Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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314294GEOMETRIÆ& , & per, HA, ipſi, GM, parallelę, BY, ℟ & , producaturque, T
S, vſque ad, B ℟, Y &
, in, P, Z, & per, SV, ducantur, VF, SL,
parallelæipſi, HA, ſunt igitur parallelogramma, BA, AY, LT,
TF, BT, TY, PA, AZ.
Igitur parabola, AGH, ad portionem,
HST, habetrationem compoſitam ex ea, quam habet parabola, H
11Diff. 12.
lib. 1.
GA, ad parallelogrammum, BA, ideſt ex ea, quam habent omnia
quadrata, H &
, (regula ſumpta pro hoc Theor. ipſa, GM,) ad om-
22Exante. nia quadrata ſemicirculi, vel ſemiellipſis, HMA;
& ex ea, quam
208[Figure 208] habet, AB, ad, BT,
335. Lib. 2. ideſt, AH, ad, HT,
ideſt omnia quadra-
449. Lib. 2. ta, &
H, ad omnia
quadrata, HZ;
& ex
55Ex antec. ea, quam habet, BT,
66Defin. 12.
lib. 1.
ad portionem, HST,
ideſt omnia quadra-
ta, HZ, ad omnia
quadrata ſemiportio-
nis, HTV, ſed etiam
omnia quadrata ſe-
micirculi, vel ſemiel-
lipſis, HMA, ad on-
nia quadrata ſemipor
tionis, HTV, ha-
bent rationem com-
poſitam ex ea, quam
habent omnia qua-
drata ſemicirculi, vel
ſemiellipſis, HMA,
ad omnia quadrata,
H &
, & ex ea, quam
habent hęc ad omnia
quadrata ſemiportio-
nis, HTV, ergo pa-
rabola, HGA, ad portionem, HST, eſt vt omnia quadrata, HM
77Lib. 3. A, ad omnia quadrata ſemiportionis, HTV, ideſt vt parallelepipe-
dum ſub altitudine, XA, baſi quadrato, AH, ad parallelepipedum
ſub altitudine, XT, baſi quadrato, TH;
vel vt cubus, AH, ad pa-
rallelepipedum ſub altitudine tripla, AT, baſi quadrato, TH, cum
cubo, TH, ſic.
n. eſſe omnia quadrata ſemicirculi, vel ſemiellipſis,
HMA, ad omnia quadrata ſemiportionis, HVT, oſtenſum eſt
Lib.
3. Propoſ. 6.

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