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">
          <pb o="270" file="0308" n="308" rhead="Apollonij Pergæi Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s10100" xml:space="preserve">Sectionum conicarum circa axim communem poſitarum datam coniſe-
              <lb/>
              <note position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">PROP.
                <lb/>
              22.
                <lb/>
              Addit.</note>
            ctionem abſcindentium non in eius vertice, quas omnes eadem recta li-
              <lb/>
            nea contingat, erunt ſingulares tantummodo parabolæ, & </s>
            <s xml:id="echoid-s10101" xml:space="preserve">circulus, elli-
              <lb/>
            pſes verò, & </s>
            <s xml:id="echoid-s10102" xml:space="preserve">hyperbole erunt infinitæ.</s>
            <s xml:id="echoid-s10103" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10104" xml:space="preserve">Quoniam circa communem axim D
              <lb/>
              <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a" number="356">
                <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0308-01"/>
              </figure>
            A conſtitui poßunt parabolæ, circulus,
              <lb/>
            infinitæ hyperbolæ, & </s>
            <s xml:id="echoid-s10105" xml:space="preserve">infinitæ ellipſes
              <lb/>
              <note position="left" xlink:label="note-0308-02" xlink:href="note-0308-02a" xml:space="preserve">Prop. 17.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            habentes ſemilatus rectum axis æqualẽ
              <lb/>
            ſingulari breuiſecanti D A in ſectione
              <lb/>
            conica B A C educto, & </s>
            <s xml:id="echoid-s10106" xml:space="preserve">hæ omnes ab-
              <lb/>
              <note position="left" xlink:label="note-0308-03" xlink:href="note-0308-03a" xml:space="preserve">Prop. 21.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ſcindunt coniſectionem B A C in A.
              <lb/>
            </s>
            <s xml:id="echoid-s10107" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s10108" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10109" xml:space="preserve">Hinc colligitur dari non poſſe coniſe-
              <lb/>
            ctionem minimam extrinſecus tangen-
              <lb/>
            tium, neque maximam intrinſecus tã-
              <lb/>
            gentium eandem coniſectionem in pun-
              <lb/>
            cto A extra verticem axis poſito.</s>
            <s xml:id="echoid-s10110" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10111" xml:space="preserve">Nam quælibet coniſectio, cuius ſemie-
              <lb/>
            rectum axis minus eſt breuiſecante ſingulari D A intrinſecus tangit ſectionem
              <lb/>
              <note position="left" xlink:label="note-0308-04" xlink:href="note-0308-04a" xml:space="preserve">Prop. 18.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            B A C in A, & </s>
            <s xml:id="echoid-s10112" xml:space="preserve">ſi ſemierectum maius fuerit eadem D A extrinſecus eandem
              <lb/>
            ſectionem B A C continget, neque vnquam ceſſant prædicti contactus extrin-
              <lb/>
              <note position="left" xlink:label="note-0308-05" xlink:href="note-0308-05a" xml:space="preserve">Prop. 19.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ſeci, vel intrinſeci quouſque ſemierectum axis efficitur æquale breuiſecanti D
              <lb/>
            A: </s>
            <s xml:id="echoid-s10113" xml:space="preserve">at tunc non amplius contingit, ſed ſecat eam in A. </s>
            <s xml:id="echoid-s10114" xml:space="preserve">Quare patet propoſi-
              <lb/>
              <note position="left" xlink:label="note-0308-06" xlink:href="note-0308-06a" xml:space="preserve">Prop. 21.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            tum.</s>
            <s xml:id="echoid-s10115" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10116" xml:space="preserve">Conſtat etiam quod parabolarum vnica tantummodò, & </s>
            <s xml:id="echoid-s10117" xml:space="preserve">circulorum vnicus
              <lb/>
            etiam abſcindit coniſectionem B A C in A, & </s>
            <s xml:id="echoid-s10118" xml:space="preserve">contingit eandem contingentem
              <lb/>
            A G in A.</s>
            <s xml:id="echoid-s10119" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10120" xml:space="preserve">At hyperbolarum, atque ellipſium abſcindentium eandem ſectionem B A C in
              <lb/>
            A, quas omnes eadem recta linea A G tangit in A non poteſt affignari maxi-
              <lb/>
            ma, neque minima.</s>
            <s xml:id="echoid-s10121" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10122" xml:space="preserve">Nam vt dictum eſt ad 17. </s>
            <s xml:id="echoid-s10123" xml:space="preserve">Additarum huius libri infinitæ hyperbolæ ſe ſe
              <lb/>
            contingentes in vertice axis deſinunt in parabolam vnicam, & </s>
            <s xml:id="echoid-s10124" xml:space="preserve">poſt parabolam
              <lb/>
            interius ſe ſe ſucceſſiuè contingunt infinitæ ellipſes ad axim maiorem adiacen-
              <lb/>
            tes, quæ deſinunt in circulum vnicum, ac poſt circulum interius eum contin-
              <lb/>
            gunt inſinitæ ellipſes ad axim minorem adiacentes, quarum omnium ſemiere-
              <lb/>
            cta latera axium æqualia ſunt breuiſecanti ſingulari D A datæ ſectionis B A C.
              <lb/>
            </s>
            <s xml:id="echoid-s10125" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s10126" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div839" type="section" level="1" n="249">
          <head xml:id="echoid-head312" xml:space="preserve">LIBRI SEXTI FINIS.</head>
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