Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ſunt omnia in axe AG, centrum L cadet infra
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centrum H, ex ijs, quæ in primo libro demonſtraui
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mus. </
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<
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>Dico eſſe KL ad LH vt cubum ex AG ad cu
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bum ex AF. </
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<
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>Quoniam enim
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ob centra grauitatis
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K
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, H, L,
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eſt vt fruſtum DC ad ſolidum
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ADE, ita ex contraria parte
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KH ad HL; erit componen
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do, vt ſolidum ABC ad ſoli
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dum ADE, ita KL ad LH:
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ſed vt
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ABC ad ſolidum
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ADE, ita eſt cubus ex AG
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ad cubum ex AF: triplieata
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enim eſt vtraque proportio eiuſ
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dem, quæ eſt ipſius AG ad ip
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ſam AF, propter ſimilitudi
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nem ſolidorum; vt igitur eſt cu
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bus ex AG ad cubum ex AF,
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ita erit KL ad LH. </
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<
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>Quod demonſtrandum erat. </
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PROPOSITIO XXVI.
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>Reſidui ſolidi ex cylindro, vel portione cylin
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drica hemiſphærio, vel hemiſphæroidi circum
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ſcripta, dempto hemiſphærio, vel hemiſphæroide,
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centrum grauitatis eſt punctum illud, in quo axis
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ſic diuiditur, vt pars baſim attingens hemiſphæ
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rij, vel hemiſphæroidis ſit tripla reliquæ. </
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<
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>Eſto hemiſphærio, vel hemſphæroidi ABC, cuius axis
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BD, circumſcriptus cylindrus, vel portio cylindrica AF:
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& ponatur D
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K
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ipſius
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K
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B tripla. </
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<
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