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-div252" type="section" level="1" n="84">
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            <s xml:id="echoid-s2825" xml:space="preserve">
              <pb o="65" file="0103" n="103" rhead="Conicor. Lib. V."/>
            eorundẽ differen-
              <lb/>
              <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a" number="82">
                <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/>
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            tias in ellipſi ſci-
              <lb/>
            licet C L ad C E
              <lb/>
            erit vt D F ad D
              <lb/>
            E, & </s>
            <s xml:id="echoid-s2826" xml:space="preserve">propterea
              <lb/>
            K F ad E I erit,
              <lb/>
            vt D F ad D E,
              <lb/>
              <note position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">Lem. 3.</note>
            & </s>
            <s xml:id="echoid-s2827" xml:space="preserve">cõparando ho-
              <lb/>
            mologorum ſum-
              <lb/>
            mas in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2828" xml:space="preserve">eorundem dif-
              <lb/>
            ferentias in elli-
              <lb/>
            pſi, K D ad D I
              <lb/>
            erit, vt D F ad D E, & </s>
            <s xml:id="echoid-s2829" xml:space="preserve">iterum comparando antecedentes ad differentias ter
              <lb/>
              <note position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Lem. 1.</note>
            minorum fiet D K ad K I, vt D F ad F E, ſeu vt latus tranſuer ſum ad rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s2830" xml:space="preserve">igitur B I eſt linea breuiſsima.</s>
            <s xml:id="echoid-s2831" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Ex 9. 10.
            <lb/>
          huius.</note>
          <p>
            <s xml:id="echoid-s2832" xml:space="preserve">Si autem componamus proportionem in hyperbola deinde abſcinda-
              <lb/>
              <note position="left" xlink:label="note-0103-04" xlink:href="note-0103-04a" xml:space="preserve">d</note>
            mus, & </s>
            <s xml:id="echoid-s2833" xml:space="preserve">reijciamus oppoſitum ab oppoſito in ellipſi, deinde inuertamus
              <lb/>
            fiet K D ad K I, vt D F ad F E, &</s>
            <s xml:id="echoid-s2834" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Sed textum mendoſum corrigi debere,
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            vt ſupra factum eſt conſtat ex præcedenti nota.</s>
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        <div xml:id="echoid-div257" type="section" level="1" n="85">
          <head xml:id="echoid-head118" xml:space="preserve">Notæ in Propoſit. LX.</head>
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            <s xml:id="echoid-s2837" xml:space="preserve">DEinde ſit perpendicularis ex C, &</s>
            <s xml:id="echoid-s2838" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2839" xml:space="preserve">Siex puncto C extra hyperbolen po-
              <lb/>
              <note position="left" xlink:label="note-0103-05" xlink:href="note-0103-05a" xml:space="preserve">a</note>
            ſito perpendicularis ad axim ducta ad centrum eius D pertingat, duci de-
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            bet pariter ex puncto C recta linea ad ſectionem, cuius portio inter axim D F,
              <lb/>
            & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">ſectionem A B ſit linea breuiſsima; </s>
            <s xml:id="echoid-s2841" xml:space="preserve">fiat C E ad E D, vt latus tranſuer ſum ad
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s2842" xml:space="preserve">ex E ducatur E B par allela axi, ſecans hyperbolen in B, & </s>
            <s xml:id="echoid-s2843" xml:space="preserve">ex B du-
              <lb/>
            catur B H perpendicularis ad axim, ſecans eum in H.</s>
            <s xml:id="echoid-s2844" xml:space="preserve"/>
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            <s xml:id="echoid-s2845" xml:space="preserve">Et quia C E ad E D, nempe C B ad B G,
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              <figure xlink:label="fig-0103-02" xlink:href="fig-0103-02a" number="83">
                <image file="0103-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-02"/>
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              <note position="left" xlink:label="note-0103-06" xlink:href="note-0103-06a" xml:space="preserve">b</note>
            &</s>
            <s xml:id="echoid-s2846" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2847" xml:space="preserve">Quia propter parallelas B E, F D eſt C E ad
              <lb/>
            E D, vt C B ad B G, & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">propter parallelas D C,
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            H B, eſt D H ad H G, vt C B ad B G, quare D H
              <lb/>
            ad H G erit, vt C E ad E D: </s>
            <s xml:id="echoid-s2849" xml:space="preserve">poſita autem fuit C
              <lb/>
            E ad E D, vt latus tranſuer ſum ad rectum; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">igi-
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            tur D H ex centro hyperboles ad H G eandem
              <lb/>
            proportionem habet, quàm latus tranſuerſum ad
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s2851" xml:space="preserve">propterea G B erit linea breuiſsima.</s>
            <s xml:id="echoid-s2852" xml:space="preserve"/>
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          <note position="right" xml:space="preserve">9. huius.</note>
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        <div xml:id="echoid-div260" type="section" level="1" n="86">
          <head xml:id="echoid-head119" xml:space="preserve">Notæ in Propoſit. LXI.</head>
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            <s xml:id="echoid-s2853" xml:space="preserve">SIt poſtea punctum C, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">perpendicularis C F, &</s>
            <s xml:id="echoid-s2855" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Si à puncto C extra
              <lb/>
              <note position="left" xlink:label="note-0103-08" xlink:href="note-0103-08a" xml:space="preserve">a</note>
            hyperbolen A B poſito, C F perpendicularis ad axim efficiat F A ſegmentũ
              <lb/>
            tranſuerſi axis maius ſemiſse eius D A, & </s>
            <s xml:id="echoid-s2857" xml:space="preserve">ponantur C E ad E F, atque D </s>
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