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 |< < (328) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div992" type="section" level="1" n="314">
          <pb o="328" file="0366" n="367" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s11571" xml:space="preserve">Fiat H M æqualis maiori H D, erit E A differentia minimæ H A, & </s>
            <s xml:id="echoid-s11572" xml:space="preserve">in-
              <lb/>
            termediæ H E minor, quàm M A, quæ eſt differentia maximæ M H, & </s>
            <s xml:id="echoid-s11573" xml:space="preserve">mi-
              <lb/>
            nimæ H A, & </s>
            <s xml:id="echoid-s11574" xml:space="preserve">A D maior eſt quàm A H, ergo E A ad M A minorem pro-
              <lb/>
            portionem habet, quàm D A ad A H, & </s>
            <s xml:id="echoid-s11575" xml:space="preserve">permutando E A ad A D habebit mi-
              <lb/>
            norem proportionem, quàm M A ad A H, & </s>
            <s xml:id="echoid-s11576" xml:space="preserve">componendo E D ad D A mino-
              <lb/>
            proportionem habebit, quàm M H, ſiue D H ad A H, & </s>
            <s xml:id="echoid-s11577" xml:space="preserve">iterum componendo
              <lb/>
            E D A ad D A minorem proportionem habebit, quàm eadem D A ad A H, & </s>
            <s xml:id="echoid-s11578" xml:space="preserve">
              <lb/>
            propterea rectangulum ſub E D A in A H minus erit quadrato D A.</s>
            <s xml:id="echoid-s11579" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div994" type="section" level="1" n="315">
          <head xml:id="echoid-head390" xml:space="preserve">LEMMA VIII.</head>
          <p style="it">
            <s xml:id="echoid-s11580" xml:space="preserve">I Iſdem poſitis ſi D H maior fuerit, quàm A H ſed minor quàm E
              <lb/>
            H, fueritque proportio E A ad A D eadem proportioni M A ad A
              <lb/>
            H, dico rectangulum ſub E D A in A H æquale eſſe quadrato D A:
              <lb/>
            </s>
            <s xml:id="echoid-s11581" xml:space="preserve">ſi verò proportio illa maior fuerit, vel minor rectangulum ſimiliter qua-
              <lb/>
            drato maius, vel minus erit.</s>
            <s xml:id="echoid-s11582" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11583" xml:space="preserve">Quia E A ad A D po-
              <lb/>
              <figure xlink:label="fig-0366-01" xlink:href="fig-0366-01a" number="435">
                <image file="0366-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0366-01"/>
              </figure>
            nitur vt M A ad A H,
              <lb/>
            componendo E D ad D A,
              <lb/>
            erit vt M H, ſeu D H ad
              <lb/>
            H A, & </s>
            <s xml:id="echoid-s11584" xml:space="preserve">iterum componen-
              <lb/>
            do E D A ad D A, erit vt
              <lb/>
            D A ad A H, & </s>
            <s xml:id="echoid-s11585" xml:space="preserve">propterea rectangulum ſub E D A in A H æquale erit qua-
              <lb/>
            drato D A.</s>
            <s xml:id="echoid-s11586" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11587" xml:space="preserve">Quando verò E A ad A D maiorem proportionem habet, quàm M A ad A
              <lb/>
            H, t@nc bis componendo E D A ad D A maiorem proportionem habebit, quàm
              <lb/>
            D A ad A H, & </s>
            <s xml:id="echoid-s11588" xml:space="preserve">propterea rectangulum ſub extremis; </s>
            <s xml:id="echoid-s11589" xml:space="preserve">ſcilicet ſub E D A in
              <lb/>
            A H maius erit quadrato intermediæ D A: </s>
            <s xml:id="echoid-s11590" xml:space="preserve">non ſecus quando E A ad A D
              <lb/>
            minorem peoportionem habet, quàm M A ad A H, oſtendetur rectangulum ſub
              <lb/>
            E D A in A H minus quadrato ex D A.</s>
            <s xml:id="echoid-s11591" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div996" type="section" level="1" n="316">
          <head xml:id="echoid-head391" xml:space="preserve">LEMMA IX.</head>
          <p style="it">
            <s xml:id="echoid-s11592" xml:space="preserve">I N hyperbola, cuius axis A C, erectus A F, præſecta H A, in-
              <lb/>
            tercepta G A, centrum D, diameter I L, eiuſque erectus I K,
              <lb/>
            @ C E ſit latus eiuſdem, ſitque diameter Q P, cuius erectus P R,
              <lb/>
            @ latus L O: </s>
            <s xml:id="echoid-s11593" xml:space="preserve">dico quod rectangulum ſub O D E in E H ab ipſo qua-
              <lb/>
            drato D E, atque Q P R ſumma laterum figuræ Diametri P Q ab L
              <lb/>
            I K ſumma laterum figuræ I L, vel ab ipſa C A F ſumma laterum
              <lb/>
            figuræ axis, vna deficiunt, vel vna æqualia ſunt, aut vna excedunt.</s>
            <s xml:id="echoid-s11594" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum