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
261 223
262 224
263 225
264 226
265 227
266 228
267 229
268 230
269 231
270 232
271 233
272 234
273 235
274 236
275 237
276 238
277 239
278 240
279 241
280 242
281 243
282 244
283 245
284 246
285 247
286 248
287 249
288 250
289 251
290 252
< >
page |< < (63) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div246" type="section" level="1" n="82">
          <pb o="63" file="0101" n="101" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div248" type="section" level="1" n="83">
          <head xml:id="echoid-head116" xml:space="preserve">Notæ in Propoſit. LVIII.</head>
          <p>
            <s xml:id="echoid-s2759" xml:space="preserve">I Am poſſumus producere ex puncto aſſignato C extra datam ſectionem
              <lb/>
              <note position="left" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">a</note>
            A B, aut intra (ſi punctum non fuerit ad axim I A) lineam diuiden-
              <lb/>
            tem ex illo inter ſectionem, & </s>
            <s xml:id="echoid-s2760" xml:space="preserve">axim lineam breuiſſimam, &</s>
            <s xml:id="echoid-s2761" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2762" xml:space="preserve">Sic legen-
              <lb/>
            dum puto. </s>
            <s xml:id="echoid-s2763" xml:space="preserve">Ex punto dato C extra, vel intra ſectionem A B, quod in axi non
              <lb/>
            ſit, lineam rectam ducere, cuius portio incercepta inter ſectionem, & </s>
            <s xml:id="echoid-s2764" xml:space="preserve">axim ſit
              <lb/>
            linea breuiſsima.</s>
            <s xml:id="echoid-s2765" xml:space="preserve"/>
          </p>
          <figure number="80">
            <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0101-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2766" xml:space="preserve">Et per C ducamus ſectionem H C B circa duas continentes illam G F,
              <lb/>
              <note position="left" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">b</note>
            I F, quæ occurrat ſectioni A B (16. </s>
            <s xml:id="echoid-s2767" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2768" xml:space="preserve">in B, &</s>
            <s xml:id="echoid-s2769" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2770" xml:space="preserve">Scilicet ducamus per
              <lb/>
            C hyperbolen H C B circa aſymptots G F, F I, & </s>
            <s xml:id="echoid-s2771" xml:space="preserve">quia aſymptoti, & </s>
            <s xml:id="echoid-s2772" xml:space="preserve">hyperbo-
              <lb/>
              <note position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">4. lib. 2.</note>
            le H C B productæ ad ſe ipſas ſemper proprius accedunt, atque parabole A B
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">14. 2.
                <lb/>
              Ex 8. 1.</note>
            producta ſemper magis ab axi A I remouetur; </s>
            <s xml:id="echoid-s2773" xml:space="preserve">igitur hyperbole H C B, & </s>
            <s xml:id="echoid-s2774" xml:space="preserve">para-
              <lb/>
            bola A B ſe mutuo ſecabunt; </s>
            <s xml:id="echoid-s2775" xml:space="preserve">ſecent ſe ſe in puncto B. </s>
            <s xml:id="echoid-s2776" xml:space="preserve">Animaduertendum eſt,
              <lb/>
            quod in textu Arabico aſſumitur hæc concluſio, vt demonſtrata in propoſitione
              <lb/>
            16. </s>
            <s xml:id="echoid-s2777" xml:space="preserve">huius quinti libri; </s>
            <s xml:id="echoid-s2778" xml:space="preserve">& </s>
            <s xml:id="echoid-s2779" xml:space="preserve">ſiquidem numeri huius citationis mendoſi non ſunt,
              <lb/>
            hæc propoſitio ſexta decima deſideratur in hoc libro.</s>
            <s xml:id="echoid-s2780" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2781" xml:space="preserve">Producatur perpendicularis B K. </s>
            <s xml:id="echoid-s2782" xml:space="preserve">Quoniam C I, &</s>
            <s xml:id="echoid-s2783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">Ex puncto B ad
              <lb/>
              <note position="left" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">c</note>
            axim ducatur perpendicularis B K, ſecans eum in K; </s>
            <s xml:id="echoid-s2785" xml:space="preserve">quoniam quando punctum
              <lb/>
            C ponitur intra parabolen, tunc B G æqualis eſt I C; </s>
            <s xml:id="echoid-s2786" xml:space="preserve">quando vero cadit extra,
              <lb/>
              <note position="right" xlink:label="note-0101-06" xlink:href="note-0101-06a" xml:space="preserve">8. lib. 2.</note>
            tunc C G eſt æqualis B I, & </s>
            <s xml:id="echoid-s2787" xml:space="preserve">addita communi B C erit I C æqualis B G, cumq;
              <lb/>
            </s>
            <s xml:id="echoid-s2788" xml:space="preserve">duæ rectæ lineæ I G, I F conuenientes in I ſecentur à rectis lineis K B, E C,
              <lb/>
            F G inter ſe parallelis, eo quod ſunt perpendiculares ad eundem axim; </s>
            <s xml:id="echoid-s2789" xml:space="preserve">ergo I G,
              <lb/>
            & </s>
            <s xml:id="echoid-s2790" xml:space="preserve">I F ſecantur in ijſdem rationibus, & </s>
            <s xml:id="echoid-s2791" xml:space="preserve">propterea E I æqualis erit K F; </s>
            <s xml:id="echoid-s2792" xml:space="preserve">ſicuti
              <lb/>
            I C æqualis erat B g, pariterque I K æqualis erit E F, ſicuti I B æqualis erat
              <lb/>
            C G; </s>
            <s xml:id="echoid-s2793" xml:space="preserve">poſita autem fuit E F æqualis ſemierecto; </s>
            <s xml:id="echoid-s2794" xml:space="preserve">igitur K I ſemiſsi lateris recti
              <lb/>
            pariter æqualis erit.</s>
            <s xml:id="echoid-s2795" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum