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
81 43
82 44
83 45
84 46
85 47
86 48
87 49
88 50
89 51
90 52
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
< >
page |< < (91) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div352" type="section" level="1" n="114">
          <pb o="91" file="0129" n="129" rhead="Conicor. Lib. V."/>
          <figure number="112">
            <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3734" xml:space="preserve">Quoniam I K, H M ſunt duæ breuiſſimæ conſtat, quod E I maximus
              <lb/>
              <note position="left" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">b</note>
            ſit ramorum cadentium ad illam ſectionem (72. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3736" xml:space="preserve">& </s>
            <s xml:id="echoid-s3737" xml:space="preserve">propinquior
              <lb/>
            illi maior eſt remotiore: </s>
            <s xml:id="echoid-s3738" xml:space="preserve">nec non; </s>
            <s xml:id="echoid-s3739" xml:space="preserve">quia H M, G N ſunt duæ breuiſſimæ
              <lb/>
              <note position="left" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">c</note>
              <note position="right" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">74. huius.</note>
            conſtat, vt dictum eſt, quod G E ſit maximus ramorum cadentium vtrin-
              <lb/>
            que ad ſectionẽ A H. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">Dico etiam, E G maiorem eſſe, quàm E I; </s>
            <s xml:id="echoid-s3741" xml:space="preserve">nam
              <lb/>
              <note position="left" xlink:label="note-0129-04" xlink:href="note-0129-04a" xml:space="preserve">d</note>
            ſi producatur I O parallela ipſi A C, & </s>
            <s xml:id="echoid-s3742" xml:space="preserve">iungatur E O, ducanturque per-
              <lb/>
              <note position="right" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">15, huius.</note>
            pendiculares I P, O Q, G R, E F S, quia G N, I K ſunt breuiſſimæ er it
              <lb/>
            D P ad P K, quæ eſt, vt proportio figuræ, vt D R ad R N; </s>
            <s xml:id="echoid-s3743" xml:space="preserve">ergo F P
              <lb/>
            ad P K minorem proportionem habet, quàm F R ad R N, & </s>
            <s xml:id="echoid-s3744" xml:space="preserve">diuidendo
              <lb/>
            F K ad K P, nempe F E ad I P, minorem proportionem habet, quàm,
              <lb/>
            F N ad N R, nempe F E ad G R: </s>
            <s xml:id="echoid-s3745" xml:space="preserve">ergo F E ad I P minorem proportio-
              <lb/>
            nem habet, quàm ad G R, & </s>
            <s xml:id="echoid-s3746" xml:space="preserve">propterea G R minor eſt, quàm I P, quæ
              <lb/>
            eſt æqualis O Q, cuius punctum O remotior eſt à vertice, quàm G,
              <lb/>
            & </s>
            <s xml:id="echoid-s3747" xml:space="preserve">ideo E G maior eſt, quàm E O. </s>
            <s xml:id="echoid-s3748" xml:space="preserve">(74. </s>
            <s xml:id="echoid-s3749" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3750" xml:space="preserve">Et quia O T æqualis
              <lb/>
            eſt T I erit O S maior quàm S I, & </s>
            <s xml:id="echoid-s3751" xml:space="preserve">S E perpendicularis ad O I eſt com-
              <lb/>
            munis; </s>
            <s xml:id="echoid-s3752" xml:space="preserve">igitur O E maior eſt, quàm E I; </s>
            <s xml:id="echoid-s3753" xml:space="preserve">& </s>
            <s xml:id="echoid-s3754" xml:space="preserve">oſtenſa eſt E G maior, quàm
              <lb/>
            O E; </s>
            <s xml:id="echoid-s3755" xml:space="preserve">Ergo E G maior eſt, quàm E I, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div355" type="section" level="1" n="115">
          <head xml:id="echoid-head158" xml:space="preserve">PROPOSITIO LXXVI.</head>
          <p>
            <s xml:id="echoid-s3757" xml:space="preserve">SI ex concurſu E in recto E B
              <lb/>
              <figure xlink:label="fig-0129-02" xlink:href="fig-0129-02a" number="113">
                <image file="0129-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-02"/>
              </figure>
              <note position="left" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">a</note>
            poſito ellipſis A B C nõ edu-
              <lb/>
            catur breuiſecans præter E B, qui
              <lb/>
            tranſeat per centrum; </s>
            <s xml:id="echoid-s3758" xml:space="preserve">erit E B ma-
              <lb/>
            ximus ramorum ſecantium ex con-
              <lb/>
            curſu ad ſectionem egredientium.</s>
            <s xml:id="echoid-s3759" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum