Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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        <div xml:id="echoid-div302" type="section" level="1" n="100">
          <pb o="77" file="0115" n="115" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div306" type="section" level="1" n="101">
          <head xml:id="echoid-head141" xml:space="preserve">PROPOSITIO LXXII.</head>
          <p>
            <s xml:id="echoid-s3228" xml:space="preserve">SI eductæ fuerint ex D duæ
              <lb/>
              <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="97">
                <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01"/>
              </figure>
            breuiſecantes D C, D B,
              <lb/>
            quorum ſegmenta G C, B K
              <lb/>
            ſint breuiſſima, & </s>
            <s xml:id="echoid-s3229" xml:space="preserve">D B propin-
              <lb/>
            quior ſit vertici ſectionis; </s>
            <s xml:id="echoid-s3230" xml:space="preserve">Di-
              <lb/>
            co, quod D B maximus eſt ra-
              <lb/>
            morum egredientium ad ſectio-
              <lb/>
              <note position="left" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">a</note>
            nem A B C, & </s>
            <s xml:id="echoid-s3231" xml:space="preserve">minimus eorũ
              <lb/>
            D C, & </s>
            <s xml:id="echoid-s3232" xml:space="preserve">ramorum egredientiũ
              <lb/>
            ad ſectionem A C, qui D B
              <lb/>
            propinquiores maiores ſunt
              <lb/>
            remotioribus, & </s>
            <s xml:id="echoid-s3233" xml:space="preserve">propinquiores
              <lb/>
            D C (ex ramis egredientibus ad ſectionem in ea parte) mino-
              <lb/>
            res ſunt remotioribus.</s>
            <s xml:id="echoid-s3234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3235" xml:space="preserve">Sit F Trutina, & </s>
            <s xml:id="echoid-s3236" xml:space="preserve">quia iam ducti ſunt ex D duo breuiſecantes, ideo
              <lb/>
            E A excedit dimidium erecti, & </s>
            <s xml:id="echoid-s3237" xml:space="preserve">D E minor eſt, quàm F (51. </s>
            <s xml:id="echoid-s3238" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3239" xml:space="preserve">ex 5.)
              <lb/>
            </s>
            <s xml:id="echoid-s3240" xml:space="preserve">his poſitis, vtique lineæ breuiſſimæ egredientes ab extremitatibus ramo-
              <lb/>
            rum qui ſunt in ſectione B C abſcindunt ab axi EA minores lineas, quàm
              <lb/>
            abſcindunt rami (51. </s>
            <s xml:id="echoid-s3241" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3242" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3243" xml:space="preserve">& </s>
            <s xml:id="echoid-s3244" xml:space="preserve">qui ducuntur ab extremitatibus egre-
              <lb/>
            dientium ad reliquas ſectiones abſcindunt lineas maiores. </s>
            <s xml:id="echoid-s3245" xml:space="preserve">Educamus ita-
              <lb/>
            que ramos D H, D I ad ſectionem B C, & </s>
            <s xml:id="echoid-s3246" xml:space="preserve">ducamus B L, L H M, & </s>
            <s xml:id="echoid-s3247" xml:space="preserve">I
              <lb/>
            M tangentes ſectionem in punctis B, H, I; </s>
            <s xml:id="echoid-s3248" xml:space="preserve">quia B K eſt breuiſsima erit
              <lb/>
              <note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            I. </s>
            <s xml:id="echoid-s3249" xml:space="preserve">B D angulus rectus, & </s>
            <s xml:id="echoid-s3250" xml:space="preserve">quia breuiſſima egrediens ex H abſcindit cum
              <lb/>
            A ab axi E A lineam minorem, quàm ſecat D H erit L H D obtuſus, & </s>
            <s xml:id="echoid-s3251" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0115-03" xlink:href="note-0115-03a" xml:space="preserve">Ex 29. 30.
                <lb/>
              huius.</note>
            iungamus D L; </s>
            <s xml:id="echoid-s3252" xml:space="preserve">igitur duo quadrata D H, H L minora ſunt, quàm qua-
              <lb/>
            dratum D L, quod eſt æquale duobus quadratis L B, D B; </s>
            <s xml:id="echoid-s3253" xml:space="preserve">verum L B
              <lb/>
            minor eſt, quàm H L (68. </s>
            <s xml:id="echoid-s3254" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3255" xml:space="preserve">ergo D B maior eſt, quàm D H. </s>
            <s xml:id="echoid-s3256" xml:space="preserve">atq;
              <lb/>
            </s>
            <s xml:id="echoid-s3257" xml:space="preserve">
              <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">Ibidem.</note>
            ſic patet, quod D H maior ſit, quàm D I, quia D H M eſt acutus, & </s>
            <s xml:id="echoid-s3258" xml:space="preserve">D
              <lb/>
              <note position="left" xlink:label="note-0115-05" xlink:href="note-0115-05a" xml:space="preserve">b</note>
            I M obtuſus: </s>
            <s xml:id="echoid-s3259" xml:space="preserve">& </s>
            <s xml:id="echoid-s3260" xml:space="preserve">D I maior ſit, quàm D C. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Quare B D maximus eſt ra-
              <lb/>
            morum egredientium ad B C, & </s>
            <s xml:id="echoid-s3262" xml:space="preserve">iam demonſtratum eſt, quod ſit maxi-
              <lb/>
              <note position="left" xlink:label="note-0115-06" xlink:href="note-0115-06a" xml:space="preserve">c</note>
            mus ramorum egredientium ad B A (64. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">65. </s>
            <s xml:id="echoid-s3264" xml:space="preserve">ex 5.)</s>
            <s xml:id="echoid-s3265" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3266" xml:space="preserve">Ponamus poſtea N extra ſectionem B C, & </s>
            <s xml:id="echoid-s3267" xml:space="preserve">iungamus D N, itaque,
              <lb/>
            linea breuiſſima egrediens ex N abſcindit ab axi E A maiorem lineam,
              <lb/>
              <note position="right" xlink:label="note-0115-07" xlink:href="note-0115-07a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
              <note position="left" xlink:label="note-0115-08" xlink:href="note-0115-08a" xml:space="preserve">d</note>
            quàm ſecat D N; </s>
            <s xml:id="echoid-s3268" xml:space="preserve">ergo tangens in N continet cum D N angulum acu-
              <lb/>
              <note position="right" xlink:label="note-0115-09" xlink:href="note-0115-09a" xml:space="preserve">Ex 29. 30.
                <lb/>
              huius.</note>
            tum: </s>
            <s xml:id="echoid-s3269" xml:space="preserve">poſtea oſtendetur, quemadmodum hic dictum eſt, quod D C mi-
              <lb/>
            nimus ſit reliquorum ramorum egredientium ad reliquas ſectiones, & </s>
            <s xml:id="echoid-s3270" xml:space="preserve">ſit
              <lb/>
            minimus ramorum egredientium ad A C, quare manifeſtum eſt, quod
              <lb/>
            D B ſit maximus ramorum, & </s>
            <s xml:id="echoid-s3271" xml:space="preserve">D C minimus, & </s>
            <s xml:id="echoid-s3272" xml:space="preserve">quod maioribus pro-
              <lb/>
            pinquiores ſunt maiores remotioribus, & </s>
            <s xml:id="echoid-s3273" xml:space="preserve">minoribus propinquiores, mi-
              <lb/>
            nores ſunt remotioribus, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3274" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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