Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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tribus ſolidis communem, poſitas in eodem plano, quæ ſunt
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AF parallelogrammum, triangulum EDF, & ſemicir
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culus, vel ſemi ellipſis ABC: & ſint ſectiones rectæ GO,
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HN, KM: hæ igitnr erunt diametri eiuſdem rationis trium
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ſectionum, ſcilicet circulorum, vel ellipſium ſirnilium, qui
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bus erit commune centrum L, in quo nimirum axis BD
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tres dictas lineas GO, HN, KM, bifariam ſecat. </
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igitur de ſolido AF diximus, ſint circa axem BL, & ſuper
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baſes circulos, vel ellipſes circa HN, KM cylindri, vel
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portiones cylindricæ HP, KQ, qui vnà cum portione
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cylindrica, vel cylindro GF ipſa ſectione facto, erunt inter
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eadem plana paral
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lela per EF, GO.
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drorum, vel cylin
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dri portionum GF,
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HP, KQ,
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ipſius GF dempto
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HP, ipſi KQ eſse
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æquale. </
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>Quoniam
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enim cylindri, & cy
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lindri portiones eiuſdem altitudinis inter ſe ſunt vt ba
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ſes, circuli autem, & ſimiles ellipſes; inter ſe, vt quæ à
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diametris eiuſdem rationis fiunt quadrata; ex Archime
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de, hoc eſt vt earum quartæ partes, quæ à ſemidiame
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tris quadrata deſcribuntur; erit vt quadratum LO ad
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quadratum LN, ita cylindrus, vel portio cylindrica
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GF ad cylindrum, vel portionem cylindricam PH: &
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diuidendo, vt rectangulum LNO bis vnà cum quadra
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to NO, ad quadratum LN, ita reliquum cylindri, vel
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portionis cylindricæ GF, dempto ipſo PH, ad ipſum
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PH: ſed vt quadratum LN ad quadratum LM, ita eſt
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vt ſupra, cylindrus, vel portio cylindrica HP ad cylin
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drum, vel portionem cylindricam KQ, ex æquali igitur, </
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