Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000162">
                <pb xlink:href="023/01/018.jpg"/>
              teſt in portione, quæ recta linea & obtuſianguli coni ſe­
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              ctione, ſeu hyperbola continetur.</s>
            </p>
            <p type="head">
              <s id="s.000163">THEOREMA IIII. PROPOSITIO IIII.</s>
            </p>
            <p type="main">
              <s id="s.000164">IN circulo & ellipſi idem eſt figuræ & graui­
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              tatis centrum.</s>
            </p>
            <p type="main">
              <s id="s.000165">SIT circulus, uel ellipſis, cuius centrum a. </s>
              <s id="s.000166">Dico a gra­
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              uitatis quoque centrum eſſe. </s>
              <s id="s.000167">Si enim fieri poteſt, ſit b cen­
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              trum grauitatis: & iuncta ab extra figuram in c produca
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              tur: quam uero proportionem habet linea ca ad ab, ha­
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              beat circulus a ad alium circulum, in quo d; uel ellipſis ad
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              aliam ellipſim: & in circulo, uel ellipſi figura rectilinea pla­
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              ne deſcribatur adco, ut tandem relinquantur portiones
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              quædam minores circulo, uel ellipſi d; quæ figura ſit abcefg
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              hklmn. </s>
              <s id="s.000168">Illud uero in circulo fieri poſſe ex duodecimo
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              elementorum libro, propoſitione ſecunda manifeſte con­
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                <figure id="id.023.01.018.1.jpg" xlink:href="023/01/018/1.jpg" number="10"/>
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              ſtat; at in ellipſi nos demonſtra­
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              uimus in commentariis in quin­
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              tam propoſitionem Archimedis
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              de conoidibus, & ſphæroidibus. </s>
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              <s id="s.000169">erit igitur a centrum grauitatis
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              ipſius figuræ, quod proxime
                <expan abbr="oſtẽ">oſten</expan>
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              dimus. </s>
              <s id="s.000170">Itaque quoniam circulus
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              a ad circulum d, uel ellipſis a ad
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              ellipſim d eandem
                <expan abbr="proportionẽ">proportionem</expan>
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              habet, quam linea ca ad ab:
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              portiones uero ſunt minores cir
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                <arrow.to.target n="marg21"/>
                <lb/>
              culo uel ellipſi d: habebit circu­
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              lus, uel ellipſis ad portiones ma­
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              iorem proportionem, quàm ca
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                <arrow.to.target n="marg22"/>
                <lb/>
              ad ab: & diuidendo figura recti­
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              linea abcefghklmn ad portiones </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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