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 |< < (262) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div814" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s9866" xml:space="preserve">
              <pb o="262" file="0300" n="300" rhead="Apollonij Pergæi"/>
            idem diametrum M A; </s>
            <s xml:id="echoid-s9867" xml:space="preserve">erunt igitur tangentes
              <lb/>
              <figure xlink:label="fig-0300-01" xlink:href="fig-0300-01a" number="347">
                <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0300-01"/>
              </figure>
            A D, & </s>
            <s xml:id="echoid-s9868" xml:space="preserve">M V parallelæ eidem N O, erat au-
              <lb/>
            tem E B parallela ipſi N O; </s>
            <s xml:id="echoid-s9869" xml:space="preserve">igitur duæ cir-
              <lb/>
            culum tangentes A B, & </s>
            <s xml:id="echoid-s9870" xml:space="preserve">M V parallelæ ſunt
              <lb/>
            idem E B; </s>
            <s xml:id="echoid-s9871" xml:space="preserve">& </s>
            <s xml:id="echoid-s9872" xml:space="preserve">propterea A D, & </s>
            <s xml:id="echoid-s9873" xml:space="preserve">E B in eo-
              <lb/>
            dem ſunt plano, vtrumque conum tangente
              <lb/>
            cum per vertices E, & </s>
            <s xml:id="echoid-s9874" xml:space="preserve">B ducatur, & </s>
            <s xml:id="echoid-s9875" xml:space="preserve">per A
              <lb/>
            D baſis circulum tangentem. </s>
            <s xml:id="echoid-s9876" xml:space="preserve">Eadem ratione
              <lb/>
            M V, & </s>
            <s xml:id="echoid-s9877" xml:space="preserve">E B ineodem plano vtrumque conum
              <lb/>
            tangente exiſtent. </s>
            <s xml:id="echoid-s9878" xml:space="preserve">Si verò recta E B plano cir-
              <lb/>
            culi non æquidiſtat producta alicubi planum
              <lb/>
            eiuſdem circuli ſecabit extra circulum ipſum,
              <lb/>
            vt in γ, & </s>
            <s xml:id="echoid-s9879" xml:space="preserve">tunc quidem à puncto γ extra,
              <lb/>
            circulum poſito ducantur duæ contingentes γ A,
              <lb/>
            & </s>
            <s xml:id="echoid-s9880" xml:space="preserve">γ M. </s>
            <s xml:id="echoid-s9881" xml:space="preserve">Manifeſtum eſt, rectas lineas A γ,
              <lb/>
            B E in eodem plano iacere: </s>
            <s xml:id="echoid-s9882" xml:space="preserve">tranſit verò præ-
              <lb/>
            dictum planum per vertices B, & </s>
            <s xml:id="echoid-s9883" xml:space="preserve">E duorum
              <lb/>
            conorum, atque per γ A tangentem circulum
              <lb/>
            baſis communis; </s>
            <s xml:id="echoid-s9884" xml:space="preserve">igitur planum A E B vtrum-
              <lb/>
            que conum contingit. </s>
            <s xml:id="echoid-s9885" xml:space="preserve">Eodem modo planum E
              <lb/>
            B M ex altera parte vtrumq; </s>
            <s xml:id="echoid-s9886" xml:space="preserve">conum tanget.
              <lb/>
            </s>
            <s xml:id="echoid-s9887" xml:space="preserve">Et hoc erat faciendum.</s>
            <s xml:id="echoid-s9888" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9889" xml:space="preserve">In qualibet coniſectione H A I
              <lb/>
              <note position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">PROP
                <lb/>
              16.
                <lb/>
              Addit</note>
            cuius diameter A L non ſit axis,
              <lb/>
            per eius verticem A aliam coniſe-
              <lb/>
            ctionem in eodem plano deſcribere,
              <lb/>
            quæ priorem abſcindat, atque eadem
              <lb/>
            recta linea vtramq; </s>
            <s xml:id="echoid-s9890" xml:space="preserve">ſectionem tangat
              <lb/>
            in puncto mutuæ earum abſcisſionis.</s>
            <s xml:id="echoid-s9891" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9892" xml:space="preserve">Sicut in conſtructione prop. </s>
            <s xml:id="echoid-s9893" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9894" xml:space="preserve">& </s>
            <s xml:id="echoid-s9895" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s9896" xml:space="preserve">addit. </s>
            <s xml:id="echoid-s9897" xml:space="preserve">factum eſt, deſcribatur conus B A
              <lb/>
            C comprehendens ſectionem H A I, cu
              <lb/>
            ius vertex B baſis circulus A M C per
              <lb/>
            ſectionis verticem A ductus, & </s>
            <s xml:id="echoid-s9898" xml:space="preserve">trian-
              <lb/>
            gulum per axim B A C efficiat diame-
              <lb/>
            trum A L: </s>
            <s xml:id="echoid-s9899" xml:space="preserve">& </s>
            <s xml:id="echoid-s9900" xml:space="preserve">in duobus circulis æqui-
              <lb/>
            diſtantibus A C M, & </s>
            <s xml:id="echoid-s9901" xml:space="preserve">in eo, qui per
              <lb/>
            ſectionis baſim H I ducitur idẽ planum
              <lb/>
            ſectionis conicæ deſignet duas parallelas
              <lb/>
            A D, H I, & </s>
            <s xml:id="echoid-s9902" xml:space="preserve">planum trianguli per axim
              <lb/>
            efficiat circulorũ diamctros C A, & </s>
            <s xml:id="echoid-s9903" xml:space="preserve">eum,
              <lb/>
            qui per L ducitur æquidiſtantes inter ſe: </s>
            <s xml:id="echoid-s9904" xml:space="preserve">
              <lb/>
            ergo ſicuti baſis H I perpendicularis eſt
              <lb/>
            ad circuli diametrum per L ductam, ſeu
              <lb/>
            ad baſim trianguli per axim, ita D </s>
          </p>
        </div>
      </text>
    </echo>
Impressum