Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="023/01/050.jpg"/>
            <p type="head">
              <s id="s.000445">THEOREMA XII. PROPOSITIO XVI.</s>
            </p>
            <p type="main">
              <s id="s.000446">In ſphæra, & ſphæroide idem eſt grauitatis, &
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              figuræ centrum.</s>
            </p>
            <p type="main">
              <s id="s.000447">Secetur ſphæra, uel ſphæroides plano per axem ducto;
                <lb/>
              quod ſectionem faciat circulum, uel ellipſim abcd, cuius
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              diameter, & ſphæræ, uel ſphæroidis axis db; & centrum e. </s>
              <lb/>
              <s id="s.000448">Dico e grauitatis etiam centrum eſſe. </s>
              <s id="s.000449">ſecetur enim altero
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              plano per e, ad planum ſecans recto, cuius ſectio ſit circu­
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              lus circa diametrum ac. </s>
              <s id="s.000450">erunt adc, abc dimidiæ portio­
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              nes ſphæræ, uel ſphæroidis. </s>
              <s id="s.000451">& quoniam portionis adc gra
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              uitatis centrum eſi in linea d, & centrum portionis abc in
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              ipſa be; totius ſphæræ, uel ſphæroidis grauitatis centrum
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              in axe db conſiſtet, Quòd ſi portionis adc centrum graui
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              tatis ponatur eſſe f & fiat ipſi fe æqualis eg:
                <expan abbr="punctũ">punctum</expan>
              g por
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                <figure id="id.023.01.050.1.jpg" xlink:href="023/01/050/1.jpg" number="39"/>
                <lb/>
                <arrow.to.target n="marg48"/>
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              tionis abc centrum erit. </s>
              <s id="s.000452">ſolidis enim figuris ſimilibus &
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              æqualibus inter ſe aptatis, & centra grauitatis ipſarum in­
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                <arrow.to.target n="marg49"/>
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              ter se aptentur neceſſe eſt. </s>
              <s id="s.000453">ex quo fit, ut magnitudinis, quæ
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              ex utilique
                <expan abbr="cõſlat">conſtat</expan>
              , hoc eſt ipſius ſphæræ, uel ſphæroidis gra
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              uitatis centrum ſit in medio lineæ fg uidelicet in e. </s>
              <s id="s.000454">Sphæ­
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              ræ igitur, uel ſphæroidis grauitatis centrum eſt idem, quod
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              centrum figuræ.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>