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

GEOMETRIÆ ſint, ET, TY, YZ, & per puncta, YZ, ducantur parabolæ axi æ-
quidiſtantes, YX, ZQ, curuæ eiuſdem indefinitè productæ occur-
rentes in punctis, X, Q, & iungantur, EX, EQ. Erit igitur ſectio,
EIX, ad ſectionem, E℟I, vt cubus, YE, ad cubum, ET, ſic enim
ſunt eorum tripla ſcilicet triangula, EIT, EXY, quod elicitur ex
prima Lib. 4. & , diuidendo, trilineum, EXI, ad ſectionem, E℟I,
erit vt parallelepipedum ter ſub, ET, ac quadrato, TY, & ter ſub,
YT, & quadrato, TE, cum cubo, TY, ad cubum, TE, vel vt horũ
ſubtripla, ſcilicet, vt parallelepipedum ſemel ſub, YT, & quadra-
to, TE, & ſub, ET, & quadrato, TY, ſcilicet ſub, YT, & rectan-
gulo, YTE, cum {1/3}. cubi, TY, ideſt cum parallelepipedo ſub, TY, & {1/3}. quadrati, TY, ad {1/ }. cubi, TE, ideſt ad parallelepipedum ſub, T
E, vel, TY, & tertia parte quadrati, TE, nempé vt parallelepipe-
dum ſub, TY, & quadr. ET, & rectangulo, YTE, & tertia parte
quadrati, YT, quod conficit parallelepipedum ſub, YT, & rectan-
gulo ſub, YET, & ſub tertia parte quadrati, YT, ad parallelepi-
pedum ſub, YT, & ſub t ertia parte quadrati, TE, & quia horum
parallelepipedorum altitudines ſunt eædem, ideò erunt, vt baſes
ſcilicet, vt rectangulum ſub, YET, cum tertia parte quadrati, TY,
ad, {1/ }. quadrati, ET. Eodem modo oſtendemus trilineum, EQX,
adtrilineum, EXI, eſſe vt exceſſus cubi, ZE, ſuper cubum, YE, ad
exceſſum cubi, YE, ſuper cubum, TE, . i. vt parallelepipedum ter
ſub, ZY, & quadrato, YE, ter ſub EY, & quadrato, YZ, cum cu-
bo, YZ, ad parallelepipedum ter ſub, ET, & quadrato, TY, ter

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