Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ cylindricum, FQ, ad fruſtum conici,
NISR, eandem rationem habere,
quam quadratum, PQ, ad rectan
gulem, ſub, PQ, LM, vna cum {1/3}. quadradifferentiæ earundem. Idem
verò fruſtum ad conicum, OPQ, eſſe
vt rectangulum ſub, PQ, & tripla,
LM, vna cum quadrato differentiæ
earundem, ad idem quadratum, P
Q. Etenim cylindricus, FQ, ad fru-
ſtum conici, NISR, habet rationem
compoſitam ex ratione cylindrici,
FQ, ad cylindricum, AQ, ideſt ex
ratione, FP, ad, PA, vel, LP, ad, BP,
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-
tionis conicus, BSR, ad fruſtum, ISRN, erit vt cubus, FH, ad
parallelepipedum ter ſub, FX, & quadrato, XF, ter ſub, XF, & quadrato, HX, cum cubo, HX. Duæ rationes autem nempè, quã
habet, FX, ad, PQ, & , PQ, ad ſui {1/3}. componunt rationem, FX, ad
{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-
to, FH, ad parallelepipedum ter ſub, HX, & quadrato, XF, ter
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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