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-div814" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s10010" xml:space="preserve">
              <pb o="267" file="0305" n="305" rhead="Conicor. Lib. VI."/>
            què anguli D, & </s>
            <s xml:id="echoid-s10011" xml:space="preserve">D A C; </s>
            <s xml:id="echoid-s10012" xml:space="preserve">dabitur quoq; </s>
            <s xml:id="echoid-s10013" xml:space="preserve">eius ſpecies ſemper eadem, immo triã-
              <lb/>
            gulum per axim inuariabile erit, qui ſemper eodem modo inclinatur ad circu-
              <lb/>
            lum baſis C A: </s>
            <s xml:id="echoid-s10014" xml:space="preserve">& </s>
            <s xml:id="echoid-s10015" xml:space="preserve">propterea conus D A C ſemper idem erit, & </s>
            <s xml:id="echoid-s10016" xml:space="preserve">eodem modo
              <lb/>
            ſectus, vnde ſectio par aboles A M eadem ſemper omnino erit, habens idem latus
              <lb/>
            rectum Z. </s>
            <s xml:id="echoid-s10017" xml:space="preserve">In hyperbole verò, aut ellipſi latera C B poſſunt ſupra, vel infra
              <lb/>
            C D parallelam ipſi A E à puncto C ductam, extendi, & </s>
            <s xml:id="echoid-s10018" xml:space="preserve">ſic efficientur tranſuer-
              <lb/>
            ſa latera A F inæqualia inter ſe, cumque coni ſectiones A N habeant latera
              <lb/>
              <note position="right" xlink:label="note-0305-01" xlink:href="note-0305-01a" xml:space="preserve">Maurol.
                <lb/>
              2. lib. 5.
                <lb/>
              Conic.</note>
            recta X æqualia inter ſe, latera verò tranſuerſa A F inæqualia, & </s>
            <s xml:id="echoid-s10019" xml:space="preserve">hyperbola-
              <lb/>
            rum commune latus rectum habentium illa maior eſt, cuius axis tranſuerſus eſt
              <lb/>
            minor: </s>
            <s xml:id="echoid-s10020" xml:space="preserve">& </s>
            <s xml:id="echoid-s10021" xml:space="preserve">duarum ellipſium commune latus rectum habentium, illa maior eſt
              <lb/>
            cuius axis tranſuerſus eſt maior; </s>
            <s xml:id="echoid-s10022" xml:space="preserve">igitur ellipſes, aut byperbole, quæ in conis
              <lb/>
            prædicta lege conſtructis deſcribuntur non ſingulares ſed infinitæ eſſe poßunt.
              <lb/>
            </s>
            <s xml:id="echoid-s10023" xml:space="preserve">Vbi notandum eſt, quod ellipſes poßunt eſſe eæ quæ ad maiores, aut ad minores
              <lb/>
            axes adiacent. </s>
            <s xml:id="echoid-s10024" xml:space="preserve">Pari modo conſtat quod ſi in conis ſuperius expoſitis fiant ſe-
              <lb/>
            ctiones conicæ conſtituentur ad eundem axim quinque ſectiones commune latus
              <lb/>
            rectum habentes ſe ſe in eodem vertice tangentes, & </s>
            <s xml:id="echoid-s10025" xml:space="preserve">earum intima erit elli-
              <lb/>
              <note position="right" xlink:label="note-0305-02" xlink:href="note-0305-02a" xml:space="preserve">Maurol.
                <lb/>
              prop. 28.
                <lb/>
              lib. 5.
                <lb/>
              Conic.</note>
            pſis, quæ ad axim minorem adiacet, & </s>
            <s xml:id="echoid-s10026" xml:space="preserve">non erit vnica, ſed multiplex, & </s>
            <s xml:id="echoid-s10027" xml:space="preserve">om-
              <lb/>
            nes cadent intra circulum, circulus verò intra ellipſim ad axim maiorem acco-
              <lb/>
            modatam cadet, hæc verò intra parabolen conſtituetur, & </s>
            <s xml:id="echoid-s10028" xml:space="preserve">inter circulum, & </s>
            <s xml:id="echoid-s10029" xml:space="preserve">
              <lb/>
            parabolen infinitæ ellipſes ſe in eodem puncto verticis tangentes collocari poſ-
              <lb/>
            ſunt. </s>
            <s xml:id="echoid-s10030" xml:space="preserve">T andem parabole compræhendetur ab infinitis alijs hyperbolis ſe ſe in eo-
              <lb/>
            dem puncto tangentibus.</s>
            <s xml:id="echoid-s10031" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10032" xml:space="preserve">Si in qualibet coniſectione B A C
              <lb/>
              <note position="right" xlink:label="note-0305-03" xlink:href="note-0305-03a" xml:space="preserve">PROP.
                <lb/>
              18.
                <lb/>
              Addit.
                <lb/>
              ex 51. 52.
                <lb/>
              lib. 5.</note>
              <figure xlink:label="fig-0305-01" xlink:href="fig-0305-01a" number="352">
                <image file="0305-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0305-01"/>
              </figure>
            ducatur breuiſecans ſingularis D A,
              <lb/>
            tunc quælibet alia coniſectio M A
              <lb/>
            N, cuius axis ſit eadem breuiſe-
              <lb/>
            cans, & </s>
            <s xml:id="echoid-s10033" xml:space="preserve">A L ſemiſſis erecti eius
              <lb/>
            minor ſit eadem ſingulari breuiſecan-
              <lb/>
            te A D. </s>
            <s xml:id="echoid-s10034" xml:space="preserve">Dico ſectionem M A N
              <lb/>
            interius contingere priorem ſectionem
              <lb/>
            B A C in A.</s>
            <s xml:id="echoid-s10035" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10036" xml:space="preserve">Quia A L minor eſt, quàm A D
              <lb/>
            ſumi poterit recta A O maior quidem quàm A L, & </s>
            <s xml:id="echoid-s10037" xml:space="preserve">minor quàm A D, & </s>
            <s xml:id="echoid-s10038" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0305-04" xlink:href="note-0305-04a" xml:space="preserve">Maurol.
                <lb/>
              pr.4.7.10.
                <lb/>
              14. lib. 5.</note>
            centro O interuallo O A deſcribatur circulus P A Q. </s>
            <s xml:id="echoid-s10039" xml:space="preserve">Manifeſtum eſt, quod
              <lb/>
            circulus P A Q ſectionem M A N exterius continget in A, at circulus P A
              <lb/>
            Q interius priorem ſectionem B A C tanget, vt oſtenſum eſt, igitur coni ſe-
              <lb/>
              <note position="right" xlink:label="note-0305-05" xlink:href="note-0305-05a" xml:space="preserve">Conic.
                <lb/>
              Prop. 12.
                <lb/>
              Addit.
                <lb/>
              lib. 5.</note>
            ctio M A N continget ſectionem B A C interius in A. </s>
            <s xml:id="echoid-s10040" xml:space="preserve">Quod erat oſtenden-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s10041" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10042" xml:space="preserve">Iiſdem poſitis ſi ſectionis T A V, cuius axis A D ſemiſſis eius e-
              <lb/>
              <note position="right" xlink:label="note-0305-06" xlink:href="note-0305-06a" xml:space="preserve">PROP.
                <lb/>
              19. Add.</note>
            recti fuerit A R maior quàm D A, quæ eſt ſingularis breuiſecans ſe-
              <lb/>
            ctionis B A C. </s>
            <s xml:id="echoid-s10043" xml:space="preserve">Dico, quod T A V exterius contingit ſectionem B A C
              <lb/>
            in A.</s>
            <s xml:id="echoid-s10044" xml:space="preserve"/>
          </p>
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