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-div493" type="section" level="1" n="154">
          <p style="it">
            <s xml:id="echoid-s5183" xml:space="preserve">
              <pb o="132" file="0170" n="170" rhead="Apollonij Pergæi"/>
            angulo D B E; </s>
            <s xml:id="echoid-s5184" xml:space="preserve">cadit verò F E infra rectam B E, quam ſecat in E, propter
              <lb/>
            curuitatem ſectionis F E B; </s>
            <s xml:id="echoid-s5185" xml:space="preserve">igitur angulus D E F obtuſus quoque erit, & </s>
            <s xml:id="echoid-s5186" xml:space="preserve">an-
              <lb/>
            gulus D F E acutus; </s>
            <s xml:id="echoid-s5187" xml:space="preserve">& </s>
            <s xml:id="echoid-s5188" xml:space="preserve">propterea recta linea D E minor erit, quàm D F; </s>
            <s xml:id="echoid-s5189" xml:space="preserve">ea-
              <lb/>
            dem ratione oſtendetur D F minor, quàm D A.</s>
            <s xml:id="echoid-s5190" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div495" type="section" level="1" n="155">
          <head xml:id="echoid-head204" xml:space="preserve">Notæ in Propoſit. XXXIX.</head>
          <p style="it">
            <s xml:id="echoid-s5191" xml:space="preserve">ALioquin ſecet illam, & </s>
            <s xml:id="echoid-s5192" xml:space="preserve">ſecemus ex,
              <lb/>
              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="168">
                <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-01"/>
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            & </s>
            <s xml:id="echoid-s5193" xml:space="preserve">D G intra ſectionem, &</s>
            <s xml:id="echoid-s5194" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5195" xml:space="preserve">Si e-
              <lb/>
            nim recta F D non contingit ellipſim A B,
              <lb/>
            ſecet eam ſi fieri poteſt in D: </s>
            <s xml:id="echoid-s5196" xml:space="preserve">quare F D pro-
              <lb/>
            ducta in directum cadet intra ſectionem, & </s>
            <s xml:id="echoid-s5197" xml:space="preserve">
              <lb/>
            in producta recta linea F D G ſumatur quod-
              <lb/>
            libet punctum G dummodo intra ſectionem
              <lb/>
            exiſtat, & </s>
            <s xml:id="echoid-s5198" xml:space="preserve">per G ad concurſum C coniunga-
              <lb/>
            tur recta linea G C, quæ producta occurrat
              <lb/>
            ſectioni in B: </s>
            <s xml:id="echoid-s5199" xml:space="preserve">& </s>
            <s xml:id="echoid-s5200" xml:space="preserve">quia ex hypotheſi recta F
              <lb/>
            D G perpendicularis erat ad maximum ramum D C, ergo in triangulo D G C
              <lb/>
            rectangulo erit hypothenuſa G C maior quàm D C, & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">ideo B C multo maior
              <lb/>
            erit quàm D C; </s>
            <s xml:id="echoid-s5202" xml:space="preserve">quod eſt abſurdum, ſuppoſita enim fuit D C omnium maxima
              <lb/>
            earum, quæ ex C ad ſectionem A B duci poſſunt.</s>
            <s xml:id="echoid-s5203" xml:space="preserve"/>
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        <div xml:id="echoid-div497" type="section" level="1" n="156">
          <head xml:id="echoid-head205" xml:space="preserve">Notæ in Propoſit. XXXXVIII.</head>
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            <s xml:id="echoid-s5204" xml:space="preserve">ALioquin occurtant in O, quia iſtæ
              <lb/>
              <figure xlink:label="fig-0170-02" xlink:href="fig-0170-02a" number="169">
                <image file="0170-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-02"/>
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            lineæ ſunt maximæ, &</s>
            <s xml:id="echoid-s5205" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5206" xml:space="preserve">Secant e-
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            nim lineæ maximæ ſemiaxim maiorem D A
              <lb/>
            in punctis M, N, & </s>
            <s xml:id="echoid-s5207" xml:space="preserve">L: </s>
            <s xml:id="echoid-s5208" xml:space="preserve">& </s>
            <s xml:id="echoid-s5209" xml:space="preserve">ſiquidem tres li-
              <lb/>
            neæ maximæ conueniunt in vnico puncto O,
              <lb/>
            erunt ſegmenta inter axim maiorem, & </s>
            <s xml:id="echoid-s5210" xml:space="preserve">ſe-
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              <note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">32. buius.</note>
            ctionem intercepta, nimirum M K, N H, L
              <lb/>
            F lineæ breuiſſimæ; </s>
            <s xml:id="echoid-s5211" xml:space="preserve">quarum duæ quæquè L
              <lb/>
            F, N H educuntur ab eodem puncto concur-
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            ſus O: </s>
            <s xml:id="echoid-s5212" xml:space="preserve">igitur (ex 54. </s>
            <s xml:id="echoid-s5213" xml:space="preserve">55. </s>
            <s xml:id="echoid-s5214" xml:space="preserve">huius) tertius ra-
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            mus O K ab eodem concurſu O eductus non erit breuiſecans; </s>
            <s xml:id="echoid-s5215" xml:space="preserve">quod eſt contra
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            hypotheſim.</s>
            <s xml:id="echoid-s5216" xml:space="preserve"/>
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        <div xml:id="echoid-div499" type="section" level="1" n="157">
          <head xml:id="echoid-head206" xml:space="preserve">LIBRI QVINTI FINIS.</head>
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