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
281 243
282 244
283 245
284 246
285 247
286 248
287 249
288 250
289 251
290 252
291 253
292 254
293 255
294 256
295 257
296 258
297 259
298 260
299 261
300 262
301 263
302 264
303 265
304 266
305 267
306 268
307 269
308 270
309 271
310 272
< >
page |< < (157) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div586" type="section" level="1" n="192">
          <p>
            <s xml:id="echoid-s6131" xml:space="preserve">
              <pb o="157" file="0195" n="195" rhead="Conicor. Lib. VI."/>
            lis alicui earum (ſi poſ-
              <lb/>
              <note position="left" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">b</note>
            ſibile eſt) ergo poſſu-
              <lb/>
              <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a" number="212">
                <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0195-01"/>
              </figure>
            mus educere in ſingulis
              <lb/>
            ſectionibus potentes,
              <lb/>
            quæ habeant ad ſua ab-
              <lb/>
            ſciſſa axium eaſdẽ pro-
              <lb/>
            portiones, & </s>
            <s xml:id="echoid-s6132" xml:space="preserve">abſciſſæ in
              <lb/>
            ter ſe ſint proportiona-
              <lb/>
            les; </s>
            <s xml:id="echoid-s6133" xml:space="preserve">ſintque illæ V M,
              <lb/>
            Y N, P K, R L. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">Quia
              <lb/>
            Y N ad N F poſita fuit,
              <lb/>
            vt R L ad L B, & </s>
            <s xml:id="echoid-s6135" xml:space="preserve">N F
              <lb/>
            ad F M, vt L B ad BK,
              <lb/>
            & </s>
            <s xml:id="echoid-s6136" xml:space="preserve">F M ad M V, vt B
              <lb/>
            K ad K P; </s>
            <s xml:id="echoid-s6137" xml:space="preserve">ergo Y N ad
              <lb/>
            M V in potentia, nem-
              <lb/>
            pe N F ad M F (cum
              <lb/>
            ſectio ſit parabola 19.
              <lb/>
            </s>
            <s xml:id="echoid-s6138" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6139" xml:space="preserve">nempe L B ad B K ex contructione erit, vt R L ad K P potentia,
              <lb/>
              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">20. lib. 1.</note>
            quæ eandem proportionem habent, quàm a L in L B ad a K in K B;
              <lb/>
            </s>
            <s xml:id="echoid-s6140" xml:space="preserve">
              <note position="right" xlink:label="note-0195-03" xlink:href="note-0195-03a" xml:space="preserve">21. lib. 1.</note>
            quia ſectio eſt hyperbolæ, aut ellipſis (20. </s>
            <s xml:id="echoid-s6141" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6142" xml:space="preserve">quare a L in L B ad a
              <lb/>
            K in K B eſt, vt L B ad B K; </s>
            <s xml:id="echoid-s6143" xml:space="preserve">quare a L eſt æqualis a K: </s>
            <s xml:id="echoid-s6144" xml:space="preserve">quod eſt abſur-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">Igitur parabole non eſt ſimilis vlli reliquarum ſectionum. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">Et hoc
              <lb/>
            erat probandum.</s>
            <s xml:id="echoid-s6147" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div588" type="section" level="1" n="193">
          <head xml:id="echoid-head247" xml:space="preserve">PROPOSITIO XIV.</head>
          <p>
            <s xml:id="echoid-s6148" xml:space="preserve">ET ſic oſtendetur, quod hyperbolæ non eſt ſimilis ellipſi.</s>
            <s xml:id="echoid-s6149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6150" xml:space="preserve">Alioquin ſequitur, quod quadratum
              <lb/>
              <figure xlink:label="fig-0195-02" xlink:href="fig-0195-02a" number="213">
                <image file="0195-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0195-02"/>
              </figure>
              <note position="left" xlink:label="note-0195-04" xlink:href="note-0195-04a" xml:space="preserve">a</note>
            R L ad quadratum K P, nempe a L in
              <lb/>
            L B ad a K in K B in hyperbola eſt, vt
              <lb/>
            quadratum Y N ad quadratum M V,
              <lb/>
            ſeu vt b N in N F ad b M in M F in el-
              <lb/>
            lipſi. </s>
            <s xml:id="echoid-s6151" xml:space="preserve">His poſitis: </s>
            <s xml:id="echoid-s6152" xml:space="preserve">quia L B ad B K po-
              <lb/>
              <note position="right" xlink:label="note-0195-05" xlink:href="note-0195-05a" xml:space="preserve">21. lib. 1.</note>
            ſita fuit, vt N F ad M F; </s>
            <s xml:id="echoid-s6153" xml:space="preserve">ergo a L ad
              <lb/>
            a K eandem proportionem habet, quàm
              <lb/>
            b N ad b M: </s>
            <s xml:id="echoid-s6154" xml:space="preserve">& </s>
            <s xml:id="echoid-s6155" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">Qua-
              <lb/>
            re ſectio A B non eſt ſimilis E F; </s>
            <s xml:id="echoid-s6157" xml:space="preserve">vt fue-
              <lb/>
            rat propoſitum.</s>
            <s xml:id="echoid-s6158" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum