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-div625" type="section" level="1" n="209">
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            <s xml:id="echoid-s6674" xml:space="preserve">
              <pb o="174" file="0212" n="212" rhead="Apollonij Pergæi"/>
            I, O L remanebunt I E, L K inæquales. </s>
            <s xml:id="echoid-s6675" xml:space="preserve">Quod eſt abſurdum: </s>
            <s xml:id="echoid-s6676" xml:space="preserve">oſtenſæ enim fue-
              <lb/>
            runt prius æquales inter ſe.</s>
            <s xml:id="echoid-s6677" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6678" xml:space="preserve">In figura autem tertia ducamus duas perpendiculares, &</s>
            <s xml:id="echoid-s6679" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">In quarto
              <lb/>
              <note position="right" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">e</note>
            caſu ſupponuntur baſes A C, & </s>
            <s xml:id="echoid-s6681" xml:space="preserve">D F per centra circulorum tranſire, eo quod
              <lb/>
            anguli A B C, & </s>
            <s xml:id="echoid-s6682" xml:space="preserve">D E F recti ſupponuntur, atque rectæ lineæ B H, E I non
              <lb/>
            ſunt perpendiculares ſuper eaſdem baſes, licet intra circulos efficiant angulos B
              <lb/>
            H C, & </s>
            <s xml:id="echoid-s6683" xml:space="preserve">E I F inter ſe æqua-
              <lb/>
            les: </s>
            <s xml:id="echoid-s6684" xml:space="preserve">perſecta igitur conſiru-
              <lb/>
              <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="235">
                <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0212-01"/>
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            ctione, vt prius ad diame-
              <lb/>
            trũ D F, ducãtur ex punctis
              <lb/>
            E, & </s>
            <s xml:id="echoid-s6685" xml:space="preserve">K perpendiculares E
              <lb/>
            Q, K S, quæ diuidẽtur bi-
              <lb/>
            fariã, & </s>
            <s xml:id="echoid-s6686" xml:space="preserve">ad angulos rectos
              <lb/>
            in P, & </s>
            <s xml:id="echoid-s6687" xml:space="preserve">R. </s>
            <s xml:id="echoid-s6688" xml:space="preserve">Et quoniam
              <lb/>
            (vt in præcedenti caſu oſtẽ-
              <lb/>
            ſum eſt) G E ad E I ean-
              <lb/>
            dem proportionem habet,
              <lb/>
            quàm M K ad K L, cum-
              <lb/>
            que latera I E, L K ſint
              <lb/>
            parallela, pariterque P E, & </s>
            <s xml:id="echoid-s6689" xml:space="preserve">K R æquidiſtent, atque baſes I P, L R in dire-
              <lb/>
            ctum poſitæ ſint, erunt triangula I E P, & </s>
            <s xml:id="echoid-s6690" xml:space="preserve">L K R æquiangula, & </s>
            <s xml:id="echoid-s6691" xml:space="preserve">ſimilia: </s>
            <s xml:id="echoid-s6692" xml:space="preserve">& </s>
            <s xml:id="echoid-s6693" xml:space="preserve">
              <lb/>
            propterea I E ad E P erit, vt. </s>
            <s xml:id="echoid-s6694" xml:space="preserve">L K ad K R: </s>
            <s xml:id="echoid-s6695" xml:space="preserve">eſt verò P E ad eius duplam E Q,
              <lb/>
            vt R K ad eius duplam K S (cum diameter ſecet eas bifariam, quas perpendi-
              <lb/>
            culariter prius ſecabat) ergo, ex æquali ordinata, erit G E ad E Q, vt M K ad
              <lb/>
            K S; </s>
            <s xml:id="echoid-s6696" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s6697" xml:space="preserve">anguli verticales G E Q, & </s>
            <s xml:id="echoid-s6698" xml:space="preserve">M K S æquales, propterea quod conti-
              <lb/>
            nẽtur à rectis lineis quæ binæ binis ſunt æquidiſtantes; </s>
            <s xml:id="echoid-s6699" xml:space="preserve">ergo triangula G E Q, & </s>
            <s xml:id="echoid-s6700" xml:space="preserve">
              <lb/>
            M K S ſimilia ſunt inter ſe: </s>
            <s xml:id="echoid-s6701" xml:space="preserve">& </s>
            <s xml:id="echoid-s6702" xml:space="preserve">propterea angulus E G Q æqualis erit angulo K M S.</s>
            <s xml:id="echoid-s6703" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s6704" xml:space="preserve">Et propterea ſegmentum E F Q maius ſimile erit ſegmento K F S mi-
              <lb/>
              <note position="right" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">f</note>
            nori: </s>
            <s xml:id="echoid-s6705" xml:space="preserve">quod eſt abſurdum, &</s>
            <s xml:id="echoid-s6706" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6707" xml:space="preserve">Legendum puto. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">Et propterea periheriæ E F
              <lb/>
            Q, & </s>
            <s xml:id="echoid-s6709" xml:space="preserve">K F S, quibus inſiſtunt æquales erunt: </s>
            <s xml:id="echoid-s6710" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s6711" xml:space="preserve">Eſt enim E
              <lb/>
            F Q ma
              <unsure/>
            ior, quàm K F S.</s>
            <s xml:id="echoid-s6712" xml:space="preserve"/>
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        <div xml:id="echoid-div633" type="section" level="1" n="210">
          <head xml:id="echoid-head265" xml:space="preserve">Notæ in Propoſit. Præmiſſ. VI.</head>
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            <s xml:id="echoid-s6713" xml:space="preserve">DEinde ſint duo anguli B, E qualeſcumque; </s>
            <s xml:id="echoid-s6714" xml:space="preserve">ſed angulus A B H, vel
              <lb/>
              <note position="right" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">a</note>
            C B H æqualis angulo D E I vel F E I, & </s>
            <s xml:id="echoid-s6715" xml:space="preserve">condictiones, vti dixi-
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              <figure xlink:label="fig-0212-02" xlink:href="fig-0212-02a" number="236">
                <image file="0212-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0212-02"/>
              </figure>
            </s>
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