Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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PROPOSITIO XXXVI.
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>Omnis portionis ſphæræ abſciſſæ duobus pla
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nis parallelis neutro per centrum acto, nec cen
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trum intercipientibus, centrum grauitatis eſt in
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axe primum bifariam ſecto: deinde ſecundum
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centrum grauitatis fruſti circa eundem axim,
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abſciſſi à cono verticem habente centrum ſphæ
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ræ; in eo puncto in quo dimidius axis maiorem
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baſim attingens ſic diuiditur, vt pars duabus præ
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dictis ſectionibus finita ſit ad eam, quæ inter ſe
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cundam, & vltimam ſectionem interijcitur, vt
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exceſſus, quo maior extrema ad triplas & ſemidia
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metri ſphæræ, & eius quæ inter centra ſphæræ,
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& minorem baſim portionis interijcitur, ſuperat
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tres deinceps proportionales, quarum maxima
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eſt, quæ inter centra ſphæræ, & minoris baſis,
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media autem, quæ inter centra ſphæræ, & maio
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ris baſis portionis interijcitur; ad maiorem extre
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mam antedictam. </
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>Sit portio ABCD, ſphæræ, cuius centrum E, ab
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ſciſsa duobus planis parallelis, neutro per E tranſeun
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te, nec E intercipientibus: axis autem portionis ſit GH,
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maior baſis circulus, cuius diameter AD, minor cuius
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diameter BC: producta autem GH vſque in E intel
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ligatur coni KEN rectanguli, cuius axis EG, fruſtum </
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