Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/018.jpg" pagenum="10"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO III.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>In ſimilibus triangulis rectæ lineæ, quæ inter
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              centra, & alia in ijs ſimiliter poſita puncta in­
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              terijciuntur, proportionales ſunt in proportione
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              laterum homologorum. </s>
            </p>
            <p type="main">
              <s>Sint triangula ſimilia, & ſimiliter poſita ABC, DEF,
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              quorum ſint centra O, P, in ijs autem triangulis ſint pun­
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              cta ſimiliter poſita K, L, quæ cadant primum in rectis
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              BG, EH, quæ ab angulis æqualibus B, E, baſes bifa­
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              riam diuidunt. </s>
              <s>Dico eſſe OK ad PL, vt eſt latus AB,
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              ad latus DE. iunctis enim AK, KC, DL, LF, quo­
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                <figure id="id.043.01.018.1.jpg" xlink:href="043/01/018/1.jpg" number="9"/>
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              niam angulus KAC, æqualis eſt angulo LDF, & angu­
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              lus KCA, angulo LFD, ob ſimiliter poſita puncta K,
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              L, triangulum AKC, triangulo LDF ſimile erit, & vt
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              KA ad AC, ita LD ad DF: ſed vt CA ad AG, ita
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              eſt FD ad DH, expræcedenti; vt igitur KA, ad AG
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              ita erit LD, ad DH, circa æquales angulos: ſimilia igi­
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              tur ſunt triangula AGK, DHL, & angulus AGK, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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