Valerio, Luca, De centro gravitatis solidorvm libri tres

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        <body>
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            <p type="main">
              <s>
                <pb xlink:href="043/01/041.jpg" pagenum="33"/>
              per præcedentem ſectæ erunt hæ diametri bifariam in pun­
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              ctis H, G, K. </s>
              <s>Quoniam igitur eſt vt EH, ad HA, ita
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              EK ad KD, parallela erit KH, ipſi AD; igitur & EC;
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              ſed recta KH, ſecat latus AE, trianguli AEC, bifariam
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              in puncto H, ergo & latus AC, bifariam ſecabit; igitur
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              in puncto G. punctum igitur G, eſt in linea KH. Rurſus,
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              quoniam eſt vt GA, ad AC, ita GH, ad EC, propter ſi­
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              militudinem triangulorum; ſed dimidia eſt GA, ipſius
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              AC, igitur & GH, erit dimidia ipſius EC, hoc eſt ipſius
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              FD. </s>
              <s>Similiter oſtenderemus dimidiam eſse KH ipſius
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              AD. vt igitur KH, ad AD, ita erit GH, ad FD: & per­
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              mutando, vt AD, ad DF, ita KH, ad HG, & diui­
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              dendo, vt AF, ad FD, hoc eſt vt parallelogrammum AE,
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              ad parallelogrammum ED, ita KG, ad GH. </s>
              <s>Quod de­
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              monſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XVI.
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              </s>
            </p>
            <p type="main">
              <s>Plana grauia æquiponderant à longitudini­
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              bus ex contraria parte reſpondentibus. </s>
            </p>
            <p type="main">
              <s>Sint plana grauia N, R, quorum centra grauitatis ſint
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              N, R, & longitudo aliqua AB: & vt eſt N, ad R, ita ſit
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              BC, ad CA. </s>
              <s>Dico ſuſpenſis magnitudinibus ſecundum
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              centra grauitatis N, in puncto A, & R, in puncto B, vtri­
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              uſque magnitudinis N, R, ſimul centrum grauitatis eſse
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              C. </s>
              <s>Nam ſi N, R, magnitudines ſint æquales, manifeſtum
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              eſt propoſitum. </s>
              <s>Si autem inæquales, abſcindatur BD,
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              æqualis AC, vt ſit AD, ad DB, vt BC, ad CA. </s>
              <s>Et quo­
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              niam ſpacio R, rectangulum æquale poteſt eſse; applice­
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              tur ad lineam BD, rectangulum BDKE, æquale quar­
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              tæ parti rectanguli æqualis ipſi R, hoc eſt quartæ parti
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              ipſius R; & poſita DG, æquali, & in directum ipſi DK, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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