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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <pb xlink:href="077/01/184.jpg" pagenum="180"/>
            <p id="N16F5D" type="main">
              <s id="N16F5F">
                <emph type="italics"/>
              Sint quatuor lineæ proportionales AB BC BD BE,
                <emph.end type="italics"/>
              ita vt AB
                <lb/>
              ad BC ſit, vt BC ad BD. & vt BC ad BD, ita ſit BD ad BE.
                <emph type="italics"/>
              &
                <lb/>
              quam proportionem habet BE ad E A, eandem habeat FG adtres quin
                <lb/>
              tas ipſius AD. quam autem proportionem habet linea æqualis duplæ i­
                <lb/>
              pſius AB, & quidruplæ ipſius BC, & ſextuplæ ipſi^{9} BD, & triplæ ipſi^{9}
                <lb/>
              BE, ad
                <expan abbr="lineã">lineam</expan>
                <expan abbr="æqualẽ">æqualem</expan>
                <expan abbr="quĩtuplæ">quintuplæ</expan>
              ipſi^{9} AB, ot decuplæ ipſi^{9} CB, & decuplæ
                <lb/>
              ipſi^{9} B D, & quintuplæ ipſius BE, eandem habeat GH ad AD. Oſteden
                <lb/>
              dum est FH duasquintas eſſe ipſius AB. Quoniam enim proportiona­
                <lb/>
              les ſunt AB BC BD BE, &
                <emph.end type="italics"/>
              ipſarum exceſſus
                <emph type="italics"/>
              AC CD DE in
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="fig81"/>
                <lb/>
                <arrow.to.target n="marg339"/>
                <emph type="italics"/>
              eadem erunt proportione. </s>
              <s id="N16F9B">&
                <emph.end type="italics"/>
              quoniam magnitudines AB BC BD
                <lb/>
              in continua ſunt proportione, & earum exceſſus AC CD DE
                <lb/>
              in eadem erunt proportione. </s>
              <s id="N16FA4">quia verò tres ſunt magnitudi­
                <lb/>
              nes proportionales AB BC BD; & alię ipſis numero çquales, &
                <lb/>
                <arrow.to.target n="marg340"/>
              in eadem proportione AC CD DE, erit in primis magnitu­
                <lb/>
              dinibus prima, & ſecunda ad tertiam, vt in ſecundis magni­
                <lb/>
              tudinibus prima, & ſecunda ad tertiam; hoc eſt
                <emph type="italics"/>
              vtra〈que〉 ſimul
                <lb/>
              AB BC ad BD eandem habebit proportionem, quam
                <emph.end type="italics"/>
              vtra〈que〉 ſimul
                <lb/>
                <arrow.to.target n="marg341"/>
              AC CD, hoc eſt
                <emph type="italics"/>
              AD ad DE; &
                <emph.end type="italics"/>
              ob eandem rationem cum
                <lb/>
                <arrow.to.target n="marg342"/>
              tres ſint proportionales magnitudines AC CD DE, aliçquè
                <lb/>
              eodem modo proportionales BC BD BE; crit vtra〈que〉 ſimul </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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