Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XLIV.
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<
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>Si conus & conoides parabolicum circa eun
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dem axim ſecentur plano baſi parallelo; fruſti co
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nici abſciſſi maiori baſi propinquius erit quàm
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parabolici centrum grauitatis. </
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>Sint conus ABC, & conoides parabolicum EBF,
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quorum communis
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axis BD, cuius per
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quoduis punctum M,
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planum ſecans ea cor
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pora plano baſium,
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quarum diametri A
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C, EF, parallelo ab
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ſcindat fruſta AKL
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C, cuius centrum gra
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uitatis N, & EGH
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F, cuius centrum gra
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uitatis O, quorum vtrumque erit in communi axe DM.
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>Dico punctum N, propinquius eſse ipſi D quàm punctum
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O. </
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>Quoniam enim eſt parabolicifruſti EGHF centrum
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grauitatis O; erit vt duplum maioris baſis, ideſt circuli
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EF vna cum minori circulo GH, ad duplum circuli GH
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vna cum circulo EF, hoc eſt vt duplum quadrati ED vna
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cum quadrato ED ita MO ad OD. </
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>Sed vt quadratum
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ED ad quadratum GM in parabola quæ conoides de
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ſcribit, cuius diameter BD, ita eſt DB ad BM, hoc eſt
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AC ad KL; vt igitur eſt dupla ipſius AC vna cum KL
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ad duplam ipſius KL vna cum AC ita erit MO ad OD:
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ſed N eſt fruſti conoici AKLC, centrum grauitatis; pun
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ctum igitur N, erit maiori baſi AC propinquius quàm </
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