Valerio, Luca, De centro gravitatis solidorvm libri tres

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        <body>
          <chap>
            <pb xlink:href="043/01/165.jpg" pagenum="78"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XLIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis conoidis hyperbolici centrum grauita­
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              tis eſt punctum illud, in quo duodecima pars axis
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              ordine quarta ab ea, quæ baſim attingit, ſic diui­
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              ditur, vt pars baſi propinquior ſit ad reliquam, vt
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              ſeſquialtera tranſuerſi lateris hyperboles, quæ
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              conoides deſcribit ad axim conoidis. </s>
            </p>
            <p type="main">
              <s>Sit conoides hyperbolicum ABC, cuius vertex B, axis
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              autem BD, qui etiam erit diameter hyperboles, quæ co­
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              noides deſcripſit, ad quam rectæ ordinatim applicantur:
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              eiuſdem autem hyperboles tranſuerſum latus ſit EB, cu­
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              ius ſit ſeſquialtera BEI, & ſumpta DQ quarta parte
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              axis BD, & DG, eiuſdem tertia, qua ratione erit FG
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              duodecima pars axis BD, & ordine quarta ab ea cuius
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              terminus D, fiat vt IB, ad BD, ita QH, ad HG.
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              </s>
              <s>Dico conoidis ABC, centrum grauitatis eſſe H. </s>
              <s>Sumpto
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              enim in linea AD quolibet puncto M, vt eſt EB ad
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              BD longitudine, ita fiat MD, ad DK ipſius AD po­
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              tentia: & abſcindatur DN, æqualis DM, & DL æqua­
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              lis DK; ſiue autem ſit DK minor, quàm DM, ſiue ma­
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              ior, ſiue eadem illi; omnibus caſibus communis erit demon
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              ſtratio. </s>
              <s>At per puncta M, N, vertice B, circa diametrum
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              BD, deſcribatur parabola MBN, & triangulum KBL.
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              </s>
              <s>Manente igitur BD, & circumductis figuris MBN,
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              KBL, deſcribantur conoides parabolicum MBN, &
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              conus KBL, quorum communis axis erit BD, baſes
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              autem circuli, quorum diametri KL, MN, in eodem
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              plano cum baſe conoidis ABC. </s>
              <s>Rurſus ſecto axe BD
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              bifariam, & ſingulis eius partibus ſemper bifariam in qua-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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