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
361 322
362 323
363 324
364 325
365 326
366 327
367 328
368 329
369 330
370 331
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
< >
page |< < (397) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1134" type="section" level="1" n="364">
          <p>
            <s xml:id="echoid-s13276" xml:space="preserve">
              <pb o="397" file="0435" n="436" rhead="Aſſumpt. Liber."/>
            pendicularis ad E D, & </s>
            <s xml:id="echoid-s13277" xml:space="preserve">D I eſt quoque perpendicularis ad A E, & </s>
            <s xml:id="echoid-s13278" xml:space="preserve">iam
              <lb/>
            ſe mutuo ſecuerunt in M, ergo E M O erit etiam perpendicularis, que-
              <lb/>
            madmodum oſtendimus in expoſitione, quàm confecimus de proprieta-
              <lb/>
            tibus triangulorum, & </s>
            <s xml:id="echoid-s13279" xml:space="preserve">cuius demonſtratio iam quidem præceſſit in ſupe-
              <lb/>
              <figure xlink:label="fig-0435-01" xlink:href="fig-0435-01a" number="503">
                <image file="0435-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0435-01"/>
              </figure>
            riori propoſitione; </s>
            <s xml:id="echoid-s13280" xml:space="preserve">Similiter quoque erit F P perpendicularis ſuper C A,
              <lb/>
            & </s>
            <s xml:id="echoid-s13281" xml:space="preserve">quia duo anguli, qui ſunt apud L, & </s>
            <s xml:id="echoid-s13282" xml:space="preserve">B ſunt recti, erit D L parallela
              <lb/>
            ipſi A B, & </s>
            <s xml:id="echoid-s13283" xml:space="preserve">pariter D I ipſi C B, igitur proportio A D ad D C eſt vt
              <lb/>
            proportio A M ad F M, immo vt proportio A O ad O P, & </s>
            <s xml:id="echoid-s13284" xml:space="preserve">proportio
              <lb/>
            C D ad D A vt proportio C N ad N E, immo vt proportio C P ad P
              <lb/>
            O, & </s>
            <s xml:id="echoid-s13285" xml:space="preserve">erat A D ſexquialtera D C, ergo A O eſt ſexquialtera O P, & </s>
            <s xml:id="echoid-s13286" xml:space="preserve">
              <lb/>
            O P ſexquialtera C P, ergo tres lineæ A O, O P, P C ſunt proportio-
              <lb/>
            nales: </s>
            <s xml:id="echoid-s13287" xml:space="preserve">& </s>
            <s xml:id="echoid-s13288" xml:space="preserve">in eadem menſura, in qua eſt P C quatuor, erit O P ſex, & </s>
            <s xml:id="echoid-s13289" xml:space="preserve">
              <lb/>
            A O nouem, & </s>
            <s xml:id="echoid-s13290" xml:space="preserve">C A nouendecim, & </s>
            <s xml:id="echoid-s13291" xml:space="preserve">quia P O æ qualis eſt E F, erit
              <lb/>
            proportio A C ad E F vt nouendecim ad ſex, igitur reperimus dictam
              <lb/>
            proportionem. </s>
            <s xml:id="echoid-s13292" xml:space="preserve">Etiam ſi fuerit A D ad D C qualiſcumque vt ſexquiter-
              <lb/>
            tia, aut ſexquiquarta, aut alia, erit iudicium, & </s>
            <s xml:id="echoid-s13293" xml:space="preserve">ratio, vti dictum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s13294" xml:space="preserve">Et hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13295" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1136" type="section" level="1" n="365">
          <head xml:id="echoid-head457" xml:space="preserve">Notæ in Propoſit. VI.</head>
          <p style="it">
            <s xml:id="echoid-s13296" xml:space="preserve">HAEc propoſitio nil prorſus differre videtur à 16. </s>
            <s xml:id="echoid-s13297" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s13298" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13299" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13300" xml:space="preserve">Pappi
              <lb/>
            Alex. </s>
            <s xml:id="echoid-s13301" xml:space="preserve">eſt tamen pars illius, & </s>
            <s xml:id="echoid-s13302" xml:space="preserve">particulariter demonſtrata, quod quidem
              <lb/>
            peccatum alicui expoſitori tribui debet; </s>
            <s xml:id="echoid-s13303" xml:space="preserve">nunquam enim Archimedes propoſitionẽ
              <lb/>
            illam, quam vniuerſaltſſimè demonſtrare potuißet, exemplis numericis tam
              <lb/>
            pueriliter oſtendiſſet. </s>
            <s xml:id="echoid-s13304" xml:space="preserve">Pappus igitur quærit menſuram diametri illius circuli,
              <lb/>
            qui in loco inter tres circunferentias circulares interijcitur, quod Arbelon ap-
              <lb/>
            pellatur, & </s>
            <s xml:id="echoid-s13305" xml:space="preserve">oſtendit quidem diametrum ſemicirculi maioris A C ſecari in duo-
              <lb/>
            bus punctis O, & </s>
            <s xml:id="echoid-s13306" xml:space="preserve">P à perpendicularibus cadentibus à terminis E, & </s>
            <s xml:id="echoid-s13307" xml:space="preserve">F dia-
              <lb/>
            metri circuli in Arbelo inſcripti, ac diuidi in tria ſegmenta A O, O P, P C
              <lb/>
            continue proportionalia in eadem ratione, quàm habet A D ad D C, & </s>
            <s xml:id="echoid-s13308" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum