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
231 193
232 194
233 195
234 196
235 197
236 198
237 199
238 200
239 201
240 202
241 203
242 204
243 205
244 206
245 207
246 208
247 209
248 210
249 211
250 212
251 213
252 214
253 215
254 216
255 217
256 218
257 219
258 220
259 221
260 222
< >
page |< < (238) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div759" type="section" level="1" n="236">
          <pb o="238" file="0276" n="276" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s8914" xml:space="preserve">Vt quadratum A C ad C B in BA,
              <lb/>
              <figure xlink:label="fig-0276-01" xlink:href="fig-0276-01a" number="321">
                <image file="0276-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0276-01"/>
              </figure>
            ita ponatur E G ad B H: </s>
            <s xml:id="echoid-s8915" xml:space="preserve">& </s>
            <s xml:id="echoid-s8916" xml:space="preserve">educa-
              <lb/>
            mus H I parallelam B C, & </s>
            <s xml:id="echoid-s8917" xml:space="preserve">exten-
              <lb/>
            datur per H I planum eleuatum ſuper
              <lb/>
            triangulum A B C ad angulos rectos
              <lb/>
            efficiens in cono ſectionem K H L.
              <lb/>
            </s>
            <s xml:id="echoid-s8918" xml:space="preserve">Dico eam æqualem eſſe ſectioni D E. </s>
            <s xml:id="echoid-s8919" xml:space="preserve">
              <lb/>
            Quia quadratum A C ad C B in B
              <lb/>
            A eſt, vt E G ad B H; </s>
            <s xml:id="echoid-s8920" xml:space="preserve">ergo poten-
              <lb/>
            tes eductæ ad axim H I in ſectione
              <lb/>
              <note position="right" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">a</note>
            K H L poſſunt applicata contenta ab
              <lb/>
            abſciſſis illarum potentium, & </s>
            <s xml:id="echoid-s8921" xml:space="preserve">ab E
              <lb/>
            G; </s>
            <s xml:id="echoid-s8922" xml:space="preserve">quare E G erit erectum ſectionis
              <lb/>
            K H, & </s>
            <s xml:id="echoid-s8923" xml:space="preserve">idem etiam eſt erectum ſectionis D E; </s>
            <s xml:id="echoid-s8924" xml:space="preserve">ergo duo erecta duarum
              <lb/>
            ſectionum ſunt æqualia, & </s>
            <s xml:id="echoid-s8925" xml:space="preserve">propterea ſectiones æquales ſunt (1. </s>
            <s xml:id="echoid-s8926" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s8927" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8928" xml:space="preserve">Et dico, quod in cono A B C reperiri non poteſt ſectio alia parabo-
              <lb/>
              <note position="right" xlink:label="note-0276-02" xlink:href="note-0276-02a" xml:space="preserve">b</note>
            lica, cuius vertex ſit ſuper A B, quæ eidem D E ſit æqualis. </s>
            <s xml:id="echoid-s8929" xml:space="preserve">Si enim
              <lb/>
            hoc eſt poſſibile, ſit axis illius ſectionis M N, qui quidem cadet in trian-
              <lb/>
            gulo A B C; </s>
            <s xml:id="echoid-s8930" xml:space="preserve">quia conus eſt rectus, & </s>
            <s xml:id="echoid-s8931" xml:space="preserve">erectum illius ſit M O; </s>
            <s xml:id="echoid-s8932" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s8933" xml:space="preserve">M O
              <lb/>
            ad M B erit, vt G E ad B H; </s>
            <s xml:id="echoid-s8934" xml:space="preserve">eſtque B H maior, quàm B M; </s>
            <s xml:id="echoid-s8935" xml:space="preserve">ergo M O
              <lb/>
              <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">ex conu.
                <lb/>
              Prop. 1.
                <lb/>
              huius.</note>
            minor eſt, quàm G E; </s>
            <s xml:id="echoid-s8936" xml:space="preserve">quare ſectio, cuius axis eſt M N non eſt æqualis
              <lb/>
            ſectioni D E; </s>
            <s xml:id="echoid-s8937" xml:space="preserve">& </s>
            <s xml:id="echoid-s8938" xml:space="preserve">tamen ſuppoſita fuit æqualis illi, quod eſt abſurdum.
