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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          <pb o="25" file="0063" n="63" rhead="Conicor. Lib. V."/>
          <p>
            <s xml:id="echoid-s1489" xml:space="preserve">QVia A E eſt line a breuiſſima, igi-
              <lb/>
              <note position="left" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">b</note>
              <figure xlink:label="fig-0063-01" xlink:href="fig-0063-01a" number="38">
                <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-01"/>
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            tur F E maior eſt illa; </s>
            <s xml:id="echoid-s1490" xml:space="preserve">itaque an-
              <lb/>
            gulus F A E maior eſt, quàm
              <lb/>
              <note position="left" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">c</note>
            A F E; </s>
            <s xml:id="echoid-s1491" xml:space="preserve">Ergo ille eſt multò maior quàm
              <lb/>
            A F D, quare F D maior eſt; </s>
            <s xml:id="echoid-s1492" xml:space="preserve">atque ſic
              <lb/>
            patet quod G E maior ſit quàm E F, & </s>
            <s xml:id="echoid-s1493" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">d</note>
            ideo angulus G F E maior eſt, quàm E
              <lb/>
            G F; </s>
            <s xml:id="echoid-s1494" xml:space="preserve">igitur angulus G F D multò maior
              <lb/>
            eſt, quàm F G D, & </s>
            <s xml:id="echoid-s1495" xml:space="preserve">propterea G D ma-
              <lb/>
            ior eſt, quàm D F, & </s>
            <s xml:id="echoid-s1496" xml:space="preserve">ſimiliter B D,
              <lb/>
            quàm G D, & </s>
            <s xml:id="echoid-s1497" xml:space="preserve">D C, quàm A D, & </s>
            <s xml:id="echoid-s1498" xml:space="preserve">hoc
              <lb/>
            erat propoſitum.</s>
            <s xml:id="echoid-s1499" xml:space="preserve"/>
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        <div xml:id="echoid-div105" type="section" level="1" n="51">
          <head xml:id="echoid-head78" xml:space="preserve">NOTÆ.</head>
          <p style="it">
            <s xml:id="echoid-s1500" xml:space="preserve">SI fuerit menſura A D minor comparata A E, &</s>
            <s xml:id="echoid-s1501" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Senſus propoſitionis
              <lb/>
              <note position="left" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve">a</note>
            clarior ſic reddetur; </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Si fuerit menſura A D minor comparata A E, quæ in
              <lb/>
            ellipſi ſumi debet in axi maiori eius (12.) </s>
            <s xml:id="echoid-s1504" xml:space="preserve">aut ſit pars lineæ breuiſsimæ; </s>
            <s xml:id="echoid-s1505" xml:space="preserve">erit
              <lb/>
            A D minimus ramorum F D, G D, B D, C D, egredientium ex origine eius in
              <lb/>
            omnibus ſectionibus, & </s>
            <s xml:id="echoid-s1506" xml:space="preserve">proximior illi, &</s>
            <s xml:id="echoid-s1507" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1508" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1509" xml:space="preserve">Quia A E eſt linea breuiſſima, igitur, &</s>
            <s xml:id="echoid-s1510" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1511" xml:space="preserve">Vt conſtructio compleatur ſu-
              <lb/>
              <note position="left" xlink:label="note-0063-05" xlink:href="note-0063-05a" xml:space="preserve">b</note>
            biungo: </s>
            <s xml:id="echoid-s1512" xml:space="preserve">Igitur ſi coniungantur rectæ lineæ E F, E G, E C, E B, & </s>
            <s xml:id="echoid-s1513" xml:space="preserve">rectæ lineæ
              <lb/>
            A F, F G, G B, A C erit F E maior, quàm A E.</s>
            <s xml:id="echoid-s1514" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1515" xml:space="preserve">Ergo hic eſt multò maior, quàm A F E, &</s>
            <s xml:id="echoid-s1516" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1517" xml:space="preserve">Senſus clarior reddetur hac
              <lb/>
              <note position="left" xlink:label="note-0063-06" xlink:href="note-0063-06a" xml:space="preserve">c</note>
            ratione: </s>
            <s xml:id="echoid-s1518" xml:space="preserve">Ergo angulus F A E multò maior erit, quàm A F D, qui eſt portio mi-
              <lb/>
            noris anguli, quarè F D ſubtendens angulum maiorem eſt maior, quàm A D.</s>
            <s xml:id="echoid-s1519" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1520" xml:space="preserve">Igitur ipſe multò maior eſt, &</s>
            <s xml:id="echoid-s1521" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1522" xml:space="preserve">Superaddo rationem illationis dicendo;
              <lb/>
            </s>
            <s xml:id="echoid-s1523" xml:space="preserve">
              <note position="left" xlink:label="note-0063-07" xlink:href="note-0063-07a" xml:space="preserve">d</note>
            Et propterea angulus G F D maiorem excedens erit multò maior, quàm F G D,
              <lb/>
            qui portio minoris eſt.</s>
            <s xml:id="echoid-s1524" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1525" xml:space="preserve">Manifeſtum eſt in prima figura propoſitionis 7. </s>
            <s xml:id="echoid-s1526" xml:space="preserve">quando A D eſt portio axis
              <lb/>
            minor comparata, quod tunc ex origine D duo tantummodo rami inter ſe æqua-
              <lb/>
            les ad vtraſque partes axis duci poſſunt ad ſectionem, & </s>
            <s xml:id="echoid-s1527" xml:space="preserve">erunt illi, qui ad ter-
              <lb/>
            minos eiuſdem ordinatim ad axim applicatæ iunguntur ab origine D, vt conſtat
              <lb/>
            ex ſuperiùs dictis.</s>
            <s xml:id="echoid-s1528" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1529" xml:space="preserve">At in ſecunda figura propoſitionis 12. </s>
            <s xml:id="echoid-s1530" xml:space="preserve">poſſunt quidem ab origine D ad ſectio-
              <lb/>
            nem duci hinc indè à breuiſsima D A, aliquando duo tantùm rami inter ſe
              <lb/>
            æquales, aliquando tres, atque etiam quatuor inter ſe æquales, quæcognitio pen-
              <lb/>
            det ex propoſitione 72. </s>
            <s xml:id="echoid-s1531" xml:space="preserve">huius libri.</s>
            <s xml:id="echoid-s1532" xml:space="preserve"/>
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