DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N11B6E" type="main">
              <s id="N11BE0">
                <pb xlink:href="077/01/053.jpg" pagenum="49"/>
              eſſe poteſt minor magnitudo, quę maiore magnitudine alte
                <lb/>
              rius nature grauior exiſtat; proindé Archimedes in ſuperiori­
                <lb/>
              bus rectè grauia nuncupauit; optimèquè in his magnitudines
                <lb/>
              vocat. </s>
              <s id="N11BF8">At verò aduertendum eſt, quòd quamuis Archimedes
                <lb/>
              in his magnitudines nominet, non propterea exiſtimandum
                <lb/>
              eſt, eum intelligere magnitudines tantùm; ſed magnitudines
                <lb/>
              grauitate pręditas, ita ut in ipſis omnino grauitatem reſpiciat.
                <lb/>
              Etenim pluribus modis intelligere poſſumus magnitudines,
                <lb/>
              vel enim ut ſint inter ſe eiuſdem ſpeciei, vel diuerſæ; nec
                <expan abbr="nõ">non</expan>
                <lb/>
              inſuper homogeneæ, vel heterogeneæ. </s>
              <s id="N11C0A">vt in hac propoſitione
                <lb/>
                <expan abbr="quãdo">quando</expan>
              Archimedes
                <expan abbr="pponit">proponit</expan>
              duas magnitudines ęquales,
                <expan abbr="tũc">tuc</expan>
                <lb/>
              intelligere poſſumus eas eſſe eiuſdem ſpeciei, & homogeneas;
                <lb/>
              quæ, cùm ſint æquales, erit & grauitas vnius grauitati alterius
                <lb/>
              æqualis. </s>
              <s id="N11C17">ſi verò conſideremus eas eſſe diuerſæ ſpeciei, & e­
                <lb/>
              tiam heterogeneas; tunc quando Archimedes proponit has
                <lb/>
              magnitudines æquales; intelligendum eſt, eas eſſe æquales in
                <lb/>
              grauitate; quæ quidem efficit, vt demonſtratio, quod propo­
                <lb/>
              ſitum eſt, concludat. </s>
              <s id="N11C21">vt ex eius demonſtratione patet. </s>
              <s id="N11C23">Et his
                <lb/>
              quo〈que〉 modis intelligere poſſumus magnitudines in ſe〈que〉n
                <lb/>
              tibus vſ〈que〉 ad nonam propoſitionem in quibus ſcilicet intel
                <lb/>
              ligere poſſumus magnitudines eſſe non ſolùm eiuſdem ſpe­
                <lb/>
              ciei, vel diuerſæ, verùm etiam & homogeneas. </s>
              <s id="N11C2D">& heteroge­
                <lb/>
              neas. </s>
              <s id="N11C31">ut poſt ſeptimam clariùs oſtendemus. </s>
              <s id="N11C33">Verùm de­
                <lb/>
              monſtrationes clariores redduntur, ſi intelligamus magnitu­
                <lb/>
              dines eſſe eiuſdem ſpeciei, & homogeneas, in quibus graui­
                <lb/>
              tas magnitudini reſpondet, vt ſi ipſarum altera fuerit alte­
                <lb/>
              rius dupla, & grauitas vnius grauitatis alterius dupla exiſtat.
                <lb/>
              Quòd ſi magnitudo fuerit alterius tripla, vel quadrupla, &c.
                <lb/>
              erit & grauitas grauitatis tripla, vel quadrupla, & ſic dein­
                <lb/>
              ceps. </s>
              <s id="N11C43">deinde ſi magnitudo bifariam diuiſa fuerit, & ipſius gra
                <lb/>
              uitas in duas ęquas partes ſit quo〈que〉 diuiſa. </s>
              <s id="N11C47">quòd ſi magnitu­
                <lb/>
              do in plures diuidatur partes, & grauitas quo〈que〉 in totidem
                <lb/>
              eiuſdem proportionis diuiſa proueniat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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