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-div265" type="section" level="1" n="88">
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        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="89">
          <head xml:id="echoid-head123" xml:space="preserve">PROPOSITIO XXXXV.</head>
          <p>
            <s xml:id="echoid-s2914" xml:space="preserve">SI autem fuerit ratio E A ad A D minor,
              <lb/>
              <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a" number="86">
                <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-01"/>
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              <note position="right" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">a</note>
            quàm proportio figuræ, ponamus E H ad H
              <lb/>
            D in proportione figuræ, & </s>
            <s xml:id="echoid-s2915" xml:space="preserve">producamus per-
              <lb/>
            pendicularem H F, & </s>
            <s xml:id="echoid-s2916" xml:space="preserve">iungamus F E, & </s>
            <s xml:id="echoid-s2917" xml:space="preserve">duca-
              <lb/>
            mus perpendicularem F I. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">Et quoniam E H ad
              <lb/>
            H D, nempe D I ad I G eſt, vt proportio figu-
              <lb/>
            ræ, erit F G linea breuiſſima (10. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2920" xml:space="preserve">Et quo-
              <lb/>
            niam iam educti ſunt ex E duo breuiſecantes
              <lb/>
            F E, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">E A (11. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2923" xml:space="preserve">tunc à terminis ramo-
              <lb/>
            rum egredientium ex E, qui terminantur ad ſe-
              <lb/>
            ctionem B F, linea breuiſſima egrediens erit re-
              <lb/>
            motior ab ipſo B, & </s>
            <s xml:id="echoid-s2924" xml:space="preserve">qui terminatur ad ſectio-
              <lb/>
            nem A F, breuiſſima egrediens ab extremitate illius erit proximior, ipſi
              <lb/>
            B (51. </s>
            <s xml:id="echoid-s2925" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2926" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2927" xml:space="preserve">& </s>
            <s xml:id="echoid-s2928" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s2929" xml:space="preserve"/>
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        <div xml:id="echoid-div270" type="section" level="1" n="90">
          <head xml:id="echoid-head124" xml:space="preserve">Notæ in Propoſ. XXXXIV.</head>
          <p style="it">
            <s xml:id="echoid-s2930" xml:space="preserve">PVto, numeros 53. </s>
            <s xml:id="echoid-s2931" xml:space="preserve">& </s>
            <s xml:id="echoid-s2932" xml:space="preserve">54. </s>
            <s xml:id="echoid-s2933" xml:space="preserve">Propoſitionum huius ſe-
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                <image file="0106-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-02"/>
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            ctionis mendoſos eſſe, nam Propoſitio 53. </s>
            <s xml:id="echoid-s2934" xml:space="preserve">poſita
              <lb/>
            fuit in præmiſſa ſectione, & </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Propoſitio 54. </s>
            <s xml:id="echoid-s2936" xml:space="preserve">inferius
              <lb/>
            appoſita reperitur; </s>
            <s xml:id="echoid-s2937" xml:space="preserve">Cenſeo igitur, eſſe Propoſitiones
              <lb/>
            XXXXIV. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">& </s>
            <s xml:id="echoid-s2939" xml:space="preserve">XXXXV.</s>
            <s xml:id="echoid-s2940" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2941" xml:space="preserve">Si ex axe recto ellipſis ſumatur menſura, &</s>
            <s xml:id="echoid-s2942" xml:space="preserve">c.
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            <s xml:id="echoid-s2943" xml:space="preserve">
              <note position="right" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">a</note>
            Hoc eſt ſi ex axe minori, recto ellipſis ſumatur menſu-
              <lb/>
            ra, quæ habeat non minorem proportionem ad ſemi-
              <lb/>
            axim rectum, quàm habet axis tranſuerſus ad ſuum
              <lb/>
            latus rectum, quilibet ramus ſecans, ab origine ad ſe-
              <lb/>
            ctionem ductus, abſcindit ex axe tranſuerſo ad ver-
              <lb/>
            ticem ſectionis minorem lineam, quàm ſecat linea breuiſsima ab eius termi-
              <lb/>
            no ad axim tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">Si vero menſura ad minorem ſemiaxim re-
              <lb/>
            ctum proportionem minorem habuerit, quàm latus tranſuer ſum ad rectum, tunc
              <lb/>
            vnicus ramus erit breuiſecans; </s>
            <s xml:id="echoid-s2945" xml:space="preserve">reliqui vero ſequentes terminum tranſuerſi, ha-
              <lb/>
            bent ſuperius expoſitas proprietates, & </s>
            <s xml:id="echoid-s2946" xml:space="preserve">ſequentes extr emitates axis recti, ſecant
              <lb/>
            ex tranſuer ſa maiorem lineam, quàm ſecet breuiſsima ab eius termino ad axim
              <lb/>
            tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Quod autem menſura neceßario ſumi debeat in axe minori
              <lb/>
            ellipſis patet, nàm ex hypotheſi rami ſunt ſecantes non quidem ex concurſu, ſed
              <lb/>
            ex origine ducti igitur origo cadit infra centrum, & </s>
            <s xml:id="echoid-s2948" xml:space="preserve">menſura maior erit medie-
              <lb/>
            tate axis vt in textu habetur; </s>
            <s xml:id="echoid-s2949" xml:space="preserve">debet autem habere menſura ad ſemiaxim rectum
              <lb/>
            maiorem aut eandem proportionem, quàm axis tranſuerſus habet ad eius latus
              <lb/>
            rectum, ergo proportio axis tranſuerſi ad ſuum latus rectum erit maioris inæqua-
              <lb/>
            litatis, & </s>
            <s xml:id="echoid-s2950" xml:space="preserve">propterea tranſuerſus axis erit maior quàm axis rectus.</s>
            <s xml:id="echoid-s2951" xml:space="preserve"/>
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