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
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
141 103
142 104
143 105
144 106
145 107
146 108
147 109
148 110
149 111
150 112
< >
page |< < (129) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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"/>
              </figure>
            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"/>
              </figure>
            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>
        </div>
        <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>
            <s xml:id="echoid-s5096" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum