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-div650" type="section" level="1" n="216">
          <pb o="184" file="0222" n="222" rhead="Apollonij Pergæi"/>
          <figure number="248">
            <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-01"/>
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          <p style="it">
            <s xml:id="echoid-s6987" xml:space="preserve">Secentur diametrorum abſciſſæ G B, & </s>
            <s xml:id="echoid-s6988" xml:space="preserve">H E in ijſdem rationibus in L, M,
              <lb/>
            N, O, & </s>
            <s xml:id="echoid-s6989" xml:space="preserve">ab ijſdem punctis educantur baſibus æquiſtantes, ſeu ad diametros or-
              <lb/>
            dinatim applicatæ P Q, R S, T V, X Y
              <unsure/>
            . </s>
            <s xml:id="echoid-s6990" xml:space="preserve">Quoniam ex hypotheſi G B ad B I
              <lb/>
            eſt, vt H E ad E K; </s>
            <s xml:id="echoid-s6991" xml:space="preserve">eſtque A G media proportionalis inter G B, & </s>
            <s xml:id="echoid-s6992" xml:space="preserve">B I; </s>
            <s xml:id="echoid-s6993" xml:space="preserve">pari-
              <lb/>
              <note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">II. lib. I.</note>
            terque D H media proportionalis eſt inter H E, & </s>
            <s xml:id="echoid-s6994" xml:space="preserve">E K; </s>
            <s xml:id="echoid-s6995" xml:space="preserve">igitur A G ad G B
              <lb/>
            eſt, vt D H ad H E; </s>
            <s xml:id="echoid-s6996" xml:space="preserve">Et quoniam inuertendo L B ad B G eſt, vt N E ad E H,
              <lb/>
            atque B G ad B I poſita fuit, vt H E ad E K; </s>
            <s xml:id="echoid-s6997" xml:space="preserve">ergo ex æquali ordinata L B ad
              <lb/>
            B I erit, vt N E ad E K, quare vt L B ad P L, mediã proportionalẽ inter L B,
              <lb/>
            & </s>
            <s xml:id="echoid-s6998" xml:space="preserve">I B, ita erit N E ad N T mediam proportionalem inter N E, & </s>
            <s xml:id="echoid-s6999" xml:space="preserve">E K. </s>
            <s xml:id="echoid-s7000" xml:space="preserve">Eo-
              <lb/>
            dem modo oſtendetur, quod R M ad M B eandem proportionem habet, quàm X
              <lb/>
            O ad O E: </s>
            <s xml:id="echoid-s7001" xml:space="preserve">& </s>
            <s xml:id="echoid-s7002" xml:space="preserve">hoc ſemper continget in quibuslibet alijs diuiſionibus proportiona-
              <lb/>
            libus abſciſſarum, ſuntque anguli G, & </s>
            <s xml:id="echoid-s7003" xml:space="preserve">H æquales; </s>
            <s xml:id="echoid-s7004" xml:space="preserve">igitur ſegmenta A B C, & </s>
            <s xml:id="echoid-s7005" xml:space="preserve">
              <lb/>
            D E F ſimilia ſunt inter ſe. </s>
            <s xml:id="echoid-s7006" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7007" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Defin. 7.
            <lb/>
          huius.</note>
        </div>
        <div xml:id="echoid-div652" type="section" level="1" n="217">
          <head xml:id="echoid-head274" xml:space="preserve">LEMMA VII.</head>
          <p style="it">
            <s xml:id="echoid-s7008" xml:space="preserve">S I in duobus ſegmentis A B C, & </s>
            <s xml:id="echoid-s7009" xml:space="preserve">D E F hyperbolicis, aut ellipti-
              <lb/>
            cis, baſes A C, & </s>
            <s xml:id="echoid-s7010" xml:space="preserve">D F cum diametris G B, & </s>
            <s xml:id="echoid-s7011" xml:space="preserve">H E, æquales
              <lb/>
            angulos G, & </s>
            <s xml:id="echoid-s7012" xml:space="preserve">H obliquos continentes, efficiant abſciſſas G B, & </s>
            <s xml:id="echoid-s7013" xml:space="preserve">H E
              <lb/>
            proportionales lateribus rectis B I, & </s>
            <s xml:id="echoid-s7014" xml:space="preserve">E K, atque tranſuerſis B Z, & </s>
            <s xml:id="echoid-s7015" xml:space="preserve">
              <lb/>
            E a, erunt ſegmenta ſimilia inter ſe.</s>
            <s xml:id="echoid-s7016" xml:space="preserve"/>
          </p>
          <figure number="249">
            <image file="0222-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-02"/>
          </figure>
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