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-div275" type="section" level="1" n="91">
          <pb o="70" file="0108" n="108" rhead="Apollonij Pergæi"/>
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        <div xml:id="echoid-div278" type="section" level="1" n="92">
          <head xml:id="echoid-head126" xml:space="preserve">SECTIO VNDECIMA</head>
          <head xml:id="echoid-head127" xml:space="preserve">Continens Propoſ. LXVIII. LXIX. LXX.
            <lb/>
          & LXXI. Apollonij.</head>
          <head xml:id="echoid-head128" xml:space="preserve">PROPOSITIO LXVIII. LXIX.</head>
          <p>
            <s xml:id="echoid-s2999" xml:space="preserve">SI occurrant duæ tangentes alicui ſectioni A B C, vt ſunt A
              <lb/>
              <note position="right" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">a</note>
            F, E F, vtique quod abſcinditur ex tangente proximiori
              <lb/>
            vertici ſectionis, qui eſt B minus eſt ſegmento abſciſſo ex alia,
              <lb/>
            nempe E F minor eſt, quàm A F.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3001" xml:space="preserve">Iuncta enim A E,
              <lb/>
              <note position="right" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">b</note>
              <figure xlink:label="fig-0108-01" xlink:href="fig-0108-01a" number="88">
                <image file="0108-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0108-01"/>
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            & </s>
            <s xml:id="echoid-s3002" xml:space="preserve">in parabola ex F
              <lb/>
            producta linea F I
              <lb/>
            parallela axi B D e-
              <lb/>
            rit illa diameter, bi-
              <lb/>
            fariam ſecans E A in
              <lb/>
            G (34. </s>
            <s xml:id="echoid-s3003" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s3004" xml:space="preserve">Simi-
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              <note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">30. lib. 2.</note>
            liter ex centro H pro-
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            ducamus H F G, quæ
              <lb/>
            eſt quoque diameter
              <lb/>
            (34. </s>
            <s xml:id="echoid-s3005" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s3006" xml:space="preserve">bifariam
              <lb/>
              <note position="left" xlink:label="note-0108-04" xlink:href="note-0108-04a" xml:space="preserve">Ibidem.</note>
            ſecans E A in G, & </s>
            <s xml:id="echoid-s3007" xml:space="preserve">
              <lb/>
            ducamus A D in pa-
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            rabola, & </s>
            <s xml:id="echoid-s3008" xml:space="preserve">hyperbola perpendicularem ſuper axim D B. </s>
            <s xml:id="echoid-s3009" xml:space="preserve">Ergo angulus
              <lb/>
            A I G in parabola eſt rectus, & </s>
            <s xml:id="echoid-s3010" xml:space="preserve">in hyperbola obtuſus; </s>
            <s xml:id="echoid-s3011" xml:space="preserve">ergo F G A erit
              <lb/>
            obtuſus in illis omnibus; </s>
            <s xml:id="echoid-s3012" xml:space="preserve">quare maior eſt, quàm angulus F G E, & </s>
            <s xml:id="echoid-s3013" xml:space="preserve">A
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            G æqualis eſt ipſi G E, & </s>
            <s xml:id="echoid-s3014" xml:space="preserve">F G communis; </s>
            <s xml:id="echoid-s3015" xml:space="preserve">igitur E F minor eſt, quàm
              <lb/>
            F A.</s>
            <s xml:id="echoid-s3016" xml:space="preserve"/>
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          <figure number="89">
            <image file="0108-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0108-02"/>
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