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

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353333LIBER IV. quadrata ſemiparabolæ, BDC, ad omnia quadrata figuræ, CBD
F, demptis omnibus quadratis trilinei, BCF, erunt vt dimidium
quadrati, DE, .
i. vt rectangulum ſub {1/8}. DF, & ſub, DF, ad rectã-
gulum ſub {2/3}.
DF, & ſub, DF, . i. vt {1/8}. DF, ad {1/3}. DF, . i. vt {1/2} {3/4}. D
F, ad {1/2} {6/4}.
DF, . i. vt 3. ad 16. quod oſtendere opus erat.
THEOREMA XXXVI. PROP. XXXVIII.
IN figura Prop. 34. adhuc oſtendemus omnia quadrata
figuræ, HBDM, demptis omnibus quadratis figuræ, B
HMF, ad omnia quadrata figuræ, CBDF, demptis omni-
bus quadratis trilinei, BCF, eſſe vt, D/M, MF, ad, FD.
Quoniam . n. omnia quadrata, AM, demptis omnibus quadra-
tis, CM, ſunt ad omnia quadrata figuræ, HBDM, demptis om-
239[Figure 239] nibus quadratis figu-
ræ, BHMF, vt, AF,
ad parabolam, DBF,
1134. huius..
ſ. vt omnia quadrata,
A F, ad omnia quadra.
ta figuræ, CBDF,
demptis omnibus qua
dratis trilinei, BCF,
ergo, permutando,
omnia quadrata, A
M, demptis omnibus
quadratis, CM, ad omnia quadrata, AF, erunt vt omnia quadra-
ta figuræ, HBDM, demptis omnibus quadratis figuræ, HBFM,
ad omnia quadrata figuræ, CBDF, dem ptis omnibus quadratis
trilinei, BCF, ſunt autem omnia quadrata, AM, demptis omnibus
quadratis, CM, ad omnia quadrata, AF, vt rectangulum bis ſub,
MF, FD, cum quadrato, FD, .
i. rectangulum ſub compoſita ex,
DM, MF, &
ſub; FD, ad quadratum, FD, . i. vt compoſita ex,
DM, MF, ad, FD, ergo omnia quadrata figuræ, DM, HB, dem-
ptis omnibus quadratis figuræ CBDF, demptis omnibus quadra.

tis trilinei, BCF, erunt vt, DM, MF, ad, FD, quod oſtendere
opus erat.

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