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-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"/>
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        <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-
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              <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;
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            </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>
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