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-div128" type="section" level="1" n="57">
          <pb o="30" file="0068" n="68" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div130" type="section" level="1" n="58">
          <head xml:id="echoid-head89" xml:space="preserve">NOTÆ.</head>
          <p style="it">
            <s xml:id="echoid-s1667" xml:space="preserve">EDucamus itaque duas perpendiculares, &</s>
            <s xml:id="echoid-s1668" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">Educamus itaque ex pun-
              <lb/>
              <note position="right" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">a</note>
            ctis B, G duas G L, B I perpendiculares ad axim ei occurrentes in L, I.
              <lb/>
            </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Et LG maior eſt, quàm B I, &</s>
            <s xml:id="echoid-s1671" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1672" xml:space="preserve">Subiungo: </s>
            <s xml:id="echoid-s1673" xml:space="preserve">Eo quod potentialis G L ma-
              <lb/>
              <note position="right" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">b</note>
            gis recedit à vertice, quàm B I; </s>
            <s xml:id="echoid-s1674" xml:space="preserve">ſi iam ducatur B M parallela axi in parabola,
              <lb/>
            & </s>
            <s xml:id="echoid-s1675" xml:space="preserve">ex centro educta in reliquis ſectionibus, ſecans G L in M, coniungaturque H
              <lb/>
            M, erit in parabola M L minor quàm G L, & </s>
            <s xml:id="echoid-s1676" xml:space="preserve">æqualis B I, & </s>
            <s xml:id="echoid-s1677" xml:space="preserve">ideo angulus M
              <lb/>
            H L minor erit angulo G H L, & </s>
            <s xml:id="echoid-s1678" xml:space="preserve">æqualis angulo F, & </s>
            <s xml:id="echoid-s1679" xml:space="preserve">propterea angulus F mi-
              <lb/>
            nor eſt, quàm G H L.</s>
            <s xml:id="echoid-s1680" xml:space="preserve"/>
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          <figure number="45">
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          <p>
            <s xml:id="echoid-s1681" xml:space="preserve">Si verò ſectio fuerit hyperbole, aut ellipſis, &</s>
            <s xml:id="echoid-s1682" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Addo: </s>
            <s xml:id="echoid-s1684" xml:space="preserve">Manifeſtum eſt
              <lb/>
              <note position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">31. lib. I.</note>
              <note position="right" xlink:label="note-0068-04" xlink:href="note-0068-04a" xml:space="preserve">C</note>
            rectam B D ex centro ductam ſectionem ſecare in B, & </s>
            <s xml:id="echoid-s1685" xml:space="preserve">propterea occurrere po-
              <lb/>
            tentiali G L à vertice remotiori, quàm B I inter puncta G, & </s>
            <s xml:id="echoid-s1686" xml:space="preserve">L, & </s>
            <s xml:id="echoid-s1687" xml:space="preserve">erit F I,
              <lb/>
            & </s>
            <s xml:id="echoid-s1688" xml:space="preserve">cætera.</s>
            <s xml:id="echoid-s1689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1690" xml:space="preserve">Erit ID ad LD, nempe B I ad M L, &</s>
            <s xml:id="echoid-s1691" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">Addo (propter parallelas B I,
              <lb/>
              <note position="right" xlink:label="note-0068-05" xlink:href="note-0068-05a" xml:space="preserve">d</note>
            M L, & </s>
            <s xml:id="echoid-s1693" xml:space="preserve">ſimilitudincm triangulorum D B I, & </s>
            <s xml:id="echoid-s1694" xml:space="preserve">D M L.)</s>
            <s xml:id="echoid-s1695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1696" xml:space="preserve">Quia angulus A F B minor eſt, quàm angulus A H G, &</s>
            <s xml:id="echoid-s1697" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">Addo: </s>
            <s xml:id="echoid-s1699" xml:space="preserve">Et
              <lb/>
              <note position="right" xlink:label="note-0068-06" xlink:href="note-0068-06a" xml:space="preserve">e</note>
            ſumpto communi angulo F H N erunt A F B, ſeu H F N, & </s>
            <s xml:id="echoid-s1700" xml:space="preserve">F H N ſimul ſumpti
              <lb/>
            minores duobus angulis G H A, F H N, qui duobus rectis æquales ſunt; </s>
            <s xml:id="echoid-s1701" xml:space="preserve">quare
              <lb/>
            B F, G H, concurrunt ad partes F, & </s>
            <s xml:id="echoid-s1702" xml:space="preserve">H, vt in N.</s>
            <s xml:id="echoid-s1703" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1704" xml:space="preserve">Pro intelligentia ſequentium propoſitionum hæc præmitti debent.</s>
            <s xml:id="echoid-s1705" xml:space="preserve"/>
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        <div xml:id="echoid-div135" type="section" level="1" n="59">
          <head xml:id="echoid-head90" xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:id="echoid-s1706" xml:space="preserve">Habeat A ad B maiorem proportionem, quàm C ad D. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">Dico, re-
              <lb/>
            ctangulum ſub extremis A, D contentum maius eſſe eo, quod ſub me-
              <lb/>
            dijs B, C continetur, & </s>
            <s xml:id="echoid-s1708" xml:space="preserve">è conuerſo.</s>
            <s xml:id="echoid-s1709" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1710" xml:space="preserve">Flat vt C ad D, ita E ad B; </s>
            <s xml:id="echoid-s1711" xml:space="preserve">patet ex elementis, A excedere ipſam E; </s>
            <s xml:id="echoid-s1712" xml:space="preserve">qua-
              <lb/>
            re rectangulum A D maius erit rectangulo E D: </s>
            <s xml:id="echoid-s1713" xml:space="preserve">eſt verò rectangulum </s>
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