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
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
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
< >
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