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-div519" type="section" level="1" n="170">
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            <s xml:id="echoid-s5523" xml:space="preserve">
              <pb o="141" file="0179" n="179" rhead="Conicor. Lib. VI."/>
            Quapropter duæ figuræ G I, H K ſunt æquales, & </s>
            <s xml:id="echoid-s5524" xml:space="preserve">ſimiles. </s>
            <s xml:id="echoid-s5525" xml:space="preserve">Quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s5526" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div523" type="section" level="1" n="171">
          <head xml:id="echoid-head225" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s5527" xml:space="preserve">SImili modo demõſtrabitur, quod
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">a</note>
            duæ ſectiones oppoſitæ ſintſimi-
              <lb/>
              <figure xlink:label="fig-0179-01" xlink:href="fig-0179-01a" number="181">
                <image file="0179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179-01"/>
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            les, & </s>
            <s xml:id="echoid-s5528" xml:space="preserve">æquales.</s>
            <s xml:id="echoid-s5529" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5530" xml:space="preserve">Eo quod axis inclinatus eſt communis',
              <lb/>
            & </s>
            <s xml:id="echoid-s5531" xml:space="preserve">erecti ſunt æquales (16. </s>
            <s xml:id="echoid-s5532" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5533" xml:space="preserve">& </s>
            <s xml:id="echoid-s5534" xml:space="preserve">prot
              <lb/>
              <note position="right" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">14. lib. 4.</note>
            pterea earum figuræ æquales quoque ſun-
              <lb/>
            inter ſe. </s>
            <s xml:id="echoid-s5535" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s5536" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div526" type="section" level="1" n="172">
          <head xml:id="echoid-head226" xml:space="preserve">PROPOSITIO X.</head>
          <p>
            <s xml:id="echoid-s5537" xml:space="preserve">PAriter conſtat, quod ſi poten-
              <lb/>
              <note position="right" xlink:label="note-0179-03" xlink:href="note-0179-03a" xml:space="preserve">a</note>
            tiales cum ſuis abſciſſis cõpræ-
              <lb/>
            hendant angulos æquales obliquos,
              <lb/>
            eadem conſequentur, quæ prius dicta ſunt.</s>
            <s xml:id="echoid-s5538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5539" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s5540" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div528" type="section" level="1" n="173">
          <head xml:id="echoid-head227" xml:space="preserve">Notæ in Propoſit. I.</head>
          <p>
            <s xml:id="echoid-s5541" xml:space="preserve">QVælibet duæ ſectiones parabolicæ,
              <lb/>
              <figure xlink:label="fig-0179-02" xlink:href="fig-0179-02a" number="182">
                <image file="0179-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179-02"/>
              </figure>
              <note position="right" xlink:label="note-0179-04" xlink:href="note-0179-04a" xml:space="preserve">a</note>
            vt A B, C D, quarum relationes
              <lb/>
            ſunt duo plana A L, C M, & </s>
            <s xml:id="echoid-s5542" xml:space="preserve">
              <lb/>
            erecti earum A I, C N æquales. </s>
            <s xml:id="echoid-s5543" xml:space="preserve">ipſæ quo-
              <lb/>
            que ſunt æquales. </s>
            <s xml:id="echoid-s5544" xml:space="preserve">Si verò duæ illæ ſectio-
              <lb/>
            nes fuerint æquales, vtique earum appli-
              <lb/>
            cata, & </s>
            <s xml:id="echoid-s5545" xml:space="preserve">erecti erunt æquales, &</s>
            <s xml:id="echoid-s5546" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5547" xml:space="preserve">Verba
              <lb/>
            illa propoſitionis (applicata ſunt duo plana
              <lb/>
            A L, C M, &</s>
            <s xml:id="echoid-s5548" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s5549" xml:space="preserve">caſu in textum irrepſiſſe
              <lb/>
            puto, eo quod rectangula illa A L, C M, ne-
              <lb/>
            dum æqualia non ſupponuntur, ſed è contra.
              <lb/>
            </s>
            <s xml:id="echoid-s5550" xml:space="preserve">conſtruuntur, atque demonſtrantur æqualia eſ-
              <lb/>
            ſe inter ſe.</s>
            <s xml:id="echoid-s5551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5552" xml:space="preserve">Quia ſi ponamus ſagittam C H ſuper ſa-
              <lb/>
              <note position="right" xlink:label="note-0179-05" xlink:href="note-0179-05a" xml:space="preserve">b</note>
            gittã A G, cadet ſectio C D ſuper ſectio-
              <lb/>
            nem A B: </s>
            <s xml:id="echoid-s5553" xml:space="preserve">11 verò non cadit ſuper illam,
              <lb/>
            ſignemus ſuper literam, in quam non ca-
              <lb/>
            dit punctum D: </s>
            <s xml:id="echoid-s5554" xml:space="preserve">&</s>
            <s xml:id="echoid-s5555" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5556" xml:space="preserve">Sic legendũ puto. </s>
            <s xml:id="echoid-s5557" xml:space="preserve"/>
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