# Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRI Æ libus figuris, in antecedentibus prop. conſideratis. Appendix au-
tem Cor 6 reſtauratione minimè indigere manifeſtum eſt. Et hæc
circa prop. lib. 4. adnotaſſe ſufficiat, reliquum eſt, vt ad lib. 5. exami-
nandum nos conferamus.

## 757.THEOREMA XXVII. PROPOS. XXVII.

IN Schemate prop. 1. lib. 5. regula eadem retenta, oſten-
poſitam ex, NB, & . {1/3}. BE.

Aſſumatur . n. ex eo paral-
lelogrammum, CE, cum ſe-
mihyperbola, BEF, & recta,
OE, necnon, MG, quæcum-
diametrum, BE, extendantur
autem, CB, FE, & fiant BD,
EQ, ſingulæ æquales ipſi, E
O, necnon, RE, AB, ſingulæ
æquales ipſi, EB, & iungan-
tur, DQ, AR, AE, quas, GM,
indefinitè quoq; producta ſecet in punctis, P, S, T. Erunt ergo, D
& in cæteris oſten demus, ergo quadratum ſolidum, BEF, & re-
ctangulum ſolidum ſub trapezio, DQEA, & triangulo, AER, erunt
proportionaliter analoga, ac in proportione quadrati, FE, & re-
ctanguli, QER, Conſimili modo probabimus quadratum ſolidum,
CE, eſſe æqualiter analogum rectangulo ſolido ſub, OB, BR, & ad
ER, ergo dicta ſolida proportionalia erunt, & permutãdo quadratũ
QB, BR, ad rectangulum ſolidum ſub, DQEA, ARE, hoc eſt vt, QE,
ad cõpoſitam ex {1/2}. QR, & {1/3}. RE, hoc eſt vt, OE; ad compoſitãex, N
B, (quæ eſt dimidia, BO,) & {1/3}. BE, igitur, viſo ſchemate dictę prop. 1 quadratum ſolidum, AF, ad quadratum ſolidum, DBF, erit vt, O
E, ad compoſitam ex, NB, & {1/3}. BE, quod demonſtrare oportebat.

39, & ſch.
40. l. 1.
17. huius.

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