Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXXIIII.
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<
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>Omnis portionis ſphæræ, vel ſphæroidis ab
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ſciſſæ duobusplanis parallelis, neutro per cen
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trum acto, nec centrum intercipientibus, centrum
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grauitatis eſt in axe, primum bifariam ſecto: de
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inde ſecundum centrum grauitatis reliqui dem
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pta portione ex cylindro, vel portione cylindrica,
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abſciſſo, vel abſciſſa vnà cum portione à cylin
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dro, vel portione cylindrica ſphæræ, vel ſphæroi
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di circa eius axem axi portionis congruentem cir
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cumſcripta; in eo puncto, in quo dimidius axis
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portionis maiorem baſim attingens ſic diuiditur,
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vt pars prima & ſecunda ſectione terminata ſit ad
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eam, quæ prima, & poſtrema ſectione terminatur,
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vt duo rectangula, alterum contentum duobus
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ſphæræ, vel ſphæroidis axis axi portionis
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cõgruen
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tis ijs ſegmentis, quæ fiunt à centro minoris baſis
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portionis: alterum axe portionis, & ſegmento,
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quod ſphæræ, vel ſphæroidis, & maioris baſis por
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tionis centra iungit, vnà cum duabus tertiis qua
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drati axis portionis, ad ſphæræ vel ſphæroidis di
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midij axis quadratum. </
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<
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>Sit ſphæræ, vel ſphæroidis, cuius centrum E portio
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ABCD, abſciſſa duobus planis parallelis, neutro per E
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tranſeunte, nec E intercipientibus: portionis autem axis
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ſit FS: maior baſis circulus, vel ellipſis, cuius diame</
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