, GC, ad, CI, vt quadratum, GH, ad quadratum, IM, vel
ad quadratum, GO, ergo, perconuerſionem rationis, GC, ad, G
I, vel ad, MO, erit vt quadratum, H
G, ad ſuireliquum, dempto quadrato,
GO, hoc autem reſiduum eſt rectan-
gulum ſub, GOH, bis, vna cum qua-
drato, OH, quod eſt æqualerectan-
gulo, FOH, nam rectangulum, GO
H, cum quadrato, OH, æquatur re-
ctangulo, GHO, . i. rectangulo ſub,
FG, OH, cui ſi iunxeris rectangulum
ſub, GO, & eadem, OH, conſurget
integrum rectangulum, FOH, æqualerectangulis ſub, GOH, bis,
vna cum quadrato, OH, ergo, CG, ad, MO, erit vt quadratum,
GH, . i. vt rectangulum, FGH, ad rectangulum, FOH, & con-
uertendo, MO, ad, CG, erit vtrectang. HOF, ad rectangulum, H
GF; codem modo oſtendemus, CG, ad, AN, eſſe vt idem rectan-
gulum, HGF, ad rectangulum, FNH, ergo ex æquali, & conuer-
tendo, AN, ad, MO, erit vt rectangulum, FNH, ad rectangulum,
FOH, quod oſtendere oportebat. Poſſunt autem vocari & , AN,
MO, ordinatim applicatæ ad baſim parabolæ, FCH, ſcilicet ad
ipſam, FH.

408.1.

38. EtSch.
40. lib. 1.
0308-01
4. 2. Elem.
3.2. Elem.
1. 2. Elem.

409. THEOREMA IV. PROPOS. IV.

SI ad baſim parabolæ ordinatim applicetur vtcunque re-
cta linea, ſiat autem parallelogrammum, & triangulum
habentia circa communem angulum dictam applicatam, & abſciſſam à baſiab vtrauis extremitatum eiuſdem, vel ſint
duæ ad baſim vtcunque ordinatim applicatæ, ſub alterutra
quarum, & ſub in cluſa ab ijſdem portione baſis ſiat paralle-
logrammum, & triangulum; dicti parallelogrammi, vel trian-

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