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

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N124E9" type="main">
              <s id="N1250F">
                <pb xlink:href="077/01/069.jpg" pagenum="65"/>
              rectælineę LK. Et non dixit, quia VC ſitipſi CX ęqualis.
                <lb/>
              Quare codicem græcum ita reſtituendum cenſeo.
                <foreign lang="grc">τὰκέντ<10>κ τῶν
                  <lb/>
                τοῦ βὰ<10>εος μεγεθῶν</foreign>
              , vt vertimus. </s>
            </p>
            <p id="N12525" type="margin">
              <s id="N12527">
                <margin.target id="marg53"/>
              *</s>
            </p>
            <p id="N1252B" type="main">
              <s id="N1252D">Ob ſe〈que〉ntis verò demonſtrationis cognitionem, hoc pro
                <lb/>
              blema priùs oſtendemus. </s>
            </p>
            <p id="N12531" type="head">
              <s id="N12533">PROBLEMA.</s>
            </p>
            <p id="N12535" type="main">
              <s id="N12537">Duarum expoſitarum magnitudinum incommenſurabi­
                <lb/>
              lium altera vtcum〈que〉 ſecetur; magnitudinem tota ſecta ma­
                <lb/>
              gnitudine minorem, & altero ſegmentomaiorem, alteri ve­
                <lb/>
              rò expoſitæ magnitudini commenſurabilem inuenire. </s>
            </p>
            <p id="N1253F" type="main">
              <s id="N12541">Sint duæ magnitudi­
                <lb/>
              nes incommenſurabiles
                <lb/>
                <arrow.to.target n="fig29"/>
                <lb/>
              AE BC. ſeceturquè ipſa­
                <lb/>
              rum altera, putà BC, vt­
                <lb/>
              cum〈que〉 in D. oportet
                <lb/>
              magnitudinem inuenire
                <lb/>
              minorem quidem BC,
                <lb/>
              maiorem verò BD, quæ ſitipſi AE commenſurabilis. </s>
              <s id="N12556">Au­
                <lb/>
              feratur ab AE pars dimidia, rurſus dimidiæ partis ipſius AE
                <lb/>
              dimidia auferatur; & eius, quæ remanet, adhuc dimidia; idquè
                <lb/>
              ſemper fiat, donec relinquatur magnitudo minor, quàm DE.
                <lb/>
              quod quidem perſpicuum eſt poſſe fieri ex prima decimi Eu­
                <lb/>
              clidis propoſitione. </s>
              <s id="N12562">ſitita〈que〉 AF, quæ minor exiſtat, quàm
                <lb/>
              DC. quippe quę AF, cùm ſit abla ta ex AE ſemper per dimi
                <lb/>
              diam partem, metietur vti〈que〉 AF ipſam AE. Deinde mul­
                <lb/>
              tiplicetur AF ſuper BD, tum demum multiplicatio vltima,
                <lb/>
              vel in puncto D cadet, vel minus. </s>
              <s id="N1256C">ſi cadet; ſeceturex DE
                <lb/>
              magnitudo DG ęqualis AF. quod quidem fiet,
                <expan abbr="quoniã">quoniam</expan>
              AF
                <lb/>
              minor eſt DC. Quoniam igitur AF metitur BD, & DG;
                <lb/>
              metietur AF totam BG. Sed & ipſam AE metitur; etgo
                <lb/>
              AF ipſarum BG AE communis exiſtit menſura, ac propte­
                <lb/>
              rea BG ipſi AE commenſurabilis exiſtir; quæ quidem BG
                <lb/>
              minor eſt BC, maior verò BD. Si verò
                <arrow.to.target n="marg54"/>
              multi­
                <lb/>
              plicatio ipſius AF ſuper BD non cadet in D. ſed in H,
                <lb/>
              erit vti〈que〉 HD minor AF. nam ſi HD ipſi AF eſſet ęqualis, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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