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-div80" type="section" level="1" n="47">
          <head xml:id="echoid-head73" xml:space="preserve">PROPOSITIO IX. & X.</head>
          <p>
            <s xml:id="echoid-s1247" xml:space="preserve">AT in hyper-
              <lb/>
              <note position="right" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">g</note>
              <figure xlink:label="fig-0056-01" xlink:href="fig-0056-01a" number="26">
                <image file="0056-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0056-01"/>
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            bola (10.)
              <lb/>
            </s>
            <s xml:id="echoid-s1248" xml:space="preserve">& </s>
            <s xml:id="echoid-s1249" xml:space="preserve">ellipſi educa-
              <lb/>
            mus rectas lineas,
              <lb/>
            G F quidem ſecã-
              <lb/>
            tem A D in a, & </s>
            <s xml:id="echoid-s1250" xml:space="preserve">
              <lb/>
            N H occurrẽtem
              <lb/>
            F G in S, & </s>
            <s xml:id="echoid-s1251" xml:space="preserve">I S
              <lb/>
            ſecantem C G in
              <lb/>
            T, pariterque M
              <lb/>
            Q ſecantem F G
              <lb/>
            in m, & </s>
            <s xml:id="echoid-s1252" xml:space="preserve">I T in X,
              <lb/>
            & </s>
            <s xml:id="echoid-s1253" xml:space="preserve">ex punctis m, S,
              <lb/>
            x educamus inter
              <lb/>
            N S, M X rectas
              <lb/>
            m y, X n, S Z pa-
              <lb/>
            rallelas ipſi C I. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">
              <lb/>
            Et quia C F ad C
              <lb/>
            G, nempe F H ad
              <lb/>
            H S poſita eſt, vt
              <lb/>
            F H ad H I erit H I æqualis H S; </s>
            <s xml:id="echoid-s1255" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">h</note>
              <figure xlink:label="fig-0056-02" xlink:href="fig-0056-02a" number="27">
                <image file="0056-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0056-02"/>
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            quadratum igitur I H eſt æquale
              <lb/>
            duplo trianguli I H S, & </s>
            <s xml:id="echoid-s1256" xml:space="preserve">quadra-
              <lb/>
            tum N H ęquale eſt duplo trape-
              <lb/>
            zij H G; </s>
            <s xml:id="echoid-s1257" xml:space="preserve">quare quadratum N I
              <lb/>
              <note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">Prop. I. h.</note>
            æquale eſt duplo trapezij I G;
              <lb/>
            </s>
            <s xml:id="echoid-s1258" xml:space="preserve">ſimiliter quadratum I Q ęquale eſt
              <lb/>
              <note position="right" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">i</note>
            duplo trianguli I Q X, & </s>
            <s xml:id="echoid-s1259" xml:space="preserve">quadra-
              <lb/>
            tum M Q eſt æquale duplo trape-
              <lb/>
            zij Q G; </s>
            <s xml:id="echoid-s1260" xml:space="preserve">itaque quadratum ex I M
              <lb/>
            æquale eſt duplo trapezij I G cum
              <lb/>
            duplo trianguli m S X, quod eſt æ-
              <lb/>
            quale plano m n: </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Et C F ad C G,
              <lb/>
            nempe proportio figuræ eſt, vt S Z,
              <lb/>
            nempe Z X ad Z m (& </s>
            <s xml:id="echoid-s1262" xml:space="preserve">hoc quidem
              <lb/>
            propter ſimilitudinem triangulorũ)
              <lb/>
            quare comparãdo priores ad ſum-
              <lb/>
              <note position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">Lem. 1. h.</note>
            mas terminorum in hyperbola, & </s>
            <s xml:id="echoid-s1263" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve">k</note>
            ad eorundem differentias in ellipſi
              <lb/>
            fiet X Z (quæ eſt æqualis ipſi X n)
              <lb/>
            ad X m, vt proportio inclinati, ſiue
              <lb/>
              <note position="right" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve">l</note>
            tranſuerſæ ad latitudinem figuræ
              <lb/>
            comparatæ; </s>
            <s xml:id="echoid-s1264" xml:space="preserve">igitur planum m n eſt exemplar, eſtque applicatum ad X n,
              <lb/>
              <note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">Def 9.</note>
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