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

Page concordance

< >
Scan Original
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
< >
page |< < (26) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div105" type="section" level="1" n="51">
          <pb o="26" file="0064" n="64" rhead="Apollonij Pergæi"/>
        </div>
        <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"/>
          </p>
        </div>
      </text>
    </echo>
Impressum