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

241[Figure 241] HM, ducatur autem intra ipſam
eidem, BG, parallela, EF, ducta
verò tangente, AC, in termino,
B, quæ erit parallela baſi, HF, pro-
ducatur verſus, FE, illi productæ
occurrens in, C, & compleatur pa-
rallelogrammum, AF, regula ve-
rò ſit, HM. Dico ergo omnia qua-
drata, AF, ad omnia quadrata fi-
guræ, CBHF, eſſe vt quadratum, HF, ad quadratum, FG, {1/2}. qua-
dtati, GH, & rectangulum ſub ſexquitertia, HG, & ſub, GF. Hęc
autem erit conſimilis demonſtrationi ſecundæ partis Theor. 32.
ideo inde colligatur.

THEOREMA XLI. PROPOS. XLIII.

IN eadem anteced. Propoſit. figura oſtendemus omnia
quadrata, AF, ad omnia quadrata figuræ, CBHF, dem-
ptis omnibus quadratis trilinei, BCE, eſſe vt parallelepi-
peduw ſub, BG, & quadrato, HF, ad reliquum parallelepi-
pedi ſub, BG, & his ſpatis . ſ. quadrato, FG, {1/2}. quadrati,
GH, & rectangulo ſub ſexquitertia, HG, & ſub, GF, ab eo-
dem dempto {1/3}. parallelepipedi ſub, CE, & quadrato, FG.

Nam omnia quadrata, AF, ad omnia quadrata, BF, ducta per,
1111.l. 2. E, ipſa, EI, æquidiſtans, HM, ſunt vt parallelepipedum ſub, AH,
& quadrato, HF, ad parallelepipedum ſub, BI, & quadrato, IE,
ſuut autem omnia quadrata, BE, ſexcupla ommum quadratorum
2230. huius. trilinei, BCE, ideò omnia quadrata, AF, ad omnia quadrata tri-

242[Figure 242] linei, BCE, erunt vt parallelepi-
pedum ſub, AH, vel, BG, & ſub
quadrato, HF, ad parallelepipedi
ſub, BI, & quadrato, IE, ſextam
partem: Quia verò omnia quadra-
ta, AF, ad omnia quadrata figuræ,
3324. huius. CBHF, ſunt vt quadratum, HF,
ad hæc ſpatia . ſ. quadratum FG,
{1/2}. quadrati, HG, & rectangulum
ſub ſexquitertia, HG, & ſub, GF, . i. ſumpta, BG, communi alti-
tudine, vt parallelepipedum ſub, BG, & quadrato, HF, ad

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