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
311 273
312 274
313 275
314 276
315 277
316 278
317 279
318 280
319 281
320 282
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
< >
page |< < (250) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div792" type="section" level="1" n="244">
          <p>
            <s xml:id="echoid-s9360" xml:space="preserve">
              <pb o="250" file="0288" n="288" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0288-01" xlink:href="fig-0288-01a" number="336">
                <image file="0288-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0288-01"/>
              </figure>
            E I eandem proportionẽ habet, quàm quadratum B Q ad C Q in Q A
              <lb/>
            eſtq; </s>
            <s xml:id="echoid-s9361" xml:space="preserve">C Q æqualis Q A, atq; </s>
            <s xml:id="echoid-s9362" xml:space="preserve">T S æqualis S E, & </s>
            <s xml:id="echoid-s9363" xml:space="preserve">T S ad S E eandẽ pro-
              <lb/>
              <note position="right" xlink:label="note-0288-01" xlink:href="note-0288-01a" xml:space="preserve">e</note>
            portionẽ habet, quã T R ad R H, ſeu quàm E V ad V H; </s>
            <s xml:id="echoid-s9364" xml:space="preserve">igitur E V æqua-
              <lb/>
            lis eſt V H; </s>
            <s xml:id="echoid-s9365" xml:space="preserve">quod eſt abſurdum; </s>
            <s xml:id="echoid-s9366" xml:space="preserve">propterea quo L O diameter, quæ ad illã
              <lb/>
            perpendicularis eſt, bifariam ſecat eam in N. </s>
            <s xml:id="echoid-s9367" xml:space="preserve">Oſtenſum igitur eſt, non repe-
              <lb/>
            riri conum alium continentem ſectionem D E F, præter ſuperius expoſi-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s9368" xml:space="preserve">Tandem ſupponamus, quadratum B Q ad quadratum Q A habere
              <lb/>
            minorem proportionem, quàm E H ad E I. </s>
            <s xml:id="echoid-s9369" xml:space="preserve">Patet quadratum L P, nẽ-
              <lb/>
              <note position="right" xlink:label="note-0288-02" xlink:href="note-0288-02a" xml:space="preserve">f</note>
            pe N E, ſeu O N in N L ad quadratum E P, nempe ad quadratum N
              <lb/>
            L, ſcilicet O N ad N L habere minorem proportionem, quàm H E ad
              <lb/>
            E I: </s>
            <s xml:id="echoid-s9370" xml:space="preserve">ponamus iam O N ad N X, vt H E ad E I, & </s>
            <s xml:id="echoid-s9371" xml:space="preserve">per X ducamus R
              <lb/>
            X Y parallelam H E, & </s>
            <s xml:id="echoid-s9372" xml:space="preserve">iungamus E R, O R, & </s>
            <s xml:id="echoid-s9373" xml:space="preserve">H R producatur ad T
              <lb/>
            quouſque ſecet E T parallelam ipſi O R. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">Oſtendetur (quemadmodum
              <lb/>
              <note position="right" xlink:label="note-0288-03" xlink:href="note-0288-03a" xml:space="preserve">g</note>
            ſupra dictum eſt) quod E T R, B A C ſunt iſoſcelia, & </s>
            <s xml:id="echoid-s9375" xml:space="preserve">ſimilia. </s>
            <s xml:id="echoid-s9376" xml:space="preserve">Et quia
              <lb/>
            E H ad E I eſt vt O N ad N X; </s>
            <s xml:id="echoid-s9377" xml:space="preserve">nempe vt O V ad V R, nempe vt O V
              <lb/>
            in V R, quod eſt æquale ipſi E V in V H ad quadratum V R; </s>
            <s xml:id="echoid-s9378" xml:space="preserve">hæc au-
              <lb/>
            tem proportio componitur ex E V, nempe S R ad V R, nempe ad E S,
              <lb/>
            & </s>
            <s xml:id="echoid-s9379" xml:space="preserve">ex proportione V H ad V R, nempe S R ad S T, ex quibus compo-
              <lb/>
            nitur proportio quadrati R S ad S T in S E; </s>
            <s xml:id="echoid-s9380" xml:space="preserve">igitur quadratum R S ad E
              <lb/>
            S in S T eandẽ proportionem habet, quàm H E ad E I; </s>
            <s xml:id="echoid-s9381" xml:space="preserve">& </s>
            <s xml:id="echoid-s9382" xml:space="preserve">propterea
              <lb/>
            planum ſectionis D E F in cono, cuius vertex eſt R, & </s>
            <s xml:id="echoid-s9383" xml:space="preserve">illius trianguli
              <lb/>
            latera R E, R T, producit ſectionem hyperbolicam, cuius inclinatus eſt
              <lb/>
            E H, & </s>
            <s xml:id="echoid-s9384" xml:space="preserve">erectus E I; </s>
            <s xml:id="echoid-s9385" xml:space="preserve">quare conus cuius vertex eſt R, continet ſectionẽ D E
              <lb/>
            F, nec non continet illam alius conus, huic cono ſimilis, cuius vertex
              <lb/>
            eſt Y; </s>
            <s xml:id="echoid-s9386" xml:space="preserve">& </s>
            <s xml:id="echoid-s9387" xml:space="preserve">hi duo coni ſunt ſimiles cono A B C, nec continet illam ter-
              <lb/>
            tius alius conus, qui ſimilis ſit cono A B C, nam (ſi hoc ſieri poſſibile
              <lb/>
            eſt) contineat illam alius conus, cuius vertex Z, & </s>
            <s xml:id="echoid-s9388" xml:space="preserve">punctum verticis
              <lb/>
            illius incidet in arcum E L H, & </s>
            <s xml:id="echoid-s9389" xml:space="preserve">iungamus O Z, quæ ſecet H E in e:
              <lb/>
            </s>
            <s xml:id="echoid-s9390" xml:space="preserve">
              <note position="right" xlink:label="note-0288-04" xlink:href="note-0288-04a" xml:space="preserve">h</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum