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-div704" type="section" level="1" n="231">
          <p style="it">
            <s xml:id="echoid-s7760" xml:space="preserve">
              <pb o="207" file="0245" n="245" rhead="Conicor. Lib. VI."/>
            les cum diametris, quæ abſciſſis ſint proportionales, & </s>
            <s xml:id="echoid-s7761" xml:space="preserve">abſciſſæ quoque inter ſe.
              <lb/>
            </s>
            <s xml:id="echoid-s7762" xml:space="preserve">Vnde ſequitur, quod portiones eiuſdem diametri E K à centro M ad omnes or-
              <lb/>
            dinatim ad diametros applicatas ſint æquales inter ſe, vt oſtenſum eſt in propo-
              <lb/>
            ſitione 13. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">huius: </s>
            <s xml:id="echoid-s7764" xml:space="preserve">quod eſt impoſſibile.</s>
            <s xml:id="echoid-s7765" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7766" xml:space="preserve">Quando verò ſectio A C eſt byperbole, ac ſectio D F eſt ellipſis, ſimiliter,
              <lb/>
            vt in 14. </s>
            <s xml:id="echoid-s7767" xml:space="preserve">propoſitione huius, oſtendetur; </s>
            <s xml:id="echoid-s7768" xml:space="preserve">quo abſciſſæ in hyperbola, & </s>
            <s xml:id="echoid-s7769" xml:space="preserve">ellipſi ſint
              <lb/>
            proportionales; </s>
            <s xml:id="echoid-s7770" xml:space="preserve">& </s>
            <s xml:id="echoid-s7771" xml:space="preserve">propterea omnes habebunt rationes maioris inæqualitatis, aut
              <lb/>
            omnes habebunt, proportiones inæqualitatis minoris, quod tamen in prædicta 14.
              <lb/>
            </s>
            <s xml:id="echoid-s7772" xml:space="preserve">propoſitione impoſſibile eſſe oſtenditur.</s>
            <s xml:id="echoid-s7773" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div706" type="section" level="1" n="232">
          <head xml:id="echoid-head292" xml:space="preserve">Notæ in Propoſit. XXIV.</head>
          <p style="it">
            <s xml:id="echoid-s7774" xml:space="preserve">SI enim hoc verum non eſt, &</s>
            <s xml:id="echoid-s7775" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7776" xml:space="preserve">Quod quælibet portio B A D ſectionis
              <lb/>
              <note position="left" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">a</note>
            conicæ A B G nullo pacto circumferentia circuli eſſe poſſit ſic oſtendetur.
              <lb/>
            </s>
            <s xml:id="echoid-s7777" xml:space="preserve">Quia in circulo rectæ lineæ diuidentes bifariam duas parallelas inter ſe ſunt
              <lb/>
            neceſſariò diametri circuli, qui perpendicu-
              <lb/>
              <figure xlink:label="fig-0245-01" xlink:href="fig-0245-01a" number="281">
                <image file="0245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0245-01"/>
              </figure>
            lariter ſecant prædictas parallelas applica-
              <lb/>
            tas; </s>
            <s xml:id="echoid-s7778" xml:space="preserve">igitur ſi curua linea B G D fuerit cir-
              <lb/>
            culi peripheria rectæ lineæ K I, L M, & </s>
            <s xml:id="echoid-s7779" xml:space="preserve">
              <lb/>
            N O diametri circuli, erunt perpendicula-
              <lb/>
            res ad ordinatim applicatas æquidiſtantes
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s7780" xml:space="preserve">ſed quia etiam A B G ſupponitur
              <lb/>
            ſectio conica, erunt K I, L M, N O axes
              <lb/>
            prædictæ ſectionis conicæ eo quod bifariam,
              <lb/>
            & </s>
            <s xml:id="echoid-s7781" xml:space="preserve">ad angulos rectos diuidunt ordinatim ap-
              <lb/>
            plicatas. </s>
            <s xml:id="echoid-s7782" xml:space="preserve">Rurſus quia prædictæ ordinatim
              <lb/>
            applicatæ non ſunt omnes inter ſe parallelæ,
              <lb/>
            eo quodex conſtructione applicatæ A B, A C,
              <lb/>
            C D non fuerunt ductæ æquidiſtantes; </s>
            <s xml:id="echoid-s7783" xml:space="preserve">igi-
              <lb/>
            tur tres axes I K, L M, N O indirectum
              <lb/>
              <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">48. lib. 2.</note>
            non coincidunt; </s>
            <s xml:id="echoid-s7784" xml:space="preserve">quare in ſectione conica B A G reperiri poſſent tres axes; </s>
            <s xml:id="echoid-s7785" xml:space="preserve">quod
              <lb/>
            eſt impoſſibile.</s>
            <s xml:id="echoid-s7786" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div708" type="section" level="1" n="233">
          <head xml:id="echoid-head293" xml:space="preserve">SECTIO NONA</head>
          <head xml:id="echoid-head294" xml:space="preserve">Continens Propoſit. XXV.</head>
          <p>
            <s xml:id="echoid-s7787" xml:space="preserve">SI duo plana æquidiſtantia conum aliquem ſecuerint, atque
              <lb/>
              <note position="left" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">b</note>
            in eo efficiant duas hyperbolas, aut ellipſes; </s>
            <s xml:id="echoid-s7788" xml:space="preserve">vtique ſectio-
              <lb/>
            nes ſimiles inter ſe erunt, ſed non erunt neceſſariò æquales.</s>
            <s xml:id="echoid-s7789" xml:space="preserve"/>
          </p>
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