              <lb/>
            </s>
            <s xml:id="echoid-s8939" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s8940" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div762" type="section" level="1" n="237">
          <head xml:id="echoid-head298" xml:space="preserve">PROPOSITIO XXVII.</head>
          <p>
            <s xml:id="echoid-s8941" xml:space="preserve">SIt deinde hyperbole A B, cuius axis C D, inclinatus B
              <lb/>
              <note position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">a</note>
            D, & </s>
            <s xml:id="echoid-s8942" xml:space="preserve">erectus B E; </s>
            <s xml:id="echoid-s8943" xml:space="preserve">atque quadratum axis F G dati coni
              <lb/>
            recti F H I ad quadratum G H ſemidiametri baſis eius, non
              <lb/>
            habeat maiorem proportionem, quàm habet figura, ſcilicet
              <lb/>
            quàm habet D B ad B E.</s>
            <s xml:id="echoid-s8944" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8945" xml:space="preserve">Sit prius proportio eadem, & </s>
            <s xml:id="echoid-s8946" xml:space="preserve">producamus I F ad K; </s>
            <s xml:id="echoid-s8947" xml:space="preserve">& </s>
            <s xml:id="echoid-s8948" xml:space="preserve">ducamus K
              <lb/>
            L ſubtendentem angulum H F K, quæ parallela ſit ipſi F G, & </s>
            <s xml:id="echoid-s8949" xml:space="preserve">æqualis
              <lb/>
            exiſtat ipſi D B; </s>
            <s xml:id="echoid-s8950" xml:space="preserve">& </s>
            <s xml:id="echoid-s8951" xml:space="preserve">per K L planum extendatur eleuatum ad angulos re-
              <lb/>
            ctos ſuper planum trianguli H F I, quod efficiet in ſuperſicie conica ſe-
              <lb/>
            ctionem hyperbolicam, cuius axis erit L M, & </s>
            <s xml:id="echoid-s8952" xml:space="preserve">inclinatus K L. </s>
            <s xml:id="echoid-s8953" xml:space="preserve">Et quia
              <lb/>
            F G parallela eſt K L, erit quadratum F G ad G I in G H, vt K L in-
              <lb/>
              <note position="left" xlink:label="note-0276-05" xlink:href="note-0276-05a" xml:space="preserve">12. lib. 1.</note>
            clinatus ad illius erectum, ſiue vt D B ad B E; </s>
            <s xml:id="echoid-s8954" xml:space="preserve">facta autem fuit K L æ-
              <lb/>
            qualis D B; </s>
            <s xml:id="echoid-s8955" xml:space="preserve">ergo erectus inclinati K L æqualis eſt B E; </s>
            <s xml:id="echoid-s8956" xml:space="preserve">& </s>
            <s xml:id="echoid-s8957" xml:space="preserve">propterea ſe-
              <lb/>
              <note position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">2. huius.</note>
              <note position="right" xlink:label="note-0276-07" xlink:href="note-0276-07a" xml:space="preserve">b</note>
            ctio, cuius axis eſt L M æqualis eſt ſectioni A B. </s>
            <s xml:id="echoid-s8958" xml:space="preserve">Nec reperiri poterit
              <lb/>
            in cono H F I alia ſectio hyperbolica, cuius vertex ſit ſuper H F, quæ
              <lb/>
            æqualis ſit A B; </s>
            <s xml:id="echoid-s8959" xml:space="preserve">quia, ſi reperiri poſſet eſſet illius axis in plano trianguli
              <lb/>
            H F I, & </s>
            <s xml:id="echoid-s8960" xml:space="preserve">eius inclinatus, ſubtendens angulum H F K æqualis eſſet D B,
              <lb/>
            nec tamen eſſet K L, nequè ipſi æquidiſtans (eo quod, ſi </s>
          </p>
        </div>
      </text>
    </echo>
Impressum