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="266" file="0304" n="304" rhead="Apollonij Pergæi"/>
            A O (cum C D, & </s>
            <s xml:id="echoid-s9981" xml:space="preserve">H B ſint parallelæ, atque D O ſit parallelogrammum) com-
              <lb/>
            ponunt verò hæ duæ proportiones rationem quadrati C A ad rectangulum F
              <lb/>
            A O: </s>
            <s xml:id="echoid-s9982" xml:space="preserve">ergo vt rectangulum A H C ad quadratum H B; </s>
            <s xml:id="echoid-s9983" xml:space="preserve">ita eſt quadratum C A
              <lb/>
            ad rectangulum F A O, & </s>
            <s xml:id="echoid-s9984" xml:space="preserve">pro-
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              <figure xlink:label="fig-0304-01" xlink:href="fig-0304-01a" number="351">
                <image file="0304-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0304-01"/>
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            pterea vt X ad A F, ita erit qua-
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            dratum A C ad rectangulum F A
              <lb/>
            O, ſed vt F A ad A D (ſum-
              <lb/>
            ptis æqualibus altitudinibus A O,
              <lb/>
            C D) ita eſt rectangulum F A O
              <lb/>
            ad rectangulum A D C; </s>
            <s xml:id="echoid-s9985" xml:space="preserve">quare ex
              <lb/>
            æquali X ad A D erit vt quadra-
              <lb/>
            tum A C ad rectangulum A D C;
              <lb/>
            </s>
            <s xml:id="echoid-s9986" xml:space="preserve">tandem vt Z latus rectum para-
              <lb/>
            boles A M ad D A ita eſt quadra-
              <lb/>
              <note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">II. lib. I.</note>
            tum A C ad rectangulum A D C;
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            </s>
            <s xml:id="echoid-s9987" xml:space="preserve">igitur X, & </s>
            <s xml:id="echoid-s9988" xml:space="preserve">Z ad eandem D A
              <lb/>
            habent eandem proportionem quàm
              <lb/>
            quadr atum A C ad rectangulum
              <lb/>
            A D C, & </s>
            <s xml:id="echoid-s9989" xml:space="preserve">propterea latera recta
              <lb/>
            X, & </s>
            <s xml:id="echoid-s9990" xml:space="preserve">Z æqualia ſunt inter ſe. </s>
            <s xml:id="echoid-s9991" xml:space="preserve">
              <lb/>
            Et quoniam in quolibet caſu ſectio-
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            nis conicæ A N latus rectum X
              <lb/>
            ſemper æquale eſt Z lateri recto
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            vnius eiuſdemq; </s>
            <s xml:id="echoid-s9992" xml:space="preserve">paraboles A M; </s>
            <s xml:id="echoid-s9993" xml:space="preserve">
              <lb/>
            ergo latera recta X reliquarum
              <lb/>
            omnium ſectionum æqualia ſunt
              <lb/>
            inter ſe, licet ſectiones illæ ſint
              <lb/>
            inæquales, & </s>
            <s xml:id="echoid-s9994" xml:space="preserve">habeant latera trã-
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            ſuerſa inæqualia, imò neque eiuſ-
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            dem ſpeciei ſint. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">Quod erat pro-
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            poſitum.</s>
            <s xml:id="echoid-s9996" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9997" xml:space="preserve">Admiratione dignum præcipuè
              <lb/>
            eſt in hac propoſitione, quod ſi ſe-
              <lb/>
            ctio A N fuerit circulus, vnicus
              <lb/>
            tantummodò erit; </s>
            <s xml:id="echoid-s9998" xml:space="preserve">nam circuli la-
              <lb/>
            tus rectum X æquale erit eius dia-
              <lb/>
            metro, ſeu axi tranſuerſo A F; </s>
            <s xml:id="echoid-s9999" xml:space="preserve">eſt-
              <lb/>
            que ſemper latus rectum eiuſdem
              <lb/>
            menſuræ, vt aſtenſum eſt; </s>
            <s xml:id="echoid-s10000" xml:space="preserve">igitur
              <lb/>
            circuli diameter F A idem ſemper erit; </s>
            <s xml:id="echoid-s10001" xml:space="preserve">& </s>
            <s xml:id="echoid-s10002" xml:space="preserve">propterea circulus, qui à tali plano
              <lb/>
            generari poteſt ſingularis erit, nimirum ille, qui in vnico cono A B C efficit
              <lb/>
            triangula per axim ſimilia, & </s>
            <s xml:id="echoid-s10003" xml:space="preserve">ſubcontraria B A C, & </s>
            <s xml:id="echoid-s10004" xml:space="preserve">B F A. </s>
            <s xml:id="echoid-s10005" xml:space="preserve">Manifeſtum
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s10006" xml:space="preserve">eſt parabolem A M ſingularem eße, nam ſupponitur idem circulus baſis A
              <lb/>
            C, & </s>
            <s xml:id="echoid-s10007" xml:space="preserve">in plano per axim coni cõmune latus A D B ſemper eoſdẽ angulos D A E,
              <lb/>
            & </s>
            <s xml:id="echoid-s10008" xml:space="preserve">D A C efficere conceditur; </s>
            <s xml:id="echoid-s10009" xml:space="preserve">igitur vt ſectio A M ſit parabole neceßariò recta à
              <lb/>
            puncto C duci debet parallela diametro par aboles A E; </s>
            <s xml:id="echoid-s10010" xml:space="preserve">cum ergo in triangulo per
              <lb/>
            axim D A C detur baſis A C inuariabilis quia circulus vnicus ſupponitur </s>
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