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 |< < (251) 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-s9390" xml:space="preserve">
              <pb o="251" file="0289" n="289" rhead="Conicor. Lib. VI."/>
            Inde demonſtrabitur, quod H E ad E I habebit neceſſario eandem pro-
              <lb/>
            portionem, quàm O e ad e Z; </s>
            <s xml:id="echoid-s9391" xml:space="preserve">quod eſt abſurdum, quia haberet eandem
              <lb/>
            proportionem, quàm O N ad N X. </s>
            <s xml:id="echoid-s9392" xml:space="preserve">Quapropter non continet illam ter-
              <lb/>
            tius alius conus ſimilis cono A B C.</s>
            <s xml:id="echoid-s9393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9394" xml:space="preserve">Supponamus iam, quadratum B Q ad quadratum Q A maiorem pro-
              <lb/>
            portionem habere, quàm H E ad E I. </s>
            <s xml:id="echoid-s9395" xml:space="preserve">Dico, exhiberi non poſſe conum
              <lb/>
              <note position="left" xlink:label="note-0289-01" xlink:href="note-0289-01a" xml:space="preserve">i</note>
            ſimilem cono A B C, qui contineat ſectionem D E F. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">Alioquin conti-
              <lb/>
            neat illam conus, cuius vertex eſt R, & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">demonſtrabitur, quod O V ad
              <lb/>
            V R ſit, vt H E ad E I, quæ habet minorem proportionem, quàm qua-
              <lb/>
            dratum B Q ad quadratum Q A, quæ oſtenſa eſt eadem, quàm O N ad
              <lb/>
            N L; </s>
            <s xml:id="echoid-s9398" xml:space="preserve">ergo O V ad V R; </s>
            <s xml:id="echoid-s9399" xml:space="preserve">nempe O N ad N X minorem, proportionem
              <lb/>
            habet, quàm eadẽ O N ad N L, quod eſt abſurdum. </s>
            <s xml:id="echoid-s9400" xml:space="preserve">Non igitur conti-
              <lb/>
            nebit ſectionem D E F conus ſimilis cono A B C. </s>
            <s xml:id="echoid-s9401" xml:space="preserve">Vt propoſitũ fuerat.</s>
            <s xml:id="echoid-s9402" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div796" type="section" level="1" n="245">
          <head xml:id="echoid-head308" xml:space="preserve">PROPOSITIO XXXI.</head>
          <p>
            <s xml:id="echoid-s9403" xml:space="preserve">SIt tandem ſectio elliptica A B C, eiuſque tranſuerſus axis A C, & </s>
            <s xml:id="echoid-s9404" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0289-02" xlink:href="note-0289-02a" xml:space="preserve">a</note>
            erectus A D, & </s>
            <s xml:id="echoid-s9405" xml:space="preserve">in plano perpendiculariter erecto ad ſectionis pla-
              <lb/>
            num A B C, fiat ſuper A C ſegmentum circuli, quod capiat angulum.
              <lb/>
            </s>
            <s xml:id="echoid-s9406" xml:space="preserve">
              <figure xlink:label="fig-0289-01" xlink:href="fig-0289-01a" number="337">
                <image file="0289-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0289-01"/>
              </figure>
            æqualem angulo F, eumque bifariam diuidamus in H, & </s>
            <s xml:id="echoid-s9407" xml:space="preserve">iungamus A H,
              <lb/>
            C H, & </s>
            <s xml:id="echoid-s9408" xml:space="preserve">ex H educamus H I, quæ ſecet circulum in K, & </s>
            <s xml:id="echoid-s9409" xml:space="preserve">occurrat ſub-
              <lb/>
              <note position="right" xlink:label="note-0289-03" xlink:href="note-0289-03a" xml:space="preserve">Lem. 10.
                <lb/>
              huius.</note>
            tenſæ extra circulum in I; </s>
            <s xml:id="echoid-s9410" xml:space="preserve">ſitque H I ad I K, vt A C ad A D: </s>
            <s xml:id="echoid-s9411" xml:space="preserve">& </s>
            <s xml:id="echoid-s9412" xml:space="preserve">e-
              <lb/>
            ducamus H L M eaſdem conditiones habens; </s>
            <s xml:id="echoid-s9413" xml:space="preserve">& </s>
            <s xml:id="echoid-s9414" xml:space="preserve">iungamus C K, A K,
              <lb/>
            ducaturque K N parallela A C, & </s>
            <s xml:id="echoid-s9415" xml:space="preserve">A N parallela H I, quæ ſecet K C
              <lb/>
              <note position="left" xlink:label="note-0289-04" xlink:href="note-0289-04a" xml:space="preserve">b</note>
            in O. </s>
            <s xml:id="echoid-s9416" xml:space="preserve">Quia H I in I K (quod eſt æquale ipſi C I in A I ad quadratum
              <lb/>
            I K) eſt vt A C ed A D; </s>
            <s xml:id="echoid-s9417" xml:space="preserve">& </s>
            <s xml:id="echoid-s9418" xml:space="preserve">proportio C I in A I ad quadratum I K
              <lb/>
            componitur ex ratione C I ad I K, nempe K N ad N O (propter </s>
          </p>
        </div>
      </text>
    </echo>
Impressum