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-s10058" xml:space="preserve">
              <pb o="269" file="0307" n="307" rhead="Conicor. Lib. VI."/>
            circulus A M C, ita vt idem planum per vertices conorum B, & </s>
            <s xml:id="echoid-s10059" xml:space="preserve">E, & </s>
            <s xml:id="echoid-s10060" xml:space="preserve">per
              <lb/>
            A D contingentem eundem circulum baſis extenſum tangat vtrumque conum
              <lb/>
            in lateribus A B, & </s>
            <s xml:id="echoid-s10061" xml:space="preserve">A E. </s>
            <s xml:id="echoid-s10062" xml:space="preserve">Poſiea ſi S A Z optatur parabole ducatur in plano
              <lb/>
            A E C ex C recta C N parallela A K axi ſectionis F A G; </s>
            <s xml:id="echoid-s10063" xml:space="preserve">ſi verò S A Z
              <lb/>
            dſideratur hyperbole, aut ellipſis producatur axis A K in directum extra aut intra
              <lb/>
            ſectionem, & </s>
            <s xml:id="echoid-s10064" xml:space="preserve">in recta linea K A O ſecetur portio A O æqualis lateri tranſuer-
              <lb/>
            ſo ſectionis S A Z, coniungaturque recta linea C O, ſecans E A in N (eo
              <lb/>
            quod axis K A in plano A E C erecto ad circulũ A M C, exiſtit) & </s>
            <s xml:id="echoid-s10065" xml:space="preserve">vertice N
              <lb/>
            fiat alter conus N C A. </s>
            <s xml:id="echoid-s10066" xml:space="preserve">Manifeſtum eſt in cono recto E A C deſignari ab eo-
              <lb/>
            dem plano D A K circulum F A G, at in cono recto N A C efficietur alia ſe-
              <lb/>
            ctio conica circa communem axim A K, quæ ſe ſe mutuo, & </s>
            <s xml:id="echoid-s10067" xml:space="preserve">eandem rectam
              <lb/>
            lineam D A tangent, in communi vertice A, atque circuli F A G, & </s>
            <s xml:id="echoid-s10068" xml:space="preserve">ſectio-
              <lb/>
              <note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">Prop. 17.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            nis genitæ in cono N A C duo latera recta erunt æqualia, & </s>
            <s xml:id="echoid-s10069" xml:space="preserve">propterea ſectio-
              <lb/>
            nis genitæ in cono N A C ſemilatus rectum æquale erit radio circuli γ ſeu di-
              <lb/>
            midio erecti ſectionis H A I, & </s>
            <s xml:id="echoid-s10070" xml:space="preserve">ſi habuerit latus tranſuerſum erit æquale A
              <lb/>
            O; </s>
            <s xml:id="echoid-s10071" xml:space="preserve">ergo ſectio genita in cono N A C, & </s>
            <s xml:id="echoid-s10072" xml:space="preserve">ſectio S A Z circa communem axim
              <lb/>
            A K habent latus rectum cummune duplum ipſius γ, & </s>
            <s xml:id="echoid-s10073" xml:space="preserve">etiam commune latus
              <lb/>
            tranſuerſum A O: </s>
            <s xml:id="echoid-s10074" xml:space="preserve">Quare ſectio genita in cono N A C, & </s>
            <s xml:id="echoid-s10075" xml:space="preserve">S A Z æquales ſunt
              <lb/>
              <note position="right" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">10. huius.</note>
            inter ſe, & </s>
            <s xml:id="echoid-s10076" xml:space="preserve">congruentes; </s>
            <s xml:id="echoid-s10077" xml:space="preserve">quapropter idem planum D A K, quod efficit in cono
              <lb/>
            Scaleno B A C ſectionem H A I, deſignat quoque in cono recto N A C ſectio-
              <lb/>
            nem S A Z: </s>
            <s xml:id="echoid-s10078" xml:space="preserve">habent verò hi duo coni circulum baſis communem, & </s>
            <s xml:id="echoid-s10079" xml:space="preserve">idem pla-
              <lb/>
            num per contingentem A D, & </s>
            <s xml:id="echoid-s10080" xml:space="preserve">per vertices B, & </s>
            <s xml:id="echoid-s10081" xml:space="preserve">N ductum vtrumque co-
              <lb/>
            num tangit; </s>
            <s xml:id="echoid-s10082" xml:space="preserve">igitur (vt demonſtratum eſt in 16. </s>
            <s xml:id="echoid-s10083" xml:space="preserve">Addit. </s>
            <s xml:id="echoid-s10084" xml:space="preserve">huius) ſectio conica
              <lb/>
            S A Z abſcindet aliam ſectionem H A I, & </s>
            <s xml:id="echoid-s10085" xml:space="preserve">ambæ tangentur ab eadem recta
              <lb/>
            linea D A in eodem puncto mutuæ abſciſſionis A. </s>
            <s xml:id="echoid-s10086" xml:space="preserve">Quod erat propoſitum.</s>
            <s xml:id="echoid-s10087" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10088" xml:space="preserve">Si in qualibet coniſectione B A C
              <lb/>
              <figure xlink:label="fig-0307-01" xlink:href="fig-0307-01a" number="355">
                <image file="0307-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0307-01"/>
              </figure>
              <note position="right" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">PROP.
                <lb/>
              21.
                <lb/>
              Addit.</note>
            ducatur breuiſecans ſingularis D A,
              <lb/>
            & </s>
            <s xml:id="echoid-s10089" xml:space="preserve">quælibet alia coniſectio I A K,
              <lb/>
            cuius axis ſit D A, atque ſemiſſis
              <lb/>
            lateris recti axis ſectionis I A K ſit
              <lb/>
            æqualis breuiſecanti D A. </s>
            <s xml:id="echoid-s10090" xml:space="preserve">Dico,
              <lb/>
            ſectionem I A K contingere eandem
              <lb/>
            rectam lineam G A, quàm tangit
              <lb/>
            ſectio B A C, & </s>
            <s xml:id="echoid-s10091" xml:space="preserve">abſcindere reli-
              <lb/>
            quam coniſectionem in eodem pun-
              <lb/>
            cto A.</s>
            <s xml:id="echoid-s10092" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10093" xml:space="preserve">Deſcribatur centro D interuallo D
              <lb/>
            A circulus T A S conſtat (ex prop. </s>
            <s xml:id="echoid-s10094" xml:space="preserve">10. </s>
            <s xml:id="echoid-s10095" xml:space="preserve">additarum libri quinti) circulum T
              <lb/>
            A S ſecare coniſectionem B A C in A, cumque circa eundem axim D A po-
              <lb/>
            nantur circulus T A S, atque coniſectio I A K, cuius lateris recti ſemiſſis æ-
              <lb/>
            qualis eſt D A radio circuli T A S, ergo coniſectio I A K abſcindit coniſectio-
              <lb/>
              <note position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">20. addit.
                <lb/>
              huius.</note>
            nem B A C in eodem puncto A, in quo ſecatur à circulo T A S, & </s>
            <s xml:id="echoid-s10096" xml:space="preserve">tanguntur
              <lb/>
            ab eadem contingente G A in puncto A. </s>
            <s xml:id="echoid-s10097" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s10098" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10099" xml:space="preserve"/>
          </p>
        </div>
      </text>
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