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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N11E17" type="main">
              <s id="N11E23">
                <pb xlink:href="077/01/058.jpg" pagenum="54"/>
                <arrow.to.target n="marg42"/>
              ſint æquales, erit G centrum grauitatis magnitudinis ex AF
                <lb/>
              compoſitæ. </s>
              <s id="N11E35">quia verò AB eſt ipſi EF æqualis, reliqua BG
                <lb/>
              ipſi GE æqualis exiſtet. </s>
              <s id="N11E39">& ſunt magnitudines BE ę〈que〉gra­
                <lb/>
              ues, erit idem G centrum grauitatis
                <expan abbr="magnitudinũ">magnitudinum</expan>
              BE. ſimili­
                <lb/>
              ter cùm ſit BC æqualis DE, relin〈que〉tur CG ipſi GD ęqua­
                <lb/>
              lis; magnitudinesquè CD ſunt ę〈que〉graues. </s>
              <s id="N11E45">ergo
                <expan abbr="pũctum">punctum</expan>
              G
                <expan abbr="cẽ">cem</expan>
                <lb/>
              trum eſt quo〈que〉 magnitudinum CD. Vnde ſequitur,
                <expan abbr="punctũ">punctum</expan>
                <lb/>
              G magnitudinis ex omnibus magnitudinibus ABCDEF
                <expan abbr="cõ-poſitæ">con­
                  <lb/>
                poſitæ</expan>
              centrum grauitatis exiſtere. </s>
            </p>
            <p id="N11E5D" type="margin">
              <s id="N11E5F">
                <margin.target id="marg42"/>
              4
                <emph type="italics"/>
              huius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N11E68" type="main">
              <s id="N11E6A">
                <arrow.to.target n="marg43"/>
              Hoc quo〈que〉 loco verba illa
                <emph type="italics"/>
              magnitudineſquè æqualem habuerint
                <lb/>
              grauitatem.
                <emph.end type="italics"/>
              Græcus codex ita mendosè legit.
                <foreign lang="grc">καὶ τὰ μέσα αὔτης ἴσον
                  <lb/>
                βάρος ἔχωντι</foreign>
              , quæ quidem verba hoc modo reſtitui poſſunt.
                <lb/>
                <foreign lang="grc">καὶ τὰ μεγέθεα ἴσον βάρος ἔχωντι. </foreign>
              </s>
            </p>
            <p id="N11E82" type="margin">
              <s id="N11E84">
                <margin.target id="marg43"/>
              *</s>
            </p>
            <p id="N11E88" type="main">
              <s id="N11E8A">In præcedenti propoſitione oſtendit Archimedes, quomo
                <lb/>
              do ſe habet centrum grauitatis magnitudinis ex duabus ma­
                <lb/>
              gnitudinibus ęqualibus compoſitæ. </s>
              <s id="N11E90">In hac autem
                <expan abbr="demõſtrat">demonſtrat</expan>
              ,
                <lb/>
              vbi ſimiliter grauitatis centrum reperitur inter plures magni­
                <lb/>
              tudines æ〈que〉graues, & inter ſe ęqualiter diſtantes. </s>
              <s id="N11E9A">ex quibus
                <lb/>
              tandem colliget fundamentum ſæpiùs dictum. </s>
              <s id="N11E9E">nempè ſi ma­
                <lb/>
              gnitudines ę〈que〉ponderare debent; ita ſe habebit magnitudi­
                <lb/>
              num grauitas ad grauitatem, ut ſe habent diſtantiæ permuta
                <lb/>
              tim, ex quibus ſuſpenduntur. </s>
              <s id="N11EA6">& hoc demonſtrat Archimedes
                <lb/>
              in duabus ſe〈que〉ntibus propoſitionibus. </s>
              <s id="N11EAA">nam magnitudines,
                <lb/>
              vel ſunt commenſurabiles interſeſe, vel incommenſurabiles.
                <lb/>
              de commenſurabilibus aget in ſe〈que〉nti: de incommenſurabi
                <lb/>
              libus verò in ſeptima propoſitione. </s>
              <s id="N11EB2">& Archimedes duas
                <expan abbr="ſe〈quẽ〉-tes">ſe〈que〉n­
                  <lb/>
                tes</expan>
              propoſitiones ueluti coniunctas proponit. </s>
              <s id="N11EBA">Nam in ſexta
                <lb/>
              inquit
                <emph type="italics"/>
              Magnitudines commenſurabiles,
                <emph.end type="italics"/>
              &c. </s>
              <s id="N11EC4">in ſeptima uerò in­
                <lb/>
              quit,
                <emph type="italics"/>
              Si autem magnitudines ſuerint incommenſurabiles,
                <emph.end type="italics"/>
              quaſi vna
                <expan abbr="tã">tam</expan>
                <lb/>
              tùm ſit propoſitio in duas partes diuiſa. </s>
              <s id="N11ED6">ita ut ne〈que〉 numeris
                <lb/>
              eſſent diſtinguende, ſed pro vna tantùm propoſitione
                <expan abbr="ſummẽ-dæ">ſummen
                  <lb/>
                dæ</expan>
              , obſe〈que〉ntis autem demonſtrationis faciliorem
                <expan abbr="intelligẽ-tiam">intelligen
                  <lb/>
                tiam</expan>
              hęc priùs præmittimus. </s>
            </p>
            <p id="N11EE7" type="head">
              <s id="N11EE9">LEMMA.</s>
            </p>
            <p id="N11EEB" type="main">
              <s id="N11EED">Si duę fuerint magnitudines in æquales, quarum maior ſit
                <lb/>
              alterius dupla, tertia verò quędam magnitudo minorem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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