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-div478" type="section" level="1" n="148">
          <pb o="129" file="0167" n="167" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div481" type="section" level="1" n="149">
          <head xml:id="echoid-head198" xml:space="preserve">PROPOSITIO XXXXVIII.</head>
          <p>
            <s xml:id="echoid-s5063" xml:space="preserve">T Res lineæ maximæ E F, G H,
              <lb/>
              <note position="left" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0167-01" xlink:href="fig-0167-01a" number="164">
                <image file="0167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0167-01"/>
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            I K ad vnum ellipſis quadrã-
              <lb/>
            tem A F B cadentens non cõueniunt
              <lb/>
            in vno puncto.</s>
            <s xml:id="echoid-s5064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5065" xml:space="preserve">Alioquin cõueniant in O, & </s>
            <s xml:id="echoid-s5066" xml:space="preserve">quia ſunt
              <lb/>
            lineæ maximæ erunt M K, H N, L F, li-
              <lb/>
            neæ breuiſſimæ (32. </s>
            <s xml:id="echoid-s5067" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s5068" xml:space="preserve">& </s>
            <s xml:id="echoid-s5069" xml:space="preserve">conueniunt
              <lb/>
            in puncto O; </s>
            <s xml:id="echoid-s5070" xml:space="preserve">quod eſt abſurdũ (54. </s>
            <s xml:id="echoid-s5071" xml:space="preserve">ex 5.)
              <lb/>
            </s>
            <s xml:id="echoid-s5072" xml:space="preserve">oſtenſum ergo eſt, quod fuerat propoſitũ.</s>
            <s xml:id="echoid-s5073" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div483" type="section" level="1" n="150">
          <head xml:id="echoid-head199" xml:space="preserve">Notæ in Propoſit. XXXII.</head>
          <p>
            <s xml:id="echoid-s5074" xml:space="preserve">L Inea maxima ſecat tranſuerſam in pũ-
              <lb/>
              <note position="left" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0167-02" xlink:href="fig-0167-02a" number="165">
                <image file="0167-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0167-02"/>
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            cto, cuius intercepta inter punctum
              <lb/>
            illud, & </s>
            <s xml:id="echoid-s5075" xml:space="preserve">ſectionem, eſt linea breuiſſima,
              <lb/>
            &</s>
            <s xml:id="echoid-s5076" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5077" xml:space="preserve">Verba, quæ in textu Arabico deſideran-
              <lb/>
            tur ſupplenda cenſui, vt æquiuocationes tolle-
              <lb/>
            rentur.</s>
            <s xml:id="echoid-s5078" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5079" xml:space="preserve">Quia G H eſt linea maxima, erit D A
              <lb/>
              <note position="left" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">b</note>
            ad A F, nempe B E ad B D, &</s>
            <s xml:id="echoid-s5080" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5081" xml:space="preserve">Quia
              <lb/>
            in 22. </s>
            <s xml:id="echoid-s5082" xml:space="preserve">huius oſtenſum eſt, lineæ maximæ G
              <lb/>
            H potentialem H O ſecare ſemiaxim minorẽ
              <lb/>
            A D in O, vt ſit D O ad O G in eadẽ propor-
              <lb/>
            tione figuræ axis minoris A C; </s>
            <s xml:id="echoid-s5083" xml:space="preserve">ſcilicet erit,
              <lb/>
            vt D A ſemiaxis minor ad A F eius ſemie-
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s5084" xml:space="preserve">ſed vt A D ad A F, ita eſt B E ſe-
              <lb/>
            miſsis lateris recti axis tranſuerſi ad B D
              <lb/>
            ſemiſſem eiuſdem tranſuerſi; </s>
            <s xml:id="echoid-s5085" xml:space="preserve">igitur D O ad
              <lb/>
            O G eandem proportionem habebit, quàm E
              <lb/>
            B ad B D; </s>
            <s xml:id="echoid-s5086" xml:space="preserve">ſed propter parallelas N D, H O,
              <lb/>
            eſt N H ad H G, vt D O ad O G; </s>
            <s xml:id="echoid-s5087" xml:space="preserve">pariter-
              <lb/>
            que propter parallelas D G, H P, erit N P ad P D, vt N H ad H G; </s>
            <s xml:id="echoid-s5088" xml:space="preserve">& </s>
            <s xml:id="echoid-s5089" xml:space="preserve">pro-
              <lb/>
            pterea N P ad P D eandem proportionem habebit, quàm D O ad O G, ſeu
              <lb/>
            quàm E B ad B D; </s>
            <s xml:id="echoid-s5090" xml:space="preserve">& </s>
            <s xml:id="echoid-s5091" xml:space="preserve">permutando D P ad P N erit, vt D B ad B E, ſeu vt
              <lb/>
              <note position="right" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">15. huius.</note>
            axis tranſuerſus ad eius, erectum; </s>
            <s xml:id="echoid-s5092" xml:space="preserve">& </s>
            <s xml:id="echoid-s5093" xml:space="preserve">propterea linea N H erit breuiſsima.</s>
            <s xml:id="echoid-s5094" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div486" type="section" level="1" n="151">
          <head xml:id="echoid-head200" xml:space="preserve">Notæ in Propoſit. XXXIII. XXXIV.</head>
          <p>
            <s xml:id="echoid-s5095" xml:space="preserve">E Contra oſtendetur, quod duæ breuiſſimæ, ſi educantur ex parte ſuæ
              <lb/>
              <note position="left" xlink:label="note-0167-05" xlink:href="note-0167-05a" xml:space="preserve">a</note>
            originis ad rectum, fient duo maximi cum relatione ad rectum: </s>
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