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 |< < (336) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1011" type="section" level="1" n="320">
          <pb o="336" file="0374" n="375" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div1013" type="section" level="1" n="321">
          <head xml:id="echoid-head397" xml:space="preserve">In Sectionem VIII. Propoſit. XXXXIIII.
            <lb/>
          XXXXV. & XXXXVI.</head>
          <head xml:id="echoid-head398" xml:space="preserve">LEMM A.X.</head>
          <p style="it">
            <s xml:id="echoid-s11762" xml:space="preserve">SI rectæ lineæ G H bifariam ſectæ in D addantur ſegmenta H A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11763" xml:space="preserve">H E atque proportio dupli E H ad H G eadem fuerit propor-
              <lb/>
            tioni G H ad H A: </s>
            <s xml:id="echoid-s11764" xml:space="preserve">dico duplum rectanguli ex G A, & </s>
            <s xml:id="echoid-s11765" xml:space="preserve">H E in H
              <lb/>
            A æquale eſſe quadratis ex G A, & </s>
            <s xml:id="echoid-s11766" xml:space="preserve">ex A H: </s>
            <s xml:id="echoid-s11767" xml:space="preserve">ſi verò proportio illa
              <lb/>
            maior fuerit, erit quoque rectangulum maius quadratis: </s>
            <s xml:id="echoid-s11768" xml:space="preserve">ſi verò propor-
              <lb/>
            tio fuerit minor, rectangulum minus erit quadratis.</s>
            <s xml:id="echoid-s11769" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11770" xml:space="preserve">Primo quia ſi duplum E H ad H G, eſt vt G H ad H A, ergo duplum re-
              <lb/>
            ctanguli E H A æquale erit quadrato G H, & </s>
            <s xml:id="echoid-s11771" xml:space="preserve">addatur communiter duplum
              <lb/>
              <figure xlink:label="fig-0374-01" xlink:href="fig-0374-01a" number="444">
                <image file="0374-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0374-01"/>
              </figure>
            rectanguli G A H, erit duplum
              <lb/>
            rectanguli ex ſumma G A, & </s>
            <s xml:id="echoid-s11772" xml:space="preserve">E H
              <lb/>
            in A H æquale duplo rectanguli G
              <lb/>
            A H cum quadrato G H; </s>
            <s xml:id="echoid-s11773" xml:space="preserve">his verò
              <lb/>
            ſpatijs æquantur quadrata ex G A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11774" xml:space="preserve">ex A H, ergo duplum rectan-
              <lb/>
            guli ex ſumma G A, E H in A H æquale erit duobus quadratis ex G A, & </s>
            <s xml:id="echoid-s11775" xml:space="preserve">
              <lb/>
            ex A H.</s>
            <s xml:id="echoid-s11776" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11777" xml:space="preserve">Secundo, quia duplum E H ad H G, maiorem proportionem habet, quàm
              <lb/>
            G H ad A H, ergo duplum rectanguli E H A maius eſt quadrato G H, & </s>
            <s xml:id="echoid-s11778" xml:space="preserve">ad-
              <lb/>
            dito communiter duplo rectanguli G A H, erit duplum rectanguli ex G A, E
              <lb/>
            H in A H maius duobus quadratis ex G A, & </s>
            <s xml:id="echoid-s11779" xml:space="preserve">ex A H.</s>
            <s xml:id="echoid-s11780" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11781" xml:space="preserve">Tertio, quia duplum E H ad H G minorem proportionem habet, quàm G H
              <lb/>
            ad A H, ergo duplum rectanguli E H A minus eſt quadrato G H, & </s>
            <s xml:id="echoid-s11782" xml:space="preserve">addito
              <lb/>
            duplo rectanguli G A H, erit duplum rectanguli ex G A, E H in A H minus
              <lb/>
            quadratis ex G A, & </s>
            <s xml:id="echoid-s11783" xml:space="preserve">ex A H.</s>
            <s xml:id="echoid-s11784" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1015" type="section" level="1" n="322">
          <head xml:id="echoid-head399" xml:space="preserve">LEMM A XI.</head>
          <p style="it">
            <s xml:id="echoid-s11785" xml:space="preserve">SI recta linea G H ſecetur exterius in A, E, & </s>
            <s xml:id="echoid-s11786" xml:space="preserve">ſit eadem G H
              <lb/>
            differentia nedum ſegmentorum G E, & </s>
            <s xml:id="echoid-s11787" xml:space="preserve">E H, ſed etiam duo-
              <lb/>
            rum ſegmentorum G A, & </s>
            <s xml:id="echoid-s11788" xml:space="preserve">A H: </s>
            <s xml:id="echoid-s11789" xml:space="preserve">dico quod quadrata ex maximo,
              <lb/>
            & </s>
            <s xml:id="echoid-s11790" xml:space="preserve">ex vno intermediorum ſegmentorum, ſcilicet ex G E, & </s>
            <s xml:id="echoid-s11791" xml:space="preserve">ex E H
              <lb/>
              <figure xlink:label="fig-0374-02" xlink:href="fig-0374-02a" number="445">
                <image file="0374-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0374-02"/>
              </figure>
            æqualia ſunt quadratis ex
              <lb/>
            reliquo intermediorum, & </s>
            <s xml:id="echoid-s11792" xml:space="preserve">
              <lb/>
            ex minimo ſegmento, ſci-
              <lb/>
            licet ex G A, & </s>
            <s xml:id="echoid-s11793" xml:space="preserve">ex A
              <lb/>
            H vna cum duplo </s>
          </p>
        </div>
      </text>
    </echo>
Impressum