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
71 33
72 34
73 35
74 36
75 37
76 38
77 39
78 40
79 41
80 42
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
< >
page |< < (72) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div285" type="section" level="1" n="95">
          <pb o="72" file="0110" n="110" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s3066" xml:space="preserve">Patet ex hoc, quod ſi producantur ex duo-
              <lb/>
              <note position="right" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">d</note>
              <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a" number="91">
                <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-01"/>
              </figure>
            bus punctis contactus in ellipſi perpendiculares
              <lb/>
            E M, A L; </s>
            <s xml:id="echoid-s3067" xml:space="preserve">& </s>
            <s xml:id="echoid-s3068" xml:space="preserve">fuerit E M minor, exempli gra-
              <lb/>
            tia, tunc tangens educta ab eius extremitate,
              <lb/>
            quæ eſt in ſectione, minor quoque eſt, &</s>
            <s xml:id="echoid-s3069" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Si
              <lb/>
            enim ex punctis E, A contactuum in ellipſi ducan-
              <lb/>
            tur ad axim minorem K C perpendiculares E M,
              <lb/>
            & </s>
            <s xml:id="echoid-s3071" xml:space="preserve">A L ſecantes eum in M, & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">L, fueritque E M
              <lb/>
            minor, quàm A L, tunc quidem punctum E magis
              <lb/>
            recedit à vertice B axis maioris, quàm punctum
              <lb/>
            A; </s>
            <s xml:id="echoid-s3073" xml:space="preserve">& </s>
            <s xml:id="echoid-s3074" xml:space="preserve">propterea, ex præmiſſa 70. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">huius libri, erit
              <lb/>
            tangens E F minor, quàm A F. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Expungo deter-
              <lb/>
            minationem ab aliquo incaute additam (quæ eſt in
              <lb/>
            ſectione) manifeſtum enim eſt ducinon poſſe contin-
              <lb/>
            gentem ellipſim à perpendicularis termino M in axi minori poſito, ſed à termi-
              <lb/>
            no E in ſectionis peripheria conſtituto.</s>
            <s xml:id="echoid-s3077" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div290" type="section" level="1" n="96">
          <head xml:id="echoid-head132" xml:space="preserve">SECTIO DVODECIMA</head>
          <head xml:id="echoid-head133" xml:space="preserve">Continens XXIX. XXX. XXXI.</head>
          <head xml:id="echoid-head134" xml:space="preserve">Propoſ. Appollonij.</head>
          <p>
            <s xml:id="echoid-s3078" xml:space="preserve">Q Vælibet linea recta A E D tangens fectionem aliquam A
              <lb/>
            F B in A extremitate lineæ breuiſſimæ A C eſt perpeudi-
              <lb/>
            cularis ſuper illam, nẽpe D A C eſt angulus rectus.
              <lb/>
            </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Et ſi fuerit perpendicularis ſuper illam vtique tanget ſectio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s3080" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3081" xml:space="preserve">Alioquin producatur perpendicu-
              <lb/>
              <note position="right" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0110-02" xlink:href="fig-0110-02a" number="92">
                <image file="0110-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-02"/>
              </figure>
            laris C E ſuper A D, erit A C maior,
              <lb/>
            quàm E C, ergo maior eſt, quàm F
              <lb/>
            C; </s>
            <s xml:id="echoid-s3082" xml:space="preserve">ſed eſt minor, cũ ſit minor, quàm
              <lb/>
            C F, quod eſt abſurdum. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Igitur an-
              <lb/>
            gulus D A C, eſt rectus, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s3084" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3085" xml:space="preserve">Si verò fuerit D A C rectus, erit
              <lb/>
              <note position="right" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">b</note>
            A D tangens, alioquin ſit tangens A
              <lb/>
            G; </s>
            <s xml:id="echoid-s3086" xml:space="preserve">ergo C A G erit rectus, ſed erat
              <lb/>
            C A D rectus, quod eſt abſurdum;
              <lb/>
            </s>
            <s xml:id="echoid-s3087" xml:space="preserve">ergo A D eſt tangens, & </s>
            <s xml:id="echoid-s3088" xml:space="preserve">hoc erat
              <lb/>
            probandum.</s>
            <s xml:id="echoid-s3089" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum