Valerio, Luca, De centro gravitatis solidorum, 1604

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/272.jpg" pagenum="93"/>
              ad OH, erit tertij exceſſus ex duobus prioribus compoſi­
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              ti centrum grauitatis O. </s>
              <s>Quoniam igitur minor propor­
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              tio eſt primi exceſſus ad ſedundum, hoc eſt MO ad OH,
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              quàm LK ad KH; erit conuertendo maior proportio HO
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              ad OM, quàm HK ad KL: ſed vt HK ad KL, ita
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              ponitur HN ad NM; maior igitur proportio eſt HO ad
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              OM, quàm HN ad NM; eiuſdem igitur lineæ HM
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              minor erit MO, quàm MN, & punctum O propinquius
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              puncto G quam punctum N. </s>
              <s>Rurſus quia vt HK ad
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              KL, ita eſt HN ad NM; erit componen do & per con­
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              uerſionem rationis, vt LH ad HK ita MH ad HN: &
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              permutando, vt HM ad HL, ita HN ad HK: ſed HM
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              eſt maior quàm HL; ergo & HN erit maior quam H
                <emph type="italics"/>
              K
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              ,
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              & punctum N propinquius puncto G quàm punctum K:
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              ſed punctum O propinquius erat puncto G quàm punctum
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              N; multo igitur erit punctum O propinquius puncto G
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              quàm punctum K. ponitur autem diſtantia GK minor
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              quantacumque longitudine propoſita: & eſt O centrum
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              grauitatis tertij exceſſus reliquo ſolido AEBFC circum­
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              ſcripti; ex ijs igitur, quæ in primo libro demonſtrauimus,
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              ſolidi AEBFC centrum grauitatis erit G. </s>
              <s>Quod demon­
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              ſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO VII.
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              </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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              quarta ab ea, quæ baſim attingit ſic diuiditur, vt
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              pars propinquior baſi ſit ad reliquam, vt ſeſquial­
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              tera tranſuerſi lateris hyperboles, quæ conoides
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              deſcribit; ad axem conoidis. </s>
            </p>
            <p type="main">
              <s>Sit conoides hyperbolicum ABC, cuius axis BD: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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