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

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9878GEOMETRIÆ

COROLLARIVM.

_H_Inc patet ipſam, BE, communem ſectionem trianguli por axem
ducti, & circuli, BRE, eſſe eiuſdem diametrum, cum per eius
centrum tranſedt.

THEOREMA XXXIII. PROPOS. XXXVI.

SI ſolidum rotundum, vel conus ſcalenus ſecentur plano
per axem, deinde ſecetur ſolidum rotundum (niſi baſim
habeat, quę circulus erit) plano ad axem recto circulum pro-
ducente, in cuius plano, & illius, qui eſt coni baſis perpen-
dicularis ducta ſit baſi figurę per axim ductę; deinde ſumpto
puncto in ambitu figuræ per axem, per illum æquidiſtans di-
ctæ perpendiculari ducta fueritrecta linea, hæc tanget dicta
ſolida, at ſi ſumptus punctus ſit extra talem ambitum, ſed in
ſuperficie ambiente dicta ſolida, quæ per ipſum ducitur ei-
dem æquidiſtans intra dicta ſolida cadet, & producta vſque
ad ſuperficiem ambientem à figura ducta per axem bifariam
diuidetur.

Sit ſolidum rotundum, ABTF, vel conus ſcalenus, APR, in
baſi circulo, PXRZ, quorum axis, AT, & ſi ſolidum rotundum
non habeat baſim, ſe-

54[Figure 54] cetur plano recto ad
axem, quod in eo pro-
ducat circulum, PXR
Z, ſecentur autem am-
bo planis per axem-
quæ producant in ſo-
lido rotundo figuram,
APTF, & in cono
triangulum, APR,
deinde in plano circu-
li, PZRX, ducatur
ipſi, PR, communi
ſectioni dicti circuli, &
figuræ per axem, perpendicularis, ZX, & ſumpto puncto in ambitu
figurę per axem, vt, 2, per ipſum ducatur recta linea parallela

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