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-div260" type="section" level="1" n="86">
          <pb o="67" file="0105" n="105" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div263" type="section" level="1" n="87">
          <head xml:id="echoid-head120" xml:space="preserve">SECTIO DECIMA</head>
          <head xml:id="echoid-head121" xml:space="preserve">Continens Propof. XXXXIV. XXXXV.
            <lb/>
          Apollonij.</head>
          <p>
            <s xml:id="echoid-s2890" xml:space="preserve">SI ex axe recto ellipſis ſumatur menſura ab origine, quæ ad
              <lb/>
              <note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">a</note>
            ſemiaxim rectum non habeat minorem proportionem, quàm
              <lb/>
            habet figura ſuæ tranſuerſæ, tunc quicumque ramus ſecans, ab
              <lb/>
            illa origine ad fectionem ductus, abſcindit ex axe tranſuerſo ad
              <lb/>
            verticem ſectionis lineam minorem ea, quàm abſcindit linea
              <lb/>
            breuiſsima egrediens ab eius termino in ſectione poſito ad tran-
              <lb/>
            ſuerſum axim; </s>
            <s xml:id="echoid-s2891" xml:space="preserve">ſi vero fuerit proportio ad ſemirectum minor,
              <lb/>
            tunc ramorum ſecantium vnus eſt breuiſecans; </s>
            <s xml:id="echoid-s2892" xml:space="preserve">reliqui vero, qui
              <lb/>
            ſequuntur extremum tranſuerſæ habent proprietates ſuperius ex-
              <lb/>
            poſitas, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">qui ſequuntur extremitatem recti, ſecant ex tranſuer-
              <lb/>
            ſa lineam maiorem ea, quàm abſcindit breuiſsima egrediens ab
              <lb/>
            eius termino.</s>
            <s xml:id="echoid-s2894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div265" type="section" level="1" n="88">
          <head xml:id="echoid-head122" xml:space="preserve">PROPOSITIO XXXXIV.</head>
          <p>
            <s xml:id="echoid-s2895" xml:space="preserve">Sit A D dimidium axis recti, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">minoris ſectionis ellipticæ
              <lb/>
              <note position="left" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">b</note>
            A B C, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">meuſura A E, quæ ſit maior, quàm A D, & </s>
            <s xml:id="echoid-s2898" xml:space="preserve">pro-
              <lb/>
            portio illius ad iſtam non ſit minor proportione figuræ ſectionis;
              <lb/>
            </s>
            <s xml:id="echoid-s2899" xml:space="preserve">Dico, quod linea breuiſsima egrediens ab extremitate cuiuſcum-
              <lb/>
            que rami ſecantis educti ex E ad ſectionem A B C, ſecat ex
              <lb/>
            tranuerſa B C cum vertice B, vel C lineam maiorem ea, quàm
              <lb/>
            abſcindit ille ramus.</s>
            <s xml:id="echoid-s2900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2901" xml:space="preserve">Ponatur ramus E F, & </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ducamus ex F ad vtrum-
              <lb/>
              <figure xlink:label="fig-0105-01" xlink:href="fig-0105-01a" number="85">
                <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0105-01"/>
              </figure>
              <note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">c</note>
            que axim duas perpendiculares F H, F I. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Et quia
              <lb/>
            proportio E A ad A D non eſt minor proportio-
              <lb/>
            ne ſiguræ, ſed minor eſt, quàm E H ad H D, nem-
              <lb/>
            pe E F ad F G, ſeu D I ad I G, erit proportio ſigu-
              <lb/>
            ræ minor, quàm D I ad I G, & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ponamus D I ad
              <lb/>
            I K, vt eſt proportio figuræ, & </s>
            <s xml:id="echoid-s2905" xml:space="preserve">iungamus F K;
              <lb/>
            </s>
            <s xml:id="echoid-s2906" xml:space="preserve">erit ergo F K linea breuiſſima (10. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2908" xml:space="preserve">& </s>
            <s xml:id="echoid-s2909" xml:space="preserve">iam
              <lb/>
              <note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">10.
                <lb/>
              huius.</note>
            ſecat K B maiorem, quàm B G, & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">G F non erit
              <lb/>
            breuiſſima; </s>
            <s xml:id="echoid-s2911" xml:space="preserve">& </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc erat propoſitum.</s>
            <s xml:id="echoid-s2913" xml:space="preserve"/>
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