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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            <s xml:id="echoid-s7815" xml:space="preserve">
              <pb o="209" file="0247" n="247" rhead="Conicor. Lib. VI."/>
            ſe{ct}iones ſunt æquales, vel ſimiles inter ſe, tunc quidem earum plana ſunt æqui-
              <lb/>
            diſtantia: </s>
            <s xml:id="echoid-s7816" xml:space="preserve">Sicuti enim in eodem cono ſcaleno deſignari poßunt circuli æquales
              <lb/>
            ſubcontrariè poſiti, ſic etiam reliquæ coniſe{ct}iones ſubcontrariè conſtitutæ effici
              <lb/>
            poſſunt æquales, & </s>
            <s xml:id="echoid-s7817" xml:space="preserve">ſimiles inter ſe: </s>
            <s xml:id="echoid-s7818" xml:space="preserve">hæc autem, ſicuti etiam quamplurima vi-
              <lb/>
            deri poſſunt in libris neotericorum.</s>
            <s xml:id="echoid-s7819" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7820" xml:space="preserve">Sed non alienum erit à noſtro inſtituto hic paucis conſiderare paſſiones, & </s>
            <s xml:id="echoid-s7821" xml:space="preserve">de-
              <lb/>
            ſcriptiones ſe{ct}ionum conicarum ſimilium, vel æqualium, quæ æquidiſtantes,
              <lb/>
            ſeu asymptoticæ vocantur. </s>
            <s xml:id="echoid-s7822" xml:space="preserve">Et licet hæ ab alijs inuentæ, & </s>
            <s xml:id="echoid-s7823" xml:space="preserve">traditæ ſint, non nul-
              <lb/>
            la tamen noua in medium afferam: </s>
            <s xml:id="echoid-s7824" xml:space="preserve">non enim rerum nouitas ex ſubie{ct}i nouita-
              <lb/>
            te tantummodò arguitur, imo de ſubie{ct}o antiquo poſſunt nouæ ſpeculationes af-
              <lb/>
            ferri, atque corrigi, & </s>
            <s xml:id="echoid-s7825" xml:space="preserve">cõpleri ea, quæ apicem perfe{ct}ionis non attingunt, & </s>
            <s xml:id="echoid-s7826" xml:space="preserve">
              <lb/>
            hæc quidem omnia noua dici poterunt, & </s>
            <s xml:id="echoid-s7827" xml:space="preserve">poſſunt, & </s>
            <s xml:id="echoid-s7828" xml:space="preserve">debent zelo veritatis e-
              <lb/>
            uulgari, nec propterea prædeceßorum nominibus, ant inuentionibus iniuria in-
              <lb/>
            fertur.</s>
            <s xml:id="echoid-s7829" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7830" xml:space="preserve">Primus itaque omnium ( quod ſciam ) Pappus Alexandrinus libro ſeptimo col-
              <lb/>
            le{ct}ionum Mathematic arum propoſitione 208. </s>
            <s xml:id="echoid-s7831" xml:space="preserve">lemmate ſexto in quintum librum
              <lb/>
            Apollonij, conſiderauit concentricas hyperbolas inter ſe ſimiles, eundẽ axim habentes,
              <lb/>
            ad eaſdem partes cauas inter ſe ſe non concurrere, ſed ſemper ad ſe ipſas vi-
              <lb/>
            cinius accedere. </s>
            <s xml:id="echoid-s7832" xml:space="preserve">Poſtea Gregorius à Santo Vincentio oſtendit, quod duæ parabo-
              <lb/>
              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">Parab.
                <lb/>
              pr 344.</note>
            læ inter ſe æquales, ſimiliter poſitæ circa communem axim, vel diametrum, pa-
              <lb/>
            riter nunquàm conueniunt, & </s>
            <s xml:id="echoid-s7833" xml:space="preserve">parallelæ ſunt inter ſe, & </s>
            <s xml:id="echoid-s7834" xml:space="preserve">in infinitum produ{ct}æ
              <lb/>
            ſemper magis ad inuicem accedunt; </s>
            <s xml:id="echoid-s7835" xml:space="preserve">atque propoſit. </s>
            <s xml:id="echoid-s7836" xml:space="preserve">139. </s>
            <s xml:id="echoid-s7837" xml:space="preserve">de Hyperbola conſidera-
              <lb/>
            uit duas hyperbolas æquales, & </s>
            <s xml:id="echoid-s7838" xml:space="preserve">ſimiles, quæ pariter in infinitd extensæ nunquàm
              <lb/>
            conueniunt, & </s>
            <s xml:id="echoid-s7839" xml:space="preserve">ſimul cum Pappo putat, rite co@cludi poſſe, quod prædi{ct}æ ſe{ct}io-
              <lb/>
            nes, in infinitum extenſæ, ſint asymptoti, & </s>
            <s xml:id="echoid-s7840" xml:space="preserve">ſemper magis, ac magis ad inui-
              <lb/>
            cem appropinquentur ex eo, quod re{ct}æ lineæ inter ſe æquidiſtantes inter duas
              <lb/>
            ſe{ct}iones interceptæ, ſucceſſiuè ſemper diminuantur. </s>
            <s xml:id="echoid-s7841" xml:space="preserve">Propoſitiones quidem recon-
              <lb/>
            ditæ, & </s>
            <s xml:id="echoid-s7842" xml:space="preserve">ſcitu iucundæ, ſed an æquè certæ, & </s>
            <s xml:id="echoid-s7843" xml:space="preserve">indubitatæ cenſeri debeant, in-
              <lb/>
            quiremus, aliquibus tamen præmiſſis.</s>
            <s xml:id="echoid-s7844" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7845" xml:space="preserve">In qualibet hyperbola I E, cuius asymptoti C A B, duarum re{ct}arum linea-
              <lb/>
              <note position="right" xlink:label="note-0247-02" xlink:href="note-0247-02a" xml:space="preserve">DEFINI
                <lb/>
              TIO
                <lb/>
              Addita.</note>
              <figure xlink:label="fig-0247-01" xlink:href="fig-0247-01a" number="284">
                <image file="0247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0247-01"/>
              </figure>
            rum F I, G K inter ſe æquidiſtantium, ab vna asymptoto A C ad hyperbolen,
              <lb/>
            edu{ct}arum, ſit F I propinquior centro, quàm G K, quando ambo cadunt infra
              <lb/>
            centrum A ad partes C; </s>
            <s xml:id="echoid-s7846" xml:space="preserve">vel F I magis à centro recedat, quando ambo </s>
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