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-div113" type="section" level="1" n="53">
          <pb o="27" file="0065" n="65" rhead="Conicor. Lib. V."/>
          <p>
            <s xml:id="echoid-s1563" xml:space="preserve">Educamus itaque E A, &</s>
            <s xml:id="echoid-s1564" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1565" xml:space="preserve">Lego: </s>
            <s xml:id="echoid-s1566" xml:space="preserve">Educamus itaq; </s>
            <s xml:id="echoid-s1567" xml:space="preserve">E A perpendicularem, & </s>
            <s xml:id="echoid-s1568" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">b</note>
            æqualem A D.</s>
            <s xml:id="echoid-s1569" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1570" xml:space="preserve">Et perducamus ex G, H perpendiculares, &</s>
            <s xml:id="echoid-s1571" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1572" xml:space="preserve">Et perducamus ex G, H
              <lb/>
              <note position="left" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">c</note>
            perpendiculares ad D A, & </s>
            <s xml:id="echoid-s1573" xml:space="preserve">ſint H L N, & </s>
            <s xml:id="echoid-s1574" xml:space="preserve">G I M, quæ ſecent F D in Q, & </s>
            <s xml:id="echoid-s1575" xml:space="preserve">D
              <lb/>
            E in M, & </s>
            <s xml:id="echoid-s1576" xml:space="preserve">N, atque à punctis Q, M educantur M P, Q O, parallelæ D A,
              <lb/>
            quæ ſecent rectum axem B D in O, P. </s>
            <s xml:id="echoid-s1577" xml:space="preserve">Addidi hæc poſtrema verba, vt conſtru-
              <lb/>
            ctio completa ſit.</s>
            <s xml:id="echoid-s1578" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1579" xml:space="preserve">Eo quod I D eſt æqualis I M, &</s>
            <s xml:id="echoid-s1580" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1581" xml:space="preserve">Quoniam ſicuti in triangulo D A E
              <lb/>
              <note position="left" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">d</note>
            ſimili triangulo D I M (propter angulum D communem, & </s>
            <s xml:id="echoid-s1582" xml:space="preserve">rectos angulos ad I,
              <lb/>
            & </s>
            <s xml:id="echoid-s1583" xml:space="preserve">A) latus D A æquale erat E A, ita latus D I æquale eſt I M.</s>
            <s xml:id="echoid-s1584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1585" xml:space="preserve">Nempe M I ad I Q, & </s>
            <s xml:id="echoid-s1586" xml:space="preserve">è contra, &</s>
            <s xml:id="echoid-s1587" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1588" xml:space="preserve">Lego: </s>
            <s xml:id="echoid-s1589" xml:space="preserve">Nempe M I ad I Q, & </s>
            <s xml:id="echoid-s1590" xml:space="preserve">per
              <lb/>
              <note position="left" xlink:label="note-0065-04" xlink:href="note-0065-04a" xml:space="preserve">e</note>
            conuerſionem rationis.</s>
            <s xml:id="echoid-s1591" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1592" xml:space="preserve">Cumque B D ſit dimidium axis recti erit perpendicularis ad A D men-
              <lb/>
              <note position="left" xlink:label="note-0065-05" xlink:href="note-0065-05a" xml:space="preserve">f</note>
            ſuram, &</s>
            <s xml:id="echoid-s1593" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1594" xml:space="preserve">Hæc verba poſtrema pariter expungi debent, niſi fortè corollarium
              <lb/>
            propoſitionis exponunt, & </s>
            <s xml:id="echoid-s1595" xml:space="preserve">tunc textus ſic reſtitui deberet. </s>
            <s xml:id="echoid-s1596" xml:space="preserve">Ex dictis conſtat, li-
              <lb/>
            neam breuiſsimam è centro ellipſis ad ſectionem ductam, perpendicularem eße
              <lb/>
            ad axim eius maiorem.</s>
            <s xml:id="echoid-s1597" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1598" xml:space="preserve">Manifeſtum eſt ex centro ellipſis ad ſectionem duci non poſſe plures, quàm
              <lb/>
            quatuor ramos inter ſe æquales, neque pauciores duobus; </s>
            <s xml:id="echoid-s1599" xml:space="preserve">tres autem nequaquam;
              <lb/>
            </s>
            <s xml:id="echoid-s1600" xml:space="preserve">nam duæ medietates cuiuslibet axis æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s1601" xml:space="preserve">quatuor rami ad
              <lb/>
            extremitates duarum applicatarum ad axim æqualiter è centro diſtantium ducti
              <lb/>
            æquales ſunt inter ſe.</s>
            <s xml:id="echoid-s1602" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div120" type="section" level="1" n="54">
          <head xml:id="echoid-head82" xml:space="preserve">SECTIO SEXTA</head>
          <head xml:id="echoid-head83" xml:space="preserve">Continens Propoſit. XIII. XIV. XV. Apollonij.</head>
          <p>
            <s xml:id="echoid-s1603" xml:space="preserve">OStendamus modò cõ-
              <lb/>
            uerſum harum pro-
              <lb/>
              <figure xlink:label="fig-0065-01" xlink:href="fig-0065-01a" number="40">
                <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/>
              </figure>
            poſitionum; </s>
            <s xml:id="echoid-s1604" xml:space="preserve">& </s>
            <s xml:id="echoid-s1605" xml:space="preserve">eſt, quod li-
              <lb/>
            nea breuiſſima B F continet
              <lb/>
            cum ſua menſura A F angu-
              <lb/>
            lum acutum, vt B F A in
              <lb/>
            omnibus ſectionibus, & </s>
            <s xml:id="echoid-s1606" xml:space="preserve">el-
              <lb/>
            lipſi (ſi tamen non egre-
              <lb/>
            diatur ex eius centro) eiuſ-
              <lb/>
            que potentialis abſcindet
              <lb/>
            menſuram (13) in parabola æqualem comparatæ (14) & </s>
            <s xml:id="echoid-s1607" xml:space="preserve">in
              <lb/>
              <note position="left" xlink:label="note-0065-06" xlink:href="note-0065-06a" xml:space="preserve">a</note>
            hyperbola (15) & </s>
            <s xml:id="echoid-s1608" xml:space="preserve">ellipſi lineam, ad quam inuerſa eſt, vt pro-
              <lb/>
            portio figuræ.</s>
            <s xml:id="echoid-s1609" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1610" xml:space="preserve">SIt centrum D, & </s>
            <s xml:id="echoid-s1611" xml:space="preserve">dimidium erecti A C. </s>
            <s xml:id="echoid-s1612" xml:space="preserve">Quia B F eſt linea breuiſſima,
              <lb/>
            erit A F maior quàm A C, eo quòd ſi eſſet æqualis (4. </s>
            <s xml:id="echoid-s1613" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1614" xml:space="preserve">ex </s>
          </p>
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    </echo>
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