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

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10080GEOMETRIÆ

Sit ſolidum rotundum, APCQ, & conusicalenus, APEQM,
vtraque autem ſecentur plano per axem, quod producat figuram, A
PCQ, in ſolido, & triangulum, APQ, in cono, deinde ſecentur
altero plano, cuius, & plani recti ad axem (quo productus ſit circu-
lus, PMQE,) communis ſectio ſit, EM, perpendicularis ipſi, PQ,
communi ſectioni eiuſdem, & plani per axem ducti. Dico figuram,
BEDM, in ſolido rotundo eſſe circa axem, & in cono circa axem,
116. Defin. vel diametrum, & axem, vel diametrum eſſe, BD, communem ſe-
ctionem productarum figurarum. Si ergo ſecundò producta figura
per axem pariter ducta eſſet, manifeſtum eſt in ſolido rotundo fore
2233. huius. figuram talem circa axem, & in cono fore triangulum, in quo axis,
3316. huius. AC, ſi ſecaret æquidiſtantes baſi talis trianguli ad angulos rectos,
cum illas bifariam diuidat, eſſet talis triangulus figura circa axem, ſi
verò ad angulos non rectos, eſſet figura circa diametrum, nempè
circa, AC. Sed non tranſeat hęc ſecunda figura per axem, ſint au-
tem puncta, B, D, extrema communis ſectionis primæ, & ſecundę
figuræ, ideſt ip-

55[Figure 55] ſius, BD, ergo
in ſolido rotun-
do (& in-cono,
dum triangulus,
APQ, per axem
ductus tranſit e-
tiam per ductam
à vertice, A, per-
pẽdicularem ipſi
baſi, PEQM,
ideſt cum trian-
gulus, APQ, eſt
erectus baſi, PE
QM,) ipſa, EM, communis ſectio ſecundi plani ſecantis, & , PQ,
444. Defin.
vndec. El. plani rectè axim ſecantis, cum ſit perpendicularis, PQ, communi ſe-
ctioni planorum, PEQM, APQ, ad inuicem erectorum, erit etiam
perpendicularis plano per axem, & ideò erit perpendicularis ad om-
nes per eam in tali plano tranſeuntes, ideò, BD, rectè ſecabit ipſam,
EM, & quæ ducuntur per extrema, BD, æquidiſtantes ipſi, EM,
tangent ipſa ſolida, vnde, B, D, erunt oppoſiti vertices figurarum,
BEDM, reſpectu ipſius, EM, ſumptarum, quare, BD, ſecabit
551. Defin. omnes illi æquidiſtantes in figura, BEDM, ductas, & quia ſumpto
66Corol. 2.
4. Huius. in figura, BEDM, puncto, qui non ſit vertex reſpectu ipſius, EM,
& ab eo ducta eidem, EM, parallela intra figuram cadit, ſit is pun-
77Coroll. 1.
4. Huius. ctus, O, à quo ipſi, EM, ſit ducta parallela ipſa, OR, igitur,

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