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
321 283
322 284
323 285
324 286
325 287
326 288
327 289
328 290
329 291
330
331 292
332 293
333 294
334 295
335 296
336 297
337 298
338 299
339 300
340 301
341 302
342 303
343 304
344 305
345 306
346 307
347 308
348 309
349 310
350 311
< >
page |< < (23) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div88" type="section" level="1" n="49">
          <p style="it">
            <s xml:id="echoid-s1423" xml:space="preserve">
              <pb o="23" file="0061" n="61" rhead="Conicor. Lib. V."/>
            H C; </s>
            <s xml:id="echoid-s1424" xml:space="preserve">igitur prædisti exceſſus tam in parabola, quàm in reliquis ſectioni-
              <lb/>
            bus æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s1425" xml:space="preserve">ideò quadrata ramorum I O, 10, I C, & </s>
            <s xml:id="echoid-s1426" xml:space="preserve">rami ipſi
              <lb/>
            æquales erunt: </s>
            <s xml:id="echoid-s1427" xml:space="preserve">cumque quilibet alius ramus ſupra, vel infra ramum I O maior,
              <lb/>
            vel minor ſit illo, non crunt plures, quam tres rami inter ſe æquales.</s>
            <s xml:id="echoid-s1428" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1429" xml:space="preserve">Secundò H D differentia abſciſſarum rami I A, & </s>
            <s xml:id="echoid-s1430" xml:space="preserve">breniſsimi I N ſupponatur
              <lb/>
            maior, quàm H C quæ eſt abſciſſa breuiſsimi rami I N; </s>
            <s xml:id="echoid-s1431" xml:space="preserve">& </s>
            <s xml:id="echoid-s1432" xml:space="preserve">producta ſimiliter
              <lb/>
            ordinata D A vltra axim ad ſectionem in a, & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">coniuncta I a; </s>
            <s xml:id="echoid-s1434" xml:space="preserve">Dico, quod duo
              <lb/>
            rami tantummodo I A, & </s>
            <s xml:id="echoid-s1435" xml:space="preserve">I a inter ſe æquales ſunt: </s>
            <s xml:id="echoid-s1436" xml:space="preserve">Quia H D maior eſt, quàm
              <lb/>
            H C, erit quadratum ex H D maius quadrato H C; </s>
            <s xml:id="echoid-s1437" xml:space="preserve">pariterque exemplar appli-
              <lb/>
            catum ad H D maius erit exemplari ei ſimili applicato ad H C, & </s>
            <s xml:id="echoid-s1438" xml:space="preserve">ideo tam.
              <lb/>
            </s>
            <s xml:id="echoid-s1439" xml:space="preserve">quadratum I A, quàm I a maius erit quadrato I C, cum quodlibet illorum ma-
              <lb/>
            iori exceſſu ſuperet quadratum breuiſsimi rami I N quam quadratqm I C, qua-
              <lb/>
            re tam ramus I A, quàm I a (qui æquales ſunt) maiores erunt, quàm I C, & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">
              <lb/>
            ideo maiores quàm intercepti inter I C, & </s>
            <s xml:id="echoid-s1441" xml:space="preserve">I N, pariterque maiores, quàm in-
              <lb/>
            terpoſiti inter I N, & </s>
            <s xml:id="echoid-s1442" xml:space="preserve">I A, & </s>
            <s xml:id="echoid-s1443" xml:space="preserve">minores omnibus alijs, qui infra ipſos cadunt. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">
              <lb/>
            Quapropter duo tantùm rami I A, I a ab origine ad ſectionem duci poſſunt in-
              <lb/>
            ter ſe æquales.</s>
            <s xml:id="echoid-s1445" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1446" xml:space="preserve">Tertiò ſint duæ abſciſſarum differentiæ H P, & </s>
            <s xml:id="echoid-s1447" xml:space="preserve">H I æquales inter ſe, & </s>
            <s xml:id="echoid-s1448" xml:space="preserve">quæ-
              <lb/>
            libet earum minor H C abſciſſa rami breuiſsimi, & </s>
