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
211 173
212 174
213 175
214 176
215 177
216 178
217 179
218 180
219 181
220 182
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
231 193
232 194
233 195
234 196
235 197
236 198
237 199
238 200
239 201
240 202
< >
page |< < (182) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div645" type="section" level="1" n="214">
          <p style="it">
            <s xml:id="echoid-s6924" xml:space="preserve">
              <pb o="182" file="0220" n="220" rhead="Apollonij Pergæi"/>
            portionem habebit, quàm latus tranſuerſum K A ad eius latus rectum: </s>
            <s xml:id="echoid-s6925" xml:space="preserve">eadem
              <lb/>
            ractione in ſectione C D erit rectangulum H L O ad quadratum ordinatim ap-
              <lb/>
            plicatæ D L, vt latus tranſuerſum M C ad eius latus rectum; </s>
            <s xml:id="echoid-s6926" xml:space="preserve">propt
              <unsure/>
            erea quod
              <lb/>
            à puncto D ducitur D O ſectionem contingens, & </s>
            <s xml:id="echoid-s6927" xml:space="preserve">D L ordinatim applicata ad
              <lb/>
            diametrum M C, ei occurrentes in L, & </s>
            <s xml:id="echoid-s6928" xml:space="preserve">O. </s>
            <s xml:id="echoid-s6929" xml:space="preserve">Et quoniam ex hypotheſi latus
              <lb/>
            tranſuerſum K A ad eius latus rectum eandem proportionem habet, quàm latus
              <lb/>
            tranſuerſum M C ad eius latus rectum, cum figuræ harum diametrorum ſup-
              <lb/>
            poſitæ ſint ſimiles; </s>
            <s xml:id="echoid-s6930" xml:space="preserve">ergo rectangulum G I N ad quadratum I B eandem propor-
              <lb/>
            tionem habet, quàm rectangulum H L O ad quadratum L D: </s>
            <s xml:id="echoid-s6931" xml:space="preserve">deinde quia in
              <lb/>
            duobus triangulis G B N, & </s>
            <s xml:id="echoid-s6932" xml:space="preserve">H O D ſunt duo anguli G B N, & </s>
            <s xml:id="echoid-s6933" xml:space="preserve">H D O equales,
              <lb/>
            nẽpe recti ( cum B N, & </s>
            <s xml:id="echoid-s6934" xml:space="preserve">D O ſectiones contingentes in terminis axium E B, & </s>
            <s xml:id="echoid-s6935" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0220-01" xlink:href="note-0220-01a" xml:space="preserve">Coruerſ.
                <lb/>
              32. lib. I.</note>
            F D efficiant cum ipſis angulos rectos ) atq; </s>
            <s xml:id="echoid-s6936" xml:space="preserve">à verticalibus angulis B, & </s>
            <s xml:id="echoid-s6937" xml:space="preserve">D du-
              <lb/>
            cuntur ad baſes rectæ lineæ B I, D L efficientes angulos I, & </s>
            <s xml:id="echoid-s6938" xml:space="preserve">L æquales, eo
              <lb/>
            quod æquales ſunt angulis æqualibus R A G, & </s>
            <s xml:id="echoid-s6939" xml:space="preserve">S C H propter æquidiſtantiam
              <lb/>
            linearum B I, A R, atque
              <lb/>
              <figure xlink:label="fig-0220-01" xlink:href="fig-0220-01a" number="246">
                <image file="0220-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0220-01"/>
              </figure>
            linearum D L, S C, & </s>
            <s xml:id="echoid-s6940" xml:space="preserve">in
              <lb/>
            ſuper rectangulum G I N ad
              <lb/>
            quadratum I B eandem pro-
              <lb/>
            portionem habet, quàm re-
              <lb/>
            ctangulum H L O ad qua-
              <lb/>
            dratum L D; </s>
            <s xml:id="echoid-s6941" xml:space="preserve">igitur trian-
              <lb/>
              <note position="left" xlink:label="note-0220-02" xlink:href="note-0220-02a" xml:space="preserve">Propoſ. 2.
