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-div507" type="section" level="1" n="165">
          <head xml:id="echoid-head217" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s5232" xml:space="preserve">CONI SIMILES ſunt, quorum axes æquè ad baſes inclinati,
              <lb/>
            ad diametros baſium proportionales ſunt.</s>
            <s xml:id="echoid-s5233" xml:space="preserve"/>
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        <div xml:id="echoid-div508" type="section" level="1" n="166">
          <head xml:id="echoid-head218" xml:space="preserve">IX.</head>
          <p>
            <s xml:id="echoid-s5234" xml:space="preserve">Et dicitur conus continere ſectionem, & </s>
            <s xml:id="echoid-s5235" xml:space="preserve">ſectio in cono po-
              <lb/>
            ſita eſse, ſi ſectio tota fuerit in ſuperſicie coni, aut cadat in illa,
              <lb/>
            ſi producatur ex parte baſis.</s>
            <s xml:id="echoid-s5236" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div509" type="section" level="1" n="167">
          <head xml:id="echoid-head219" xml:space="preserve">NOTÆ.</head>
          <p style="it">
            <s xml:id="echoid-s5237" xml:space="preserve">DEſinitiones huius ſeſti libri ferè omnes ſunt Appollonij, in paucis quidem
              <lb/>
            alteratæ ab interprete Arabico: </s>
            <s xml:id="echoid-s5238" xml:space="preserve">quod quidem conſtat teſtimonio Eutocij
              <lb/>
            Aſcalonitæ, qui in tertiam propoſitionem ſecundi æquiponder antium Archime-
              <lb/>
            dis affert definitionem ſimilium portionum conicarum ſectionum, traditam ab
              <lb/>
            Apollonio in eius ſeſto libro: </s>
            <s xml:id="echoid-s5239" xml:space="preserve">& </s>
            <s xml:id="echoid-s5240" xml:space="preserve">ſanè ordo doctrinæ exigebat, vt prius ſectio-
              <lb/>
            nes æquales, & </s>
            <s xml:id="echoid-s5241" xml:space="preserve">ſimiles definirentur, vt poſtea earum symptomata demonſtrari
              <lb/>
            poſſent: </s>
            <s xml:id="echoid-s5242" xml:space="preserve">ſed animaduertendum eſt, hactenus nomen ſectionis conicæ ſignificaſſe
              <lb/>
            quamlibet indeterminatam portionem curuæ lineæ in coni ſuper ſicie ortam ex ſe-
              <lb/>
            ctione alicuius plani non per verticem coni ducti, non conſiderando termiuos eius
              <lb/>
            neque menſuram. </s>
            <s xml:id="echoid-s5243" xml:space="preserve">Segmentum verò ſignificat portionem aliquam ſectionis conicæ
              <lb/>
            determinatæ menſuræ, & </s>
            <s xml:id="echoid-s5244" xml:space="preserve">certis finibus terminatam; </s>
            <s xml:id="echoid-s5245" xml:space="preserve">at multoties ſignificat ſu-
              <lb/>
            perficiem à coniſectione, & </s>
            <s xml:id="echoid-s5246" xml:space="preserve">recta linea eam ſubtendente contenta. </s>
            <s xml:id="echoid-s5247" xml:space="preserve">Igitur ad
              <lb/>
            confuſionem vitandam vocabo huiuſmodi ſuperficiem planam, Mixtam ſuperficiẽ
              <lb/>
            ſectionis conicæ. </s>
            <s xml:id="echoid-s5248" xml:space="preserve">Modò in relatis definitionibus prius quænam coniſectiones vo-
              <lb/>
            cari debeant inter ſe æquales exponit Apollonius.</s>
            <s xml:id="echoid-s5249" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5250" xml:space="preserve">I. </s>
            <s xml:id="echoid-s5251" xml:space="preserve">Et primo; </s>
            <s xml:id="echoid-s5252" xml:space="preserve">Si fuerint duæ quælibet coni-
              <lb/>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="170">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0172-01"/>
              </figure>
            ſectiones B A C, E D F, quarum axes A G,
              <lb/>
            D H; </s>
            <s xml:id="echoid-s5253" xml:space="preserve">vertices verò A, & </s>
            <s xml:id="echoid-s5254" xml:space="preserve">D, & </s>
            <s xml:id="echoid-s5255" xml:space="preserve">ſiquidem
              <lb/>
            intelligatur ſectio B A C ſuperpoſita ſectioni
              <lb/>
            E D F, vt nimirum vertex A ſuper verti-
              <lb/>
            cem D cadat, atque axis A G ſuper axim
              <lb/>
            D H, atque pariter peripheriæ B A C, & </s>
            <s xml:id="echoid-s5256" xml:space="preserve">E
              <lb/>
            D F ſibi mutuò congruant: </s>
            <s xml:id="echoid-s5257" xml:space="preserve">tunc quidem vo-
              <lb/>
            cantur duæ dictæ ſectiones conicæ æquales in-
              <lb/>
            ter ſe. </s>
            <s xml:id="echoid-s5258" xml:space="preserve">V bi notandum eſt, non oportere lon-
              <lb/>
            gitudinem curuæ B A C æqualem eſſe longi-
              <lb/>
            tudini curuæ E D F; </s>
            <s xml:id="echoid-s5259" xml:space="preserve">ſicuti, vt duo anguli
              <lb/>
            rectilinei dicantur æquales, & </s>
            <s xml:id="echoid-s5260" xml:space="preserve">ſibi mu-
              <lb/>
            tuò congruentes, neceſſe non eſt, vt rectæ li-
              <lb/>
            neæ, angulos continentes, ſint æquales longi-
              <lb/>
            tudine, dummodo certum ſit, quod lineæ ipſæ
              <lb/>
            vlterius productæ ſemper ſibi mutuò congruant; </s>
            <s xml:id="echoid-s5261" xml:space="preserve">ſic pariter peripheriæ conicarũ
              <lb/>
            ſectionum A B, & </s>
            <s xml:id="echoid-s5262" xml:space="preserve">D E, ſi vlterius producantur, ſemper ſibi mutuò congruent.</s>
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