            <s xml:id="echoid-s1449" xml:space="preserve">producantur perpendicula-
              <lb/>
            res ad axim L P, B I, donec conueniant ex altera parte cum ſectione in l, & </s>
            <s xml:id="echoid-s1450" xml:space="preserve">b,
              <lb/>
            coniunganturque rami ad l, b. </s>
            <s xml:id="echoid-s1451" xml:space="preserve">Dico, quatuor ramos I B, I L, I l, I b æquales
              <lb/>
            inter ſe tantummodo duci poſſe; </s>
            <s xml:id="echoid-s1452" xml:space="preserve">quia, vt dictum eſt, quilibet eorum ſuperat ra-
              <lb/>
            mum breuiſsimum I N potentia eodem exceſſu, erunt radij ipſi I B, I L, I l, I b
              <lb/>
            æquales inter ſe, reliqui verò ſupra, & </s>
            <s xml:id="echoid-s1453" xml:space="preserve">infra ipſos maiores, aut minores erunt,
              <lb/>
            & </s>
            <s xml:id="echoid-s1454" xml:space="preserve">ideo non poſſunt duci plures, quàm quatuor rami iam dicti æquales. </s>
            <s xml:id="echoid-s1455" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s1456" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1457" xml:space="preserve">Et inſuper quadratum rami
              <lb/>
              <note position="right" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">PROP.
                <lb/>
              IV. Add.</note>
            à breuiſsimo remotioris ſuper at
              <lb/>
            quadratum rami propinquioris,
              <lb/>
              <figure xlink:label="fig-0061-01" xlink:href="fig-0061-01a" number="34">
                <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01"/>
              </figure>
            in parabola quidem rectangulo
              <lb/>
            ſub exceſſu, & </s>
            <s xml:id="echoid-s1458" xml:space="preserve">ſub aggregato
              <lb/>
            differẽtiali ſuarum abſciſſarum
              <lb/>
            ab abſciſſa rami breuiſsimi, in
              <lb/>
            reliquis verò ſectionibus rectã-
              <lb/>
            gulo ſub codem exceſſu differen-
              <lb/>
            tiali, & </s>
            <s xml:id="echoid-s1459" xml:space="preserve">ſub recta linea, ad quam
              <lb/>
            ſumma differentialis eandem
              <lb/>
            proportionem habet, quam latus
              <lb/>
            tranſuer ſum ad ſummam in hy-
              <lb/>
            perbola, & </s>
            <s xml:id="echoid-s1460" xml:space="preserve">ad differentiam in ellipſi laterum recti, & </s>
            <s xml:id="echoid-s1461" xml:space="preserve">tranſuerſi.</s>
            <s xml:id="echoid-s1462" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1463" xml:space="preserve">Quoniam in parabola quadratum I L ſuperat quadratum I M eodem exceſſu,
              <lb/>
            quo quadratum H P ſuperat quadratum H Q (cum quadratum H P, atque qua-
              <lb/>
              <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">Ex 8. hu.</note>
            dratum I N ſimul ſumpta æqualia ſint quadrato L I, & </s>
            <s xml:id="echoid-s1464" xml:space="preserve">quadrata ex H Q, & </s>
            <s xml:id="echoid-s1465" xml:space="preserve">
              <lb/>
            ex I N æqualia ſint quadrato I M) ſed exceſſus quadrati H P ſupra quadratum
              <lb/>
            H Q æqualis eſt rectangulo ſub P Q differentia, & </s>
            <s xml:id="echoid-s1466" xml:space="preserve">P H, H Q, ſumma laterum
              <lb/>
            eorundem quadratorum contento; </s>
            <s xml:id="echoid-s1467" xml:space="preserve">igitur quadratum I L ſuperat quadratum ra-
              <lb/>
            mi I M propinquioris breuiſsimo I N rectangulo ſub P Q exceſſu, & </s>
            <s xml:id="echoid-s1468" xml:space="preserve">P H </s>
          </p>
        </div>
      </text>
    </echo>
Impressum