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 |< < (42) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div172" type="section" level="1" n="70">
          <p style="it">
            <s xml:id="echoid-s2068" xml:space="preserve">
              <pb o="42" file="0080" n="80" rhead="Apollonij Pergæi"/>
            pter parallelas D E,
              <lb/>
              <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a" number="57">
                <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-01"/>
              </figure>
            B G, & </s>
            <s xml:id="echoid-s2069" xml:space="preserve">ſimilitudinẽ
              <lb/>
            triangulorum E D I,
              <lb/>
            & </s>
            <s xml:id="echoid-s2070" xml:space="preserve">B G I, eſt D I ad I
              <lb/>
            G, vt E D ad B G;
              <lb/>
            </s>
            <s xml:id="echoid-s2071" xml:space="preserve">igitur D I ad I G ma-
              <lb/>
            iorem proportionem
              <lb/>
            habet, quàm G F ad
              <lb/>
            F D, & </s>
            <s xml:id="echoid-s2072" xml:space="preserve">componendo
              <lb/>
            D G ad G I maio rem
              <lb/>
            rationem habebit,
              <lb/>
            quàm eadem G D ad
              <lb/>
            D F; </s>
            <s xml:id="echoid-s2073" xml:space="preserve">& </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Ideo I G mi-
              <lb/>
            nor eſt, quàm D F.</s>
            <s xml:id="echoid-s2075" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">c</note>
          <p style="it">
            <s xml:id="echoid-s2076" xml:space="preserve">Igitur G F æqua-
              <lb/>
            lis eſt GO, ergo G
              <lb/>
            O ad O M, &</s>
            <s xml:id="echoid-s2077" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Igi-
              <lb/>
            tur G F æqualis eſt G
              <lb/>
            O, & </s>
            <s xml:id="echoid-s2079" xml:space="preserve">quia F O ſecatur
              <lb/>
            bifariam in G, & </s>
            <s xml:id="echoid-s2080" xml:space="preserve">non
              <lb/>
            bifariam in M (ex
              <lb/>
            lemmate ſexto huius
              <lb/>
            libri) habebit ſemisſis G O ad vnum ſegmentorum inæqualium M O maiorem pro-
              <lb/>
            portionem, quàm reliquum ſegmentum M F ad alteram medietatem F G, ſed pro-
              <lb/>
            pter parallelas P M, B G, & </s>
            <s xml:id="echoid-s2081" xml:space="preserve">ſimilitudinem triangulorum B G O, P M O eſt G O ad
              <lb/>
            O M, vt B G ad P M, ergo B G ad P M maiorem proportionem habet, quàm M F ad
              <lb/>
            F G: </s>
            <s xml:id="echoid-s2082" xml:space="preserve">habet verò B G ad minorem M K maiorem proportionem, quàm ad M P (cum
              <lb/>
            punctum P tangentis cadat extra ſectionem); </s>
            <s xml:id="echoid-s2083" xml:space="preserve">ergo B G ad K M adhuc maiorem pro-
              <lb/>
            portionem habet, quàm M F ad F G.</s>
            <s xml:id="echoid-s2084" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2085" xml:space="preserve">Itaque K M in M F minus eſt, quàm B G in G F, &</s>
            <s xml:id="echoid-s2086" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">Quoniam prima B G
              <lb/>
              <note position="right" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">d</note>
            ad ſecundam K M maiorem proportionem habet, quàm tertia M F ad quartam F G;
              <lb/>
            </s>
            <s xml:id="echoid-s2088" xml:space="preserve">ergo ex lemmate quinto huius librirectangulum ſub intermedijs contentum K M F
              <lb/>
            minus erit rectangulo B G F ſub extremis cõtento; </s>
            <s xml:id="echoid-s2089" xml:space="preserve">poſtea, quia H ad B G ex hypotheſi
              <lb/>
            erat, vt G F ad F D, poſita autem fuit E D maior, quàm H, quæ eſt prima propor-
              <lb/>
            tionalium; </s>
            <s xml:id="echoid-s2090" xml:space="preserve">ergo E D ad B G maiorem proportionem habet, quàm G F ad F D, & </s>
            <s xml:id="echoid-s2091" xml:space="preserve">pro-
              <lb/>
              <note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">Lem. 5.</note>
            pterea rectangulum ſub extremis E D F maius erit rectangulo ſub intermedijs con-
              <lb/>
            tento B G F; </s>
            <s xml:id="echoid-s2092" xml:space="preserve">fuit autem rectangulum B G F maius rectangulo K M F; </s>
            <s xml:id="echoid-s2093" xml:space="preserve">igitur rectan-
              <lb/>
            gulum E D F multò maius eſt, quàm rectangulum K M F, & </s>
            <s xml:id="echoid-s2094" xml:space="preserve">ideo, ex eodem lemma-
              <lb/>
            te quinto, E D ad M K, nempe D R ad R M (propter ſimilitudinem triangulorum
              <lb/>
            E D R, & </s>
            <s xml:id="echoid-s2095" xml:space="preserve">K M R) maiorem rationem habet, quàm M F ad F D.</s>
            <s xml:id="echoid-s2096" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2097" xml:space="preserve">Et componendo patet, quod D F, &</s>
            <s xml:id="echoid-s2098" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2099" xml:space="preserve">Quoniam D R ad R M maiorem ratio-
              <lb/>
              <note position="right" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">e</note>
            nem habet, quàm M F ad F D, componendo D M ad M R habebit maiorem propor-
              <lb/>
            tionem, quàm eadem M D ad D F, & </s>
            <s xml:id="echoid-s2100" xml:space="preserve">propterea D F mator eſt, quàm R M, eſt verò
              <lb/>
            ſemisſis erecti A C æqualis D F ex conſtructione, igitur M R minor eſt A C medieta-
              <lb/>
            te lateris recti, & </s>
            <s xml:id="echoid-s2101" xml:space="preserve">propterea breuiſsima educta ex K ſecat ex axi ſegmentum maius,
              <lb/>
              <note position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">8. huius.</note>
            quàm M R; </s>
            <s xml:id="echoid-s2102" xml:space="preserve">ideoque cadit extra, ſcilicet infra ramum K R E.</s>
            <s xml:id="echoid-s2103" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum