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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N1196C" type="main">
              <s id="N11AB0">
                <pb xlink:href="077/01/051.jpg" pagenum="47"/>
              tur, ſi appendantur pondera AB ex C, æ〈que〉ponderare. </s>
              <s id="N11AB6">&
                <lb/>
              è conuerſo, ſi AB pondera ex C æ〈que〉ponderant, ergo C
                <lb/>
              centrum grauitatis exiſtit. </s>
              <s id="N11ABC">ex quibus ſequitur lineam AB,
                <expan abbr="põ">pom</expan>
                <lb/>
              deraquè manere eo modo, quo reperiuntur. </s>
              <s id="N11AC4">vt in noſtro me­
                <lb/>
              chanicorum libro in codem tractatu de libra demonſtraui­
                <lb/>
              mus, & aduerſus illos, qui aliter ſentiunt, abundè
                <arrow.to.target n="marg36"/>
              diſpu­
                <lb/>
              tauimus. </s>
            </p>
            <p id="N11AD0" type="margin">
              <s id="N11AD2">
                <margin.target id="marg36"/>
                <emph type="italics"/>
              poſt quar­
                <lb/>
              tam propo
                <lb/>
              ſitionem.
                <emph.end type="italics"/>
                <lb/>
              *</s>
            </p>
            <figure id="id.077.01.051.1.jpg" xlink:href="077/01/051/1.jpg" number="27"/>
            <figure id="id.077.01.051.2.jpg" xlink:href="077/01/051/2.jpg" number="28"/>
            <figure id="id.077.01.051.3.jpg" xlink:href="077/01/051/3.jpg" number="29"/>
            <p id="N11AEC" type="main">
              <s id="N11AEE">In demonſtratione autem huius quartæ propoſitionis in­
                <lb/>
              quit Archimedes.
                <emph type="italics"/>
              Quòd autem ſit in linea AB, præostenſum eſt.
                <emph.end type="italics"/>
              qua
                <lb/>
              ſi dicat Archimedes, ſe priùs oſtendiſſe centrum grauitatis ma
                <lb/>
              gnitudinis ex AB compoſitæ eſſe in linea AB; quod tamen
                <lb/>
              in ijs, quæ dicta ſunt, non videtur expreſſum. </s>
              <s id="N11AFE">virtute tamen ſi
                <lb/>
              conſideremus ea, quę in prima, tertiaquè propoſitione dicta
                <lb/>
              ſunt, facilè ex his concludi poteſt, centrum grauitatis magni­
                <lb/>
              tudinis ex duabus magnitudinibus compoſitæ eſſe in recta li
                <lb/>
              nea, quæ ipſarum centra grauitatis coniungit. </s>
              <s id="N11B08">Quare memi­
                <lb/>
              niſſe oportet eorum, quę a nobis in expoſitione primi poſtu
                <lb/>
              lati huius dicta fuere, nempè Archimedem ſupponere, diſtan­
                <lb/>
              tias eſſe in vna, eademquè recta linea conſtitutas. </s>
              <s id="N11B10">ideoquè in
                <lb/>
              prima propoſitio nec inquit, Grauia, quę ex
                <expan abbr="diſtãtijs">diſtantijs</expan>
              ęquali
                <lb/>
              bus
                <expan abbr="æ〈que〉põderãt">æ〈que〉ponderant</expan>
              , æqualia eſſe inter ſe; Archimedes què
                <expan abbr="demõ">demom</expan>
                <lb/>
              ſtrat, quòd quando æ〈que〉ponderant, ſunt æqualia: ex dictis
                <lb/>
              ſequitur, ſi æ〈que〉ponderant, ergo centrum grauitatis magni­
                <lb/>
              tudinis ex ipſis compoſitę erit in eo puncto, vbi æ〈que〉ponde­
                <lb/>
              rant; hoc eſt in medio diſtantiarum, lineę ſcilicet, quę
                <expan abbr="grauiũ">grauium</expan>
                <lb/>
              centra grauitatis coniungit. </s>
              <s id="N11B30">quod idem eſt, ac ſi Archimedes
                <lb/>
              dixiſſet. </s>
              <s id="N11B34">Grauia, quę habent centrum grauitatis in medio li­
                <lb/>
              neę, quę magnitudinum centra grauitatis coniungit, ęqua­
                <lb/>
              lia ſunt inter ſe. </s>
              <s id="N11B3A">cuius quidem hęc quarta propoſitio videtur
                <lb/>
              eſſe conuerſa. </s>
              <s id="N11B3E">quamuis Archimedes loco grauium nominet
                <lb/>
              magnitudines. </s>
              <s id="N11B42">Pręterea in tertia propoſitione, quoniam
                <expan abbr="oſtẽ-dit">oſten­
                  <lb/>
                dit</expan>
              Archimedes, inęqualia grauia ę〈que〉ponderare ex
                <expan abbr="diſtãtijs">diſtantijs</expan>
                <lb/>
              inęqualibus, ita vt grauius ſit in minori diſtantia, ſequitur er
                <lb/>
              go centrum grauitatis eſt in eo puncto, vbi æ〈que〉ponderant;
                <lb/>
              & idem eſt, ac ſi dixiſſet, in æqualium grauium centrum gra­
                <lb/>
              uitatis eſt in recta linea, quæ ipſorum centra grauitatis con­
                <lb/>
              iungit; ita vt ſit propinquius grauiori, remotius uerò leuiori. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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