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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          <pb o="124" file="0162" n="162" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s4915" xml:space="preserve">Erit angulus BHE ma-
              <lb/>
              <figure xlink:label="fig-0162-01" xlink:href="fig-0162-01a" number="155">
                <image file="0162-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0162-01"/>
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              <note position="right" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">b</note>
            ior, i
              <unsure/>
            quàm E B H, &</s>
            <s xml:id="echoid-s4916" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4917" xml:space="preserve">Eo
              <lb/>
            quod ramorum omnium ab
              <lb/>
            origine E ad ellipſim C B H
              <lb/>
            cadentium maximus ſuppo-
              <lb/>
            nitur E B; </s>
            <s xml:id="echoid-s4918" xml:space="preserve">ergo maior erit,
              <lb/>
            quàm E H, & </s>
            <s xml:id="echoid-s4919" xml:space="preserve">propterea
              <lb/>
            angulus E B H minori late-
              <lb/>
            ri oppoſitus minor erit angu-
              <lb/>
            lo E H B: </s>
            <s xml:id="echoid-s4920" xml:space="preserve">cadit vero recta
              <lb/>
            H F infra H E; </s>
            <s xml:id="echoid-s4921" xml:space="preserve">propterea
              <lb/>
            quod punctum F infra pun-
              <lb/>
            ctum E exiſtit; </s>
            <s xml:id="echoid-s4922" xml:space="preserve">igitur angu-
              <lb/>
            lus F H B maior eſt angulo
              <lb/>
            E H B; </s>
            <s xml:id="echoid-s4923" xml:space="preserve">& </s>
            <s xml:id="echoid-s4924" xml:space="preserve">ideo angulus F H B multo maior erit angulo F B H; </s>
            <s xml:id="echoid-s4925" xml:space="preserve">igitur ramus
              <lb/>
            F B, maiorem angulum ſubtendens, maior erit, quàm F H, &</s>
            <s xml:id="echoid-s4926" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4927" xml:space="preserve"/>
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        <div xml:id="echoid-div458" type="section" level="1" n="140">
          <head xml:id="echoid-head186" xml:space="preserve">SECTIO DECIMAOCTAVA</head>
          <head xml:id="echoid-head187" xml:space="preserve">Continens XXXII. XXXIII. XXXIV. XXXV.
            <lb/>
          XXXVI. XXXVII. XXXVIII. XXXIX.
            <lb/>
          XXXX. XXXXVII. XXXXVIII.</head>
          <head xml:id="echoid-head188" xml:space="preserve">Propoſit. Apollonij.</head>
          <head xml:id="echoid-head189" xml:space="preserve">PROPOSITIO XXXII.</head>
          <p>
            <s xml:id="echoid-s4928" xml:space="preserve">IN ellipſi A B C rami cuiuslibet
              <lb/>
              <figure xlink:label="fig-0162-02" xlink:href="fig-0162-02a" number="156">
                <image file="0162-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0162-02"/>
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              <note position="right" xlink:label="note-0162-02" xlink:href="note-0162-02a" xml:space="preserve">a</note>
            maximi G H vtrumque axim ſe-
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            cantis portio N H inter axim maio-
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            rem, & </s>
            <s xml:id="echoid-s4929" xml:space="preserve">ſectionem intercepta, eſt li-
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            nea breuiſsima.</s>
            <s xml:id="echoid-s4930" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4931" xml:space="preserve">Producatur rectus axis minor A D vl-
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            tra centrum D ad I, G, & </s>
            <s xml:id="echoid-s4932" xml:space="preserve">ex I, G ad ſe-
              <lb/>
            ctionem ducantur duo rami maximi G H,
              <lb/>
            I K, qui ſecent tranſuerſum B D in N,
              <lb/>
            M, & </s>
            <s xml:id="echoid-s4933" xml:space="preserve">ſit B E dimidium erecti axis B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s4934" xml:space="preserve">A F dimidium erecti axis A G; </s>
            <s xml:id="echoid-s4935" xml:space="preserve">& </s>
            <s xml:id="echoid-s4936" xml:space="preserve">edu-
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            cantur perpendiculares ad axes H O, H
              <lb/>
            P, K Q, K R. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">Dico, N H breuiſsimum
              <lb/>
            eſſe ramorum egredientium ex H. </s>
            <s xml:id="echoid-s4938" xml:space="preserve">Quia
              <lb/>
            G H eſt linea maxima, erit D A ad A F,
              <lb/>
            nempe B E ad B D, vt D O ad O G (22.
              <lb/>
            </s>
            <s xml:id="echoid-s4939" xml:space="preserve">
              <note position="right" xlink:label="note-0162-03" xlink:href="note-0162-03a" xml:space="preserve">b</note>
            ex 5.) </s>
            <s xml:id="echoid-s4940" xml:space="preserve">nempe N H ad H G, ſeu N P </s>
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