                <lb/>
              pręmiſſ.</note>
            gula G B N, & </s>
            <s xml:id="echoid-s6942" xml:space="preserve">H D O ſi-
              <lb/>
            milia ſunt inter ſe; </s>
            <s xml:id="echoid-s6943" xml:space="preserve">& </s>
            <s xml:id="echoid-s6944" xml:space="preserve">pro-
              <lb/>
            pterea angulus G æqualis e-
              <lb/>
            rit angulo H.</s>
            <s xml:id="echoid-s6945" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6946" xml:space="preserve">Et proportio vniuſcu-
              <lb/>
            inſque eorum, nempe G
              <lb/>
            P, P R ad P A eſt, vt
              <lb/>
            proportio H Q, Q S ad
              <lb/>
            C O; </s>
            <s xml:id="echoid-s6947" xml:space="preserve">&</s>
            <s xml:id="echoid-s6948" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6949" xml:space="preserve">In triangulis enim ſimilibus G P A, & </s>
            <s xml:id="echoid-s6950" xml:space="preserve">H Q C circa angulos rectos
              <lb/>
            P, & </s>
            <s xml:id="echoid-s6951" xml:space="preserve">Qerit G P ad P A, vt H Q ad Q C: </s>
            <s xml:id="echoid-s6952" xml:space="preserve">pariter in duobus triangulis ſi-
              <lb/>
            milibus R P A, & </s>
            <s xml:id="echoid-s6953" xml:space="preserve">S Q C habebit R P ad P A eandem porportionem quàm, S
              <lb/>
            Q ad Q C; </s>
            <s xml:id="echoid-s6954" xml:space="preserve">proportio verò rectanguli G P R ad quadratum P A componitur ex
              <lb/>
            ijſdem rationibus laterum circa angulum rectum P: </s>
            <s xml:id="echoid-s6955" xml:space="preserve">pariterque proportio rectan-
              <lb/>
            guli H Q S ad quadratum Q C ex rationibus laterum circa angulum rectum
              <lb/>
            Q componitur, ſuntque oſtenſæ prædictæ componentes proportiones eædem inter
              <lb/>
            ſe; </s>
            <s xml:id="echoid-s6956" xml:space="preserve">igitur rectangulum G P R ad quadratum P A eandem proportionem habe-
              <lb/>
            bit, quàm rectangulum H Q S ad quadratum Q C; </s>
            <s xml:id="echoid-s6957" xml:space="preserve">ſed habet rectangulum G
              <lb/>
            P R ad quadratum P A eandem proportionem, quàm axis tranſuerſus E B ad
              <lb/>
              <note position="left" xlink:label="note-0220-03" xlink:href="note-0220-03a" xml:space="preserve">37. lib. I.</note>
            eius latus rectum ( propterea quod ab eodem puncto A ſectionis ducitur contin-
              <lb/>
            gens A R, & </s>
            <s xml:id="echoid-s6958" xml:space="preserve">ordinatim applicata ad axim A P) atque eodem modo rectangu-
              <lb/>
              <note position="left" xlink:label="note-0220-04" xlink:href="note-0220-04a" xml:space="preserve">Ibidem.</note>
            lum H Q S ad quadratum Q C eandem proportionem habet, quàm axis tran-
              <lb/>
            ſuerſus F D ad eius latus rectum; </s>
            <s xml:id="echoid-s6959" xml:space="preserve">igitur axis tranſuerſus E B ad eius latus
              <lb/>
            rectum eandem proportionem habet, quàm latus tranſuerſum F D ad eius latus
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s6960" xml:space="preserve">& </s>
            <s xml:id="echoid-s6961" xml:space="preserve">propterea figuræ axium duarum ſectionum A B, & </s>
            <s xml:id="echoid-s6962" xml:space="preserve">C D ſimiles in-
              <lb/>
            ter ſe erunt; </s>
            <s xml:id="echoid-s6963" xml:space="preserve">& </s>
            <s xml:id="echoid-s6964" xml:space="preserve">ideo conicæ ſectiones ſimiles erunt.</s>
            <s xml:id="echoid-s6965" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">12. huius.</note>
        </div>
      </text>
    </echo>
Impressum