## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ cylindricum, FQ, ad fruſtum conici,
NISR, eandem rationem habere,
verò fruſtum ad conicum, OPQ, eſſe
vt rectangulum ſub, PQ, & tripla,
Q. Etenim cylindricus, FQ, ad fru-
ſtum conici, NISR, habet rationem
compoſitam ex ratione cylindrici,
FQ, ad cylindricum, AQ, ideſt ex
vel exceſius, PQ, ſuper, LM, (qui
ſit, FX,) ad, PQ, & ex ratione cylindri-
ci, AQ, ad conicum, BSR, ideſt ex
ea, quam habet, PQ, ad {1/3}. PQ, & tandem ex ratione conici, BSR, ad
fruſtum, ISRN, quæ eſt eadem ei, quam habet cubus, PQ, vel, F
H, ad parallelepipedum ter ſub, HX, & quadrato, XF, ter ſub, F
X, & quadrato, XH, cum cubo, FX, eſt enim conicus, BSR, ſimi-
lis conico, BIN, & ideò, BSR, ad, BIN, eſt vt cubus, PQ, vel, FH,
ad cubum, LM, ſeu ad cubum, XH, vnde cum cubus, FH, æquæ-
tur cubis, FX, XH, cum parallelepipedis ter ſub, FX, & quadrato,
XH, & ter ſub, HX, & quadrato, XF, ideò per conuerſionem ra-
parallelepipedum ter ſub, FX, & quadrato, XF, ter ſub, XF, & quadrato, HX, cum cubo, HX. Duæ rationes autem nempè, quã
{1/3}. PQ, vel triplæ, FX, ad, PQ, ſeu, FH, vel, ſumpto pro communi
baſi quadrato, FH, componunt rationem parallelepipedi ſub tri-
pla, FX, & ſub quadrato, FH, ad cubum, FH, quæ proportio cum
ea, quam d ximus habere cubum, FH, ad paralleiepipedum ter ſub
HX, & quadrato, XF, ter ſub, XF, & quadrato, HX, cum, cubo,
FX, componit rationem parallelepipedi ſub tripla, FX, & quadra-
ſub, XF, & quadrato, HX, cum cubo, XF, ergo cylindricus, FQ,
ad fruſtum, ISRN, erit vt parallelepipedum ſub tripla, FX, & qua-
drato, FH, ad dicta ſex parailelepipeda cum cubo, FX, vel vt eo-
rum ſub tripla, idéſt vt parallelepipedum ſub, FX, & quadrato, F

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