Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ABCD abſciſsa duobus planis parallelis altero ducto
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per E, & ſectionem faciente circulum maximum, vel
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ellipſim per centrum, cuius diameter AED: axis autem
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portionis ſit EF, cui congruens ſphæræ, vel ſphæroidis axis
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GFER: ſit autem FE bifariam ſectus in puncto H: &
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FH bifariam in puncto K, ſitque in EH, ſic enim erit,
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portionis ABCD centrum grauitatis L. </
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ad KL, vt rectangulum GFR, vnà cum duabus tertiis
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quadrati EF ad quadratum EG. </
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portio cylindrica AM circa axim FE abſciſſa ijſdem pla
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nis cum portione AB
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CD, ex cylindro, vel
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portione cylindrica cir
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ca axim GR ſphæ
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ræ, vel ſphæroidi AG
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DR circumſcripta.
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<
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>Quoniam igitur ſolidi
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AM eſt centrum gra
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uitatis H: reliqui au
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tem dempta ABCD
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portione centrum gra
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uitatis K: & portionis
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ABCD ponitur cen
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trum grauitatis L; erit
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vt portio ABCD ad reliquum ſolidi AM, ita ex con
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traria parte KH ad HL. componendo igitur vt in antece
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denti, & per conuerſionem rationis, & conuertendo, erit
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vt portio ABCD ad ſolidum AM; hoc eſt vt rectangu
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lum GFR, vnà cum duabus tertiis quadrati EF ad qua
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dratum EG, ita HK ad KL. </
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<
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erat. </
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