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-div105" type="section" level="1" n="51">
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        <div xml:id="echoid-div110" type="section" level="1" n="52">
          <head xml:id="echoid-head79" xml:space="preserve">SECTIO QVINTA</head>
          <head xml:id="echoid-head80" xml:space="preserve">Continens XI. Propoſit. Apollonij.</head>
          <p>
            <s xml:id="echoid-s1533" xml:space="preserve">LInearum egredientium ex D centro ellipſis A B C, breuiſſi-
              <lb/>
            ma eſt ſemiaxis minor rectus
              <lb/>
            illius, qui ſit B D, maxima verò eſt
              <lb/>
              <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a" number="39">
                <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0064-01"/>
              </figure>
            ſemiaxis tranſuerſus, qui ſit A D, & </s>
            <s xml:id="echoid-s1534" xml:space="preserve">
              <lb/>
            propinquiores maiori ſunt maiores
              <lb/>
            remotioribus, vt H D, quam G D,
              <lb/>
            & </s>
            <s xml:id="echoid-s1535" xml:space="preserve">quadratum cuiuslibet rami, vt G
              <lb/>
            D (exempli gratia) excedit quadra-
              <lb/>
              <note position="right" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">a</note>
            tum breuiſſimę B D exemplari appli-
              <lb/>
            cato ad inuerſam illius I D.</s>
            <s xml:id="echoid-s1536" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1537" xml:space="preserve">EDucamus itaque E A æqualem A D, & </s>
            <s xml:id="echoid-s1538" xml:space="preserve">abſcindamus ex illa A F ęqua-
              <lb/>
              <note position="right" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">b</note>
            lem dimidio erecti, & </s>
            <s xml:id="echoid-s1539" xml:space="preserve">iungamus D F, D E, & </s>
            <s xml:id="echoid-s1540" xml:space="preserve">perducamus ex G, H
              <lb/>
            perpendiculares ad D A, & </s>
            <s xml:id="echoid-s1541" xml:space="preserve">ſint G I M, H L N. </s>
            <s xml:id="echoid-s1542" xml:space="preserve">Quia quadratum G I æ-
              <lb/>
              <note position="right" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">c</note>
            quale eſt duplo trapezij I F (prima ex quinto) & </s>
            <s xml:id="echoid-s1543" xml:space="preserve">quadratum I D eſt æqua-
              <lb/>
            le duplo trianguli I D M, eo quod I D eſt æqualis I M, erit quadratum
              <lb/>
              <note position="right" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">d</note>
            D G æquale duplo trianguli A D F (quod eſt æquale quadrato B D (2. </s>
            <s xml:id="echoid-s1544" xml:space="preserve">ex
              <lb/>
            quinto) vnà cum duplo trianguli Q M D, quod eſt æquale rectangulo Q
              <lb/>
            P; </s>
            <s xml:id="echoid-s1545" xml:space="preserve">igitur quadrati G D exceſſus ſupra quadratum B D eſt æqualis plano
              <lb/>
            Q P, & </s>
            <s xml:id="echoid-s1546" xml:space="preserve">quia D A, nempe E A ad A F eſt, vt D I, nempe M I ad I Q,
              <lb/>
              <note position="right" xlink:label="note-0064-05" xlink:href="note-0064-05a" xml:space="preserve">e</note>
            & </s>
            <s xml:id="echoid-s1547" xml:space="preserve">per conuerſionem rationis A E ad E F, ſcilicet dimidium tranſuerſæ
              <lb/>
            ad illius exceſſum ſuper A F dimidium erecti, eſt, vt M I, nempe M P
              <lb/>
            ad M Q; </s>
            <s xml:id="echoid-s1548" xml:space="preserve">igitur planum Q P ſimile eſt figuræ comparatæ, & </s>
            <s xml:id="echoid-s1549" xml:space="preserve">M P æqua-
              <lb/>
            lis eſt D I. </s>
            <s xml:id="echoid-s1550" xml:space="preserve">Similiter patet, quod quadratum D H excedit quadratum B
              <lb/>
              <note position="left" xlink:label="note-0064-06" xlink:href="note-0064-06a" xml:space="preserve">Def. 8. 9.
                <lb/>
              huius.</note>
            D exemplari applicato ad D L, & </s>
            <s xml:id="echoid-s1551" xml:space="preserve">quadratum D A ſuperat quadratum
              <lb/>
            B D exemplari applicato ad D A: </s>
            <s xml:id="echoid-s1552" xml:space="preserve">Eſt verò D I minor, quàm D L, & </s>
            <s xml:id="echoid-s1553" xml:space="preserve">
              <lb/>
            D L, quàm D A; </s>
            <s xml:id="echoid-s1554" xml:space="preserve">igitur B D (quæ eſt dimidium recti) minor eſt, quàm
              <lb/>
              <note position="right" xlink:label="note-0064-07" xlink:href="note-0064-07a" xml:space="preserve">f</note>
            G D, & </s>
            <s xml:id="echoid-s1555" xml:space="preserve">G D, quàm D H, & </s>
            <s xml:id="echoid-s1556" xml:space="preserve">D H quàm D A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1557" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div113" type="section" level="1" n="53">
          <head xml:id="echoid-head81" xml:space="preserve">NOTÆ.</head>
          <p style="it">
            <s xml:id="echoid-s1558" xml:space="preserve">ET debet eſſe linea breuiſſima perpendicularis ad menſuram, nempe B
              <lb/>
              <note position="right" xlink:label="note-0064-08" xlink:href="note-0064-08a" xml:space="preserve">a</note>
            D perpendicularis D A, &</s>
            <s xml:id="echoid-s1559" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1560" xml:space="preserve">Hæc omnino expungi debent, tanquam
              <lb/>
            ſuperuacanea, axes enim eſſe nequeunt, niſi ad inuicem perpendiculares ſint;
              <lb/>
            </s>
            <s xml:id="echoid-s1561" xml:space="preserve">quare cenſeo ab aliquo verba illa addita textui Apollonij fuiſſe.</s>
            <s xml:id="echoid-s1562" xml:space="preserve"/>
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