Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXIII.
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<
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>Circuli, & Ellypſis idem eſt centrum grauita
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tis, & figuræ. </
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>Sit circulus, vel ellypſis ABCD, cuius centrum E.
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>Dico centrum grauitatis figuræ ABCD, eſse punctum E.
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>Ducantur enim duæ diametri ad rectos inter ſe angulos
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AC, BD; in ellypſi autem ſint diametri coniugatæ.
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>Quoniam igitur omnes rectæ lineæ, quæ in ſemicirculo,
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vel dimidia ellypſi diametro ducantur parallelæ bifariam
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ſecantur à ſemidiametro, & quo à baſi remotiores, eo ſunt
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minores; erit centrum grauitatis ſemicirculi, ſiue dimidiæ
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ellypſis ABC, in linea BE; ſicut & ſemicirculi, ſiue di
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midiæ ellypſis ADC, centrum grauitatis in linea DE.
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eſt autem BED, vna recta linea: in diametro igitur BD,
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erit centrum grauitatis circuli, ſiue ellypſis ABCD.
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<
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>Eadem ratione oſtenderemus idem centrum grauitatis eſse
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in altera diametro AC: in communi igitur vtriuſque ſe
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ctione puncto E. </
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<
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>Quod demonſtrandum erat. </
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