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-s9866" xml:space="preserve">
              <pb o="262" file="0300" n="300" rhead="Apollonij Pergæi"/>
            idem diametrum M A; </s>
            <s xml:id="echoid-s9867" xml:space="preserve">erunt igitur tangentes
              <lb/>
              <figure xlink:label="fig-0300-01" xlink:href="fig-0300-01a" number="347">
                <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0300-01"/>
              </figure>
            A D, & </s>
            <s xml:id="echoid-s9868" xml:space="preserve">M V parallelæ eidem N O, erat au-
              <lb/>
            tem E B parallela ipſi N O; </s>
            <s xml:id="echoid-s9869" xml:space="preserve">igitur duæ cir-
              <lb/>
            culum tangentes A B, & </s>
            <s xml:id="echoid-s9870" xml:space="preserve">M V parallelæ ſunt
              <lb/>
            idem E B; </s>
            <s xml:id="echoid-s9871" xml:space="preserve">& </s>
            <s xml:id="echoid-s9872" xml:space="preserve">propterea A D, & </s>
            <s xml:id="echoid-s9873" xml:space="preserve">E B in eo-
              <lb/>
            dem ſunt plano, vtrumque conum tangente
              <lb/>
            cum per vertices E, & </s>
            <s xml:id="echoid-s9874" xml:space="preserve">B ducatur, & </s>
            <s xml:id="echoid-s9875" xml:space="preserve">per A
              <lb/>
            D baſis circulum tangentem. </s>
            <s xml:id="echoid-s9876" xml:space="preserve">Eadem ratione
              <lb/>
            M V, & </s>
            <s xml:id="echoid-s9877" xml:space="preserve">E B ineodem plano vtrumque conum
              <lb/>
            tangente exiſtent. </s>
            <s xml:id="echoid-s9878" xml:space="preserve">Si verò recta E B plano cir-
              <lb/>
            culi non æquidiſtat producta alicubi planum
              <lb/>
            eiuſdem circuli ſecabit extra circulum ipſum,
              <lb/>
            vt in γ, & </s>
            <s xml:id="echoid-s9879" xml:space="preserve">tunc quidem à puncto γ extra,
              <lb/>
            circulum poſito ducantur duæ contingentes γ A,
              <lb/>
            & </s>
            <s xml:id="echoid-s9880" xml:space="preserve">γ M. </s>
            <s xml:id="echoid-s9881" xml:space="preserve">Manifeſtum eſt, rectas lineas A γ,
              <lb/>
            B E in eodem plano iacere: </s>
            <s xml:id="echoid-s9882" xml:space="preserve">tranſit verò præ-
              <lb/>
            dictum planum per vertices B, & </s>
            <s xml:id="echoid-s9883" xml:space="preserve">E duorum
              <lb/>
            conorum, atque per γ A tangentem circulum
              <lb/>
            baſis communis; </s>
            <s xml:id="echoid-s9884" xml:space="preserve">igitur planum A E B vtrum-
              <lb/>
            que conum contingit. </s>
            <s xml:id="echoid-s9885" xml:space="preserve">Eodem modo planum E
              <lb/>
            B M ex altera parte vtrumq; </s>
            <s xml:id="echoid-s9886" xml:space="preserve">conum tanget.
              <lb/>
            </s>
            <s xml:id="echoid-s9887" xml:space="preserve">Et hoc erat faciendum.</s>
            <s xml:id="echoid-s9888" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9889" xml:space="preserve">In qualibet coniſectione H A I
              <lb/>
              <note position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">PROP
                <lb/>
              16.
                <lb/>
              Addit</note>
            cuius diameter A L non ſit axis,
              <lb/>
            per eius verticem A aliam coniſe-
              <lb/>
            ctionem in eodem plano deſcribere,
              <lb/>
            quæ priorem abſcindat, atque eadem
              <lb/>
            recta linea vtramq; </s>
            <s xml:id="echoid-s9890" xml:space="preserve">ſectionem tangat
              <lb/>
            in puncto mutuæ earum abſcisſionis.</s>
            <s xml:id="echoid-s9891" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9892" xml:space="preserve">Sicut in conſtructione prop. </s>
            <s xml:id="echoid-s9893" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9894" xml:space="preserve">& </s>
            <s xml:id="echoid-s9895" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s9896" xml:space="preserve">addit. </s>
            <s xml:id="echoid-s9897" xml:space="preserve">factum eſt, deſcribatur conus B A
              <lb/>
            C comprehendens ſectionem H A I, cu
              <lb/>
            ius vertex B baſis circulus A M C per
              <lb/>
            ſectionis verticem A ductus, & </s>
            <s xml:id="echoid-s9898" xml:space="preserve">trian-
              <lb/>
            gulum per axim B A C efficiat diame-
              <lb/>
            trum A L: </s>
            <s xml:id="echoid-s9899" xml:space="preserve">& </s>
            <s xml:id="echoid-s9900" xml:space="preserve">in duobus circulis æqui-
              <lb/>
            diſtantibus A C M, & </s>
            <s xml:id="echoid-s9901" xml:space="preserve">in eo, qui per
              <lb/>
            ſectionis baſim H I ducitur idẽ planum
              <lb/>
            ſectionis conicæ deſignet duas parallelas
              <lb/>
            A D, H I, & </s>
            <s xml:id="echoid-s9902" xml:space="preserve">planum trianguli per axim
              <lb/>
            efficiat circulorũ diamctros C A, & </s>
            <s xml:id="echoid-s9903" xml:space="preserve">eum,
              <lb/>
            qui per L ducitur æquidiſtantes inter ſe: </s>
            <s xml:id="echoid-s9904" xml:space="preserve">
              <lb/>
            ergo ſicuti baſis H I perpendicularis eſt
              <lb/>
            ad circuli diametrum per L ductam, ſeu
              <lb/>
            ad baſim trianguli per axim, ita D </s>
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