Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ctangulum contentum lateribus homologis baſium oppo
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ſitarum, vna cum tertia parte quadrati differentiæ, ad ma
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ioris lateris quadratum; idem igitur fruſtum pyramidis
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ad idem priſma, erit vt rectangulum DCF, vna cum
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tertia parte quadrati DF ad quadratum CD: deficit
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autem vtrumque & pyramidis fruſtum fruſto CB inſcri
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ptum ab ipſo CB fruſto, & priſma ipſi CG inſcriptum
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ab ìpſo CG, minori ſpacio quantacumque propoſita ma
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gnitudine; per tertiam igitur huius, erit vt rectangulum
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DCF vna cum tertia parte quadrati DF, ad CD qua
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dratum, ita fruſtum CB ad cylindrum, vel portionem
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cylindricam CG. </
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>Cum igitur conus, vel coni portio E
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CD ſit pars tertia cylindri, vel portionis cylindricæ CG,
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erit ex æquali, vt idem rectangulum DCF, vna cum ter
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tia parte quadrati DF, ad tertiam partem quadrati CD,
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ita fruſtum BC, ad conum vel coni portionem ECD. Præ
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terea, quia quadratum CD æquale eſt duobus quadratis
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ex CF, FD, vna cum rectangulo bis ex CF, FD: quorum
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rectangulo CFD, vna cum quadrato CF æquale eſt rectan
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gulum DCF; erit quadratum CD æquale rectangulo
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DCF vna cum quadrato DF; demptis igitur rectangu
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lo DCF, & tertia parte quadrati DF; quod remanet
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CD quadrati erit rectangulum CFD vna cum duabus
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tertiis quadrati DF. quoniam igitur eſt conuertendo vt
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quadratum CD ad rectangulum DCF, vna cum tertia
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parte quadrati DF, ita cylindris, vel portio cylindrica
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CG ad fruſtum CB, erit per conuerſionem rationis, &
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conuertendo; vt rectangulum CFD vna cum duabus ter
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tiis DF quadrati, ad quadratum CD, ita reliquum cy
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lindri, vel portionis cylindricæ CG dempto fruſto CB,
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ad cylindrum, vel portionem cylindricam. </
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eſt igitur propoſitum. </
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