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
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
311 273
312 274
313 275
314 276
315 277
316 278
317 279
318 280
319 281
320 282
< >
page |< < (319) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div967" type="section" level="1" n="306">
          <p style="it">
            <s xml:id="echoid-s11362" xml:space="preserve">
              <pb o="319" file="0357" n="358" rhead="Conicor. Lib. VII."/>
            rectangulum ſub A G E in E H æquale quadrato ex G E, & </s>
            <s xml:id="echoid-s11363" xml:space="preserve">ſi pro-
              <lb/>
            portio illa maior fuerit, erit quoque rectangulum maius quadrato; </s>
            <s xml:id="echoid-s11364" xml:space="preserve">& </s>
            <s xml:id="echoid-s11365" xml:space="preserve">
              <lb/>
            ſi illa proportio minor fuerit, Rectangulum quadrato miuus erit.</s>
            <s xml:id="echoid-s11366" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11367" xml:space="preserve">Et primo, quia A G ad G E ponitur vt G H ad H E; </s>
            <s xml:id="echoid-s11368" xml:space="preserve">componendo A G E
              <lb/>
            ad G E, erit vt G E ad E H, & </s>
            <s xml:id="echoid-s11369" xml:space="preserve">rectangulum ſub extremis contentum, ni-
              <lb/>
            mirum ſub A G E in E H, æquale erit quadrato ex intermedia G E.</s>
            <s xml:id="echoid-s11370" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11371" xml:space="preserve">Secundo, ſi A G ad G E maiorem proportionem habuerit, quàm G H ad H
              <lb/>
            E, componendo A G E ad G E maiorem proportionem habebit, quàm G E ad
              <lb/>
            E H, & </s>
            <s xml:id="echoid-s11372" xml:space="preserve">ideo Rectangulum ſub A G E in E H maius erit quadrato ex G E.
              <lb/>
            </s>
            <s xml:id="echoid-s11373" xml:space="preserve">pari ratione ſi A G ad G E minorem proportionem habuerit, quàm G H ad
              <lb/>
            H E, oſtendetur Rectangulum ex A G E in E H minus quadrato G E.</s>
            <s xml:id="echoid-s11374" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div969" type="section" level="1" n="307">
          <head xml:id="echoid-head380" xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:id="echoid-s11375" xml:space="preserve">IN hyperbola, cuius axis C A, & </s>
            <s xml:id="echoid-s11376" xml:space="preserve">erectus A F, præſecta H A, in-
              <lb/>
            tercepta G A, diameter L I, cuius erectus I K, latus C E, & </s>
            <s xml:id="echoid-s11377" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0357-01" xlink:href="fig-0357-01a" number="425">
                <image file="0357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0357-01"/>
              </figure>
            diameter Q P, cuius erectus P R, latus C O: </s>
            <s xml:id="echoid-s11378" xml:space="preserve">Dico quod erectus P
              <lb/>
            R ab ipſo erecto I K, vel ab A F atque rectangulum ſub O G E in
              <lb/>
            G H ab ipſo quadrato G E, vel rectangulum ex O G A in A H ab
              <lb/>
            ipſo quadrato G A, vna deficiunt, vel vna æqualia ſunt, aut vna
              <lb/>
            excedunt.</s>
            <s xml:id="echoid-s11379" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11380" xml:space="preserve">Et primo ponatur rectangulum ſub O G E in E H æquale quadrato E G, er-
              <lb/>
            go idem rectangulum ſub O G E in E O ad rectangulum ſub E G O in E H,
              <lb/>
            ſeu E O ad E H eandem proportionem habet, quàm ad quadratum G E, & </s>
            <s xml:id="echoid-s11381" xml:space="preserve">
              <lb/>
            propterea E O ad E H erit vt rectangulum ſub E G O in E O ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum