Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Sit conus, cuius vertex, A, baſis circulus, CEFD, ſecetur autem
prius plano per axem, quod in eo producat triangulum, ACF, ſe-
cetur deinde altero plano baſim ſecante ſecundum rectam, ED, per-
pendicularem ipfi, CF, cuius in cono concepta ſit figura, BED,
erit ergo hæc figura circa axem, vel diametrum, BV, quę ſit paral-
lela ipſi, AF, cuius vertex reſpectu ipſius, ED, erit, B; ducaturà
puncto, M, qui non ſit punctus, B, ſed vtcumque ſumptus in linea,
EBD, extra baſim, ED, ipſi, ED, recta ęquidiſtans, MO, pro-
ducta vſq; ad ambientem ſuperficiem, cui occurrat in, O, igitur hęc
erit vna ex ordinatim applicatis ad axim, vel diametrum, BV, ęqui-
diſtans ipſi, ED, quę bifariam diuidetur ab ipſa, BV, in puncto, N,
ducatur per, N, ipſi, CF, parallela, HR, eſt verò etiam, MO, ipſi,
ED, parallela, ergo planum tranſiens per, HR, MO, æquidiſta-
bit baſi, CEFD, & quatuor puncta, H, M, R, O, erunt in circuli
periphæria, cuius diameter, HR, quem
ſecat, MO, perpendiculariter, nam an-
gulus, HNM, æquatur angulo, CVE,
quirectus eſt, ergo quadratum, MN, æ-
quatur rectangulo, HNR, & quadra-
tum, EV, rectangulo, CVF, eſt autem
rectangulum, CVF, ad rectangulum, H
NR, (quia eorum altitudines, VF, NR,
ſunt æ quales, cum ſint parallelogrammi,
NF, oppoſita latera) vt baſis, CV, ad,
HN, ex prima Sexti Elem. vel ex quinta
libro ſequentis independénter ab hac de-
monſtrata, & quia, HN, eſt parallela
ipſi, CV, trianguli, BHN, BCV, ſunt æquianguli, ideò, vt, C
V, ad, HN, ita, VB, ad, BN, ergo rectangulum, CVF, ad re-
ctangulum, HNR, ideſt quadratum, EV, ad quadratum, MN,
erit vt, VB, ad, BN, eſt autem quadratum, ED, quadruplum
quadrati, EV, nam eſt æquale quadratis, EV, VD, & rectangulis
fub, EVD, bis, ideſt duobus quadratis, EV, quæ cum prædictis
conficiunt quatuor quadrata, EV, & eadem ratione quadratum, M
O, eſt quadruplum quadrati, MN, ergo quadratum, ED, ad qua-
dratum, MO, erit vt, BV, ad, BN, quæſunt abſciſſæ ab ipſa axi,
vel diametro, BV, verſus verticem, B, per ipſas, ED, MO, ordi-
natim adipſam, BV, applicatas, quod oſtendere opus erat; hęc au-
tem vocatur ab Apolonio Parabola.

129.1.

16, huius.
Ex antec.
15. Vnde-
cim. El.
0102-01
15. huius.
14. Secun.
Elem.
4. Sexti
Elem.
4. Secun.
Elem.

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