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
371 332
372 333
373 334
374 335
375 336
376 337
377 338
378 339
379 340
380 341
381 342
382 343
383 344
384 345
385 346
386 347
387 348
388 349
389 350
390 351
391 352
392 353
393 354
394 355
395 356
396 357
397 358
398 359
399 360
400 361
< >
page |< < (350) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1041" type="section" level="1" n="330">
          <pb o="350" file="0388" n="389" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s12153" xml:space="preserve">Tertio ſi duplum O H ad H G minorem proportionem habuerit, quàm G H
              <lb/>
            ad H E, eodem progreſſu oſtendetur, quod duplum rectanguli ex differentia
              <lb/>
            ipſarum E H, & </s>
            <s xml:id="echoid-s12154" xml:space="preserve">G O in H O minus eſt quadratis ex G O, & </s>
            <s xml:id="echoid-s12155" xml:space="preserve">ex H O, quod erat
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s12156" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1043" type="section" level="1" n="331">
          <head xml:id="echoid-head410" xml:space="preserve">LEMMA XIV.</head>
          <p style="it">
            <s xml:id="echoid-s12157" xml:space="preserve">Ilſdem poſitis ſit G E minimum ſegmentorum, dico quod duo qua-
              <lb/>
            drata ex E H, & </s>
            <s xml:id="echoid-s12158" xml:space="preserve">ex G E, ſcilicet ex maximo, & </s>
            <s xml:id="echoid-s12159" xml:space="preserve">minimo ſeg-
              <lb/>
            mentorum æqualia ſunt duobus quadratis ex O H, & </s>
            <s xml:id="echoid-s12160" xml:space="preserve">ex G O inter-
              <lb/>
            medijs ſegmentis vna cum duplo rectanguli ſub differentijs minimæ G
              <lb/>
            E à duabus intermedijs G O, & </s>
            <s xml:id="echoid-s12161" xml:space="preserve">H O.</s>
            <s xml:id="echoid-s12162" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12163" xml:space="preserve">Fiat H a æqualis G E,
              <lb/>
              <figure xlink:label="fig-0388-01" xlink:href="fig-0388-01a" number="459">
                <image file="0388-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0388-01"/>
              </figure>
            ergo O a erit differentia ipſa-
              <lb/>
            rum E H, & </s>
            <s xml:id="echoid-s12164" xml:space="preserve">G E, ſicuti O
              <lb/>
            E eſt differentia ipſarum G O,
              <lb/>
            & </s>
            <s xml:id="echoid-s12165" xml:space="preserve">G E. </s>
            <s xml:id="echoid-s12166" xml:space="preserve">Et quia duo quadra-
              <lb/>
            ta ex maximo, & </s>
            <s xml:id="echoid-s12167" xml:space="preserve">ex mini-
              <lb/>
            mo ſegmentorum, ſcilicet ex
              <lb/>
            H E, & </s>
            <s xml:id="echoid-s12168" xml:space="preserve">ex E G æqualia ſunt
              <lb/>
            duplo quadrati ex G D ſe-
              <lb/>
            miße totius, cũ duplo quadrati
              <lb/>
            ex E D intermedia ſectione;
              <lb/>
            </s>
            <s xml:id="echoid-s12169" xml:space="preserve">eſtque duplum quadrati ex E D ſemiſſe ipſius E a æquale duplo rectanguli E O
              <lb/>
            a ex inæqualibus ſegmentis vna cum duplo quadrati ex intermedia ſectione O
              <lb/>
            D, ergo duo quadrata ex G E, & </s>
            <s xml:id="echoid-s12170" xml:space="preserve">ex E H æqualia ſunt his omnibus ſpatijs,
              <lb/>
            ſcilicet duplo quadrati ex G D, & </s>
            <s xml:id="echoid-s12171" xml:space="preserve">duplo quadrati ex D O cum duplo rectan-
              <lb/>
            guli E O a, ſed duo quadrata ex inæqualibus ſegmentis G O, & </s>
            <s xml:id="echoid-s12172" xml:space="preserve">ex O H æqua-
              <lb/>
            lia ſunt duplo quadrati ex ſemiſſe totius G D cum duplo quadrati ex interme-
              <lb/>
            dia ſectione O D, igitur exceßus ſummæ quadratorum ex G E, & </s>
            <s xml:id="echoid-s12173" xml:space="preserve">ex E H,
              <lb/>
            ſupra ſummam quadratorum ex G O, & </s>
            <s xml:id="echoid-s12174" xml:space="preserve">O H æqualis eſt duplo rectanguli ex E
              <lb/>
            O a, quod erat oſtendendum.</s>
            <s xml:id="echoid-s12175" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1045" type="section" level="1" n="332">
          <head xml:id="echoid-head411" xml:space="preserve">LEMMA XV.</head>
          <p style="it">
            <s xml:id="echoid-s12176" xml:space="preserve">IN ellypſi, cuius axis A C, erectus A F, diameter I L, eiuſq; </s>
            <s xml:id="echoid-s12177" xml:space="preserve">erectus
              <lb/>
            I K, & </s>
            <s xml:id="echoid-s12178" xml:space="preserve">latus C E, & </s>
            <s xml:id="echoid-s12179" xml:space="preserve">ſimiliter altera diameter Q P, cuius ere-
              <lb/>
            ctus P R, & </s>
            <s xml:id="echoid-s12180" xml:space="preserve">latus C O: </s>
            <s xml:id="echoid-s12181" xml:space="preserve">dico quod duplum rectanguli ex differentia
              <lb/>
            ipſarum E H, G O, in H O à duobus quadratis ex G O, & </s>
            <s xml:id="echoid-s12182" xml:space="preserve">ex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum