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-div346" type="section" level="1" n="112">
          <pb o="89" file="0127" n="127" rhead="Conicor. Lib. V."/>
          <p>
            <s xml:id="echoid-s3659" xml:space="preserve">Erigamus itaque ſuper D perpendicularem D B occurrentem E G in,
              <lb/>
              <note position="left" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">b</note>
            L; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">ergo eſt dimidium recti, & </s>
            <s xml:id="echoid-s3661" xml:space="preserve">E non eſt indirectum, quia non egredi-
              <lb/>
            tur ex E, niſi vnicus breuiſecans; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">inſuper lineæ breuiſſimæ egredien-
              <lb/>
              <note position="left" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">c</note>
            tes ab extremitatibus reliquorum ramorum abſcindunt ab axi A C cum
              <lb/>
            C, lineam maiorem, quàm ſecant rami illi. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">(51. </s>
            <s xml:id="echoid-s3664" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3666" xml:space="preserve">His po-
              <lb/>
            ſitis manifeſtum eſt, quod E C F eſt acutus; </s>
            <s xml:id="echoid-s3667" xml:space="preserve">atque E C minima eſt linea-
              <lb/>
            rum egredientium ex E ad quadrantem E B, & </s>
            <s xml:id="echoid-s3668" xml:space="preserve">illi propinquior, minor
              <lb/>
            eſt remotiore; </s>
            <s xml:id="echoid-s3669" xml:space="preserve">modo demonſtrandum eſt, quod E K maior quoque eſt,
              <lb/>
              <note position="left" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">d</note>
            quàm E B, producamus itaque B M, M K tangentes, ergo M B E eſt
              <lb/>
            obtuſus, & </s>
            <s xml:id="echoid-s3670" xml:space="preserve">M K E acutus (29. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3672" xml:space="preserve">quia breuiſſima egrediens ex K
              <lb/>
            abſcindit cum A minorem lineam, quàm ſecat K E (57. </s>
            <s xml:id="echoid-s3673" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3674" xml:space="preserve">eo quod
              <lb/>
            K cadit inter duas lineas L B, L G; </s>
            <s xml:id="echoid-s3675" xml:space="preserve">& </s>
            <s xml:id="echoid-s3676" xml:space="preserve">iungamus M E; </s>
            <s xml:id="echoid-s3677" xml:space="preserve">ergo duo qua-
              <lb/>
            drata M B, B E minora ſunt, quàm quadratum M E, quare minora,
              <lb/>
            erunt duobus quadratis M K, K E, & </s>
            <s xml:id="echoid-s3678" xml:space="preserve">M B maior eſt, quàm M K, ergo
              <lb/>
              <note position="right" xlink:label="note-0127-04" xlink:href="note-0127-04a" xml:space="preserve">70. huius.</note>
            B E minor eſt, quàm K E; </s>
            <s xml:id="echoid-s3679" xml:space="preserve">& </s>
            <s xml:id="echoid-s3680" xml:space="preserve">ſic demonſtratur, quod G E maior ſit,
              <lb/>
            quàm K E; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Nam ſi producamus G N tangentem, tunc N G E eſt re-
              <lb/>
            ctus, quia G I eſt breuiſſima, & </s>
            <s xml:id="echoid-s3682" xml:space="preserve">N K E obtuſus; </s>
            <s xml:id="echoid-s3683" xml:space="preserve">ergo G E maior eſt,
              <lb/>
              <note position="right" xlink:label="note-0127-05" xlink:href="note-0127-05a" xml:space="preserve">30. huius.</note>
            quàm E K; </s>
            <s xml:id="echoid-s3684" xml:space="preserve">itaque G E maximus eſt ramorum egredientium ex E ad ſe-
              <lb/>
            ctionem G C, & </s>
            <s xml:id="echoid-s3685" xml:space="preserve">minimus eorum E C, atque propinquior E C minor
              <lb/>
            eſt remotiore.</s>
            <s xml:id="echoid-s3686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3687" xml:space="preserve">Educamus ex E ad ſectionem A G, E A, E O, oſtendetur quod
              <lb/>
              <note position="left" xlink:label="note-0127-06" xlink:href="note-0127-06a" xml:space="preserve">e</note>
            E G maior ſit, quàm E O, & </s>
            <s xml:id="echoid-s3688" xml:space="preserve">E O, quàm E A. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">Erigamus
              <lb/>
            itaque ad A C perpendicularem A P; </s>
            <s xml:id="echoid-s3690" xml:space="preserve">ergo E A P eſt
              <lb/>
            obtuſus, & </s>
            <s xml:id="echoid-s3691" xml:space="preserve">producamus P O Q tangentem; </s>
            <s xml:id="echoid-s3692" xml:space="preserve">ergo
              <lb/>
            P O E eſt acutus, quia linea breuiſſima egre-
              <lb/>
              <note position="right" xlink:label="note-0127-07" xlink:href="note-0127-07a" xml:space="preserve">57. huius.</note>
            diens ex O ſecat cum A lineam maiorem;
              <lb/>
            </s>
            <s xml:id="echoid-s3693" xml:space="preserve">ergo E O maior eſt, quàm E A: </s>
            <s xml:id="echoid-s3694" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s3695" xml:space="preserve">
              <lb/>
            ſic patet, quod E G maior ſit,
              <lb/>
            quàm E O (29. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3697" xml:space="preserve">quia
              <lb/>
            Q G E eſt rectus, & </s>
            <s xml:id="echoid-s3698" xml:space="preserve">
              <lb/>
            Q O E obtuſus,
              <lb/>
            & </s>
            <s xml:id="echoid-s3699" xml:space="preserve">G Q
              <lb/>
            maior, quàm O Q, ergo E G maximus eſt ramorum
              <lb/>
            egredientium ex E ad ſectionem A B C, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">
              <lb/>
            minimus eorum E C, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">propinquiores
              <lb/>
            minimo, remotioribus minores ſunt,
              <lb/>
            & </s>
            <s xml:id="echoid-s3702" xml:space="preserve">propinquiores maximo, ma-
              <lb/>
            iores ſunt remotioribus; </s>
            <s xml:id="echoid-s3703" xml:space="preserve">
              <lb/>
            quod erat oſtenden-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s3704" xml:space="preserve"/>
          </p>
          <figure number="110">
            <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0127-01"/>
          </figure>
        </div>
      </text>
    </echo>
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