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

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        <div xml:id="echoid-div645" type="section" level="1" n="214">
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            <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"/>
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            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>
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