Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

530. COROLLARIVM XXVI.

N Propoſitione 49. aſſumpta de figura Propoſit. 46. parabola,

ZAG, cum axi, AQ, & illi parallela, DP, abſcindatur ab axi,
AQ, ipſa, AV, exceſſus, AQ,
ſuper, DP, & vt fiat ſolitum
exemplum, reuoluantur tũ
fruſtum maius, ZADP, tum
fruſtum minus, DPG, circa
communem axem, DP, vt
ex fruſto maiori, DAZP,
fiat aceruus maior parabo
licus, ZADON, & ex fruſto
minori, DPG, fiat aceruus
minor parabolicus, RDG: Patet ergo ex hac Propoſ. aceruum
minorem, RDG, ad aceruum maiorem, ZADON, habere ratio-
nem compoſitam ex ea, quam habet compoſita ex {1/3}. ZP, & {1/6}. PG,
ad ZP, & ex ratione parallelepipedi ſub, DP, & quadrato, PG, ad
parallelepipedum ſub, AQ, & his ſpatijs. ſ. quadrato, PQ, {1/2}. qua-
drati, QZ, & rectangulo ſub ſexquitertia, ZQ, & ſub, QP, dempto
ab eodem {1/6}. parallelepipedi ſub, AV, & quadrato, QP: Sic autem
erit etiam quodlibet ſolidum ſimilare genitum ex fruſto minori,
DPG, ad ſibi ſimilare genitum ex figura, CAZP, Prop. 46. dem-
pto ſolido ſimilari genit o ex trilineo, ACD, iuxta communem re-
gulam, ZG.

530.1.

0383-01

531. COROLLARIVM XXVII.

N Propoſitione 50. de figura Propoſit. 46. ſumatur fruſtum

minus parabolæ, quod eſt, DGP, quodque ſecatur per rectam,
TI, æquidiſtantem ipſi, PG, acci-
piantur inſuper duæ integræ, ZG,
SI, & vt fiat noſtrum exemplum,
reuoluatur, DPG, fruſtum circa
manentem axim, DP, vt ex, DPG,
ſiat aceruus minor, RDG, & ex,
DTI, eius fruſtum, YDI, patet er-
go ex hoc Theorem. aceruum mi-
norem, RDG, ad reſectum fruſtum, YDI, habere rationem com-
poſitam ex ea, quam habet rectangulum, ZPG, cum {1/2}. quadrati,

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer