Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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5333LIBERI.

THEOREMA XIV. PROPOS. XVII.

SI conicus ſecetur vtcumque planis per verticem, diuidi-
tur ab eiſdem in conicos: Etſiſecetur vtcumque planis
coincidentibus omnibus eiuſdem lateribus, ſolida ab ijſdem
abſciſſa verſus verticem erunt pariter conici, & eorum baſes
ipſæ ſiguræ abſcindentes.

Sit quilibet conicus, AMV, ſectus plano vtcum que per verticem
ducto, quod in eo producat triangulum, ACD. Dico ab hoc pla-
no ſecante in conicos, ACVD, ACMD, fuiſſe diuiſum. Sin. in-
telligamus latus trianguli, ACD, quod ſit, AC, vel, AD, inni-
xum puncto, A, indefinitè productum ferri per rectam, CD, ipſa
deſcribet ſuperriciem trianguli, ACD, ad modum ſuperficiei coni-
cularis, eſt autem reliqua, quę inſiſtit ambitui, CVD, ſic deſcripta,

26[Figure 26] ergo tota ſuperficies, ACDV, eſt co-
11AD, ef.4. nicularis deſcripta latere, AC, vel, AD,
properante per circuitum figuræ planæ,
CVD, ergo erit, ACVD, conicus,
cuius baſis ipſa figura, CVD, & ver-
tex, A. Eodem modo oſtendemus, A
CMD, eſſe conicum, cuius baſis, CM
D, vertex, A. Secetur nunc plano vt-
cumque omnibus conici, AMV, late-
ribus concidente, quod in eo producat
figuram, BNEO. Dico, ANO, eſſe
conicum, cuius baſis figura, BNEO,
vertex, A, nam dum latus conici, AM
V, properat per circuitum baſis, CMD
V, vt deſcribat eius conicularem ſuperficiem, properat etiam per
circuitum figurę, BNEO, & deſcribit ſupra ipiam ſuperficiem co-
nicularem, igitur ſuperficies ab eadem figura, BE, ablciſia verſus,
A, eſt conicularis, & ſolidum comprehenſum ab ipſa, & figura pla-
na, BNEO, erit conicus, & eiuſdem baſis ipſa figura, BNEO,
vertex autem, A, quod oſtendere opus erat.

COROLLARIVM.

_H_Inc habetur, ſi planum tranſeat per verticem conici, & quamli-
bet rectam lineam intra baſim conici exiſtentem, qui quidem ſe-
cetur alio plano coincidente cum omnibus eiuſdem conici

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