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

GEOMETRIÆ . n. nabemus parallelepipedum ſub, AB, & rectangulo, ADC, & ſub, AB, & rectingulo, BCD,. . ſub, BC, & rectangulo ſub, A
B, CD, cui ſi iunxeris parallelepipedum ſub, BC, & rectangulo ſub,
BD, DC, componeour parallelepipedum ſub, BC, & rectangulo,
pipedo ſub, AB, & eodem re-
rallelepipedum ſub, AC, & re-
æquale erit alteri ſummæ prædi-
ctæ, nempè parallelepipedo ſub,
BC, & rectangulo ſub, BD, D
C, vna cum, {1/3}, cubi, BC, ergo & eorum tripla æqualia erunt ſci-
licet parallelepipedum ter ſub, AC, & rectangulo, ADC, ſeu ter
ſub, AD, & rectangulo, ACD, æquabitur parallelepipedo ter ſub,
BC, & rectangulo, BDC, ſeu ter ſub, BD, & rectangulo, BCD,
cum cubo, BC, additis verò communibus cubis, AC, CD, fiet pa-
rallelepipedum ter ſub, AD, & rectangulo, ACD, cum cubis, A
C, CD, ideſt totus cubus, AD, æqualis parallelepipedo ter ſub, B
D, & rectangulo, BCD, cum cubis, BC, CD, (quæ integrant
cubum, BD,) & cum cubo, AC, eſt igitur cubus, AD, æqualis
duobus cubis, AC, BD. Poſſibile eſt ergo facere, quod propoſi-
tum fuit.

29. Sex.
lem,
E. Cor. 4
Gen. 34.
huius.
35. huius.
Schol. 35.
huius.
38. huius.
38. huius.

## 296.COROLLARIVM.

EX hoc manifeſtum eſt, ſi, AC, ſit latus dati cubi, & ſit etiam da-
tarecta linea, vt, AB, minor, AC, poſſibile eſſe inuenire duos
eubos, vt, AD, DB, ita vt eorum differentia ſit æqualis cubo dato,
AC, & laterun cubicorum, AD, DB, ſcilicet, AB, pariter diffe-
rentia ſit data, eſt. n. cubus, AC, æqualis dictæ cuborum, AD, DB,
differentiæ, vt eſtenſum eſt. Cum verò ſimilia ſolida quæunq; ſint in
tripla ratione linearum, ſeu later um bomologorum eorumdem, ideò
erunt, vt cubi ipſarum linearum, ſeu laterum bomologoroum, & ideò
ſaedra, AC, BD, ergo Icoſaedrum, AD, æquabitur Icoſaedris, AC,
BD, & ſuperabit Icoſaedrum, BD, Icoſaedro, AC, ergo ſi datum fuiſ-

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