Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/067.jpg" pagenum="59"/>
              guli ABC, quatuor rectæ inter ſe parallelæ AD, BE,
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              CF, NM, tres autem magnitudines æquales habeant cen
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              tra grauitatis G, H, K, in tribus AD, BE, CF. </s>
              <s>Di­
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              co trium magnitudinum ſimul, quarum centra grauitatis
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              G, H, K, eſſe in linea NM. </s>
              <s>Iungantur enim rectæ GH,
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              H
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              , GK, BNP; & per punctum P, recta PL, ipſi MN,
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              parallela, & iungatur LH. </s>
              <s>Quoniam igitur rectæ BP, LH,
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              iungunt duas parallelas LP, BH; erunt quatuor rectæ BH,
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              LP, BP, LH, in eodem plano. </s>
              <s>Et
                <expan abbr="quoniã">quoniam</expan>
              planum quadran
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              guli PH, ſecat planum trianguli ABC, à communi autem
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              ſectione BP, ſurgunt
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              duæ parallelæ PL, MN;
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              quarum PL, eſt in pla­
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              no quadranguli PH,
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              erit etiam MN, in eo­
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              dem plano quadranguli
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              PH: & ſecabit LH. ſe­
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              cet in puncto O: qùare
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              vt LO, ad OH, ita erit
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              PN, ad NB, propter
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              parallelas: ſed PN, eſt
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              dimidia ipſius NB; er­
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              go & LO, eſt dimidia ip
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              ſius OH. </s>
              <s>Eadem ratio­
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              ne, quoniam AP, æqua­
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                <figure id="id.043.01.067.1.jpg" xlink:href="043/01/067/1.jpg" number="43"/>
                <lb/>
              lis eſt PC, erit & GL, æqualis LK. </s>
              <s>Duarum igitur
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              magnitudinum G, K, ſimul centrum grauitatis erit L: ſed
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              reliquæ magnitudinis, quæ ad H, eſt centrum grauitatis
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              H; & vt compoſitum ex duabus magnitudinibus G,
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              K, ad magnitudinem H, ita ex contraria parte eſt HO,
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              ad OL; Trium igitur magnitudinum G, H, K, ſimul cen­
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              trum grauitatis erit O, & in linea MN. </s>
              <s>Quod demon­
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              ſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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