Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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043/01/138.jpg
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51
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lelogrammis circumſcribatur figuræ ABC, altera tertia fi
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gura, quemadmodum diximus in præcedenti, cuius cen
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trum grauitatis H, in linea GD cadat & ſit minor pro
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portio reſidui huius tertiæ figuræ circumſcriptæ ipſi ABC,
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ad figuram ABC, quàm FG ad GD. </
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<
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>Multo ergo mi
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nor proportio erit dicti reſidui ad figuram ABC quam F
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H ad HD, fiat igitur vt prædictum reſiduum ad figuram
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ABC, ita ex contraria parte FH ad HDK; prædicti igi
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tur reſidui centrum grauitatis erit K, extra ipſius terminos,
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quod fieri non poteſt: Non igitur F centrum grauitatis fi
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guræ ABC cadit in puncto E, nec ſupra; ergo infra pun
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ctum E: & ponitur E centrum grauitatis cuiuslibet figuræ
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ex cylindris, vel cylindri portionibus, vel parallelogrammis
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æqualium altitudinum quo modo diximus ipſi ABC cir
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cumſcriptæ. </
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<
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>Manifeſtum eſt igitur propoſitum. </
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PROPOSITIO XXXI.
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<
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>Omni prædictæ figuræ figura quædam ex cylin
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dris, vel cylindri portionibus, vel parallelogram
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mis æqualium altitudi
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num circumſcribi po
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teſt, cuius centri graui
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tatis diſtantia à prædi
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ctæ figuræ centro gra
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uitatis ſit minor quan
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tacunque longitudine
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propoſita. </
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<
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>Sit figura ABC in
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alterã
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partem
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deficiẽs
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ſupradicta,
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cuius centrum grauitatis F, propoſita autem
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quantacũque
">quantacumque</
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<
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lõgitudine
">longitudine</
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minor ſit FG ipſius BF. </
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<
s
>Dico figuræ ABC figu-</
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