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-div187" type="section" level="1" n="72">
          <pb o="46" file="0084" n="84" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s2190" xml:space="preserve">Et ponamus quamlibet duarum proportionum C F ad F D, & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">I S ad S C,
              <lb/>
              <note position="right" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">b</note>
            vt proportio figuræ, & </s>
            <s xml:id="echoid-s2192" xml:space="preserve">educamus ex E, S, &</s>
            <s xml:id="echoid-s2193" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Ideſt fiat diſtantia ex centro
              <lb/>
            vſque ad perpendicularem E D ad eius portionem D F in hyperbola, vt ſumma late-
              <lb/>
            ris tranſuerſi, & </s>
            <s xml:id="echoid-s2195" xml:space="preserve">recti ad latus rectum, & </s>
            <s xml:id="echoid-s2196" xml:space="preserve">vt eorum differentia in ellipſi ad latus
              <lb/>
            rectum ita fiat C D ad eius productionem D F; </s>
            <s xml:id="echoid-s2197" xml:space="preserve">tunc enim C F ad F D diuidendo in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s2198" xml:space="preserve">compo-
              <lb/>
              <figure xlink:label="fig-0084-01" xlink:href="fig-0084-01a" number="61">
                <image file="0084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0084-01"/>
              </figure>
            nendo in ellipſi habe-
              <lb/>
            bit eandem propor-
              <lb/>
            tionem, quàm latus
              <lb/>
            tranſuerſum ad re-
              <lb/>
            ctum; </s>
            <s xml:id="echoid-s2199" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s2200" xml:space="preserve">fