Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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vel ellipſis circa NO baſibus AQTC portionis parallelæ
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qua ratione cylindrus, vel portionis cylindricæ FX eiuſ
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dem altitudinis portioni AQTC, baſis erit circulus
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æqualis circulo maximo, vel ellipſis ſimilis, & æqualis ei,
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cuius diameter NDO, baſibus AQTC portionis paral
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lelæ. </
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<
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>Dico portionem AQTC ad cylindrum, vel por
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tionem cylindricam FX, eſſe vt duo rectangula BSR,
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DES, vnà cum duabus tertiis quadrati ES, ad quadra
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tum BD. </
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>Ijſdem enim conſtructis, & notatis, quæ in an
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tecedenti, excepto cylindro, vel portione cylindrica, quæ
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circa axim ED ſteterat:
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planum præterea minoris
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baſis QT portionis AQ
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TC extendatur: & ſe
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cans tria ſolida, & figuras
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planas per axim poſitas in
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eodem plano, faciat ternas
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ſectiones, circulos, vel elli
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pſes ſimiles ei, quæ eſt cir
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ca NO: & earum diame
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tros IX, PV, QT, in
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eadem recta linea commu
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ni ſectione extenſi plani, &
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eius, quod per axem: quæ quidem diametri ſectæ erunt om
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nes bifariam in centro S communi trium prædictarum pla
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narum
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<
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>Denique coni, vel portionis conicæ HDG
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fruſto PKIV abſciſſo vnà cum portione AQTC, ſit
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circa axim SE circumſcriptus cylindrus vel portio cylin
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drica ZV. </
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<
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>Quoniam igitur per XIIII huius, reliquum
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ſolidi FX, dempta portione AQTC, æquale eſt fruſto
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PKLV; erit reliqua portio AQTC, reliquo eiuſdem
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ſolidi FX, dempto fruſto PKLV æqualis. </
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<
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>Et quoniam
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eſt vt PV ad KL, ita SD, DE, propter ſimilitudinem
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triangulorum: & vt rectangulum ex KL, & differentia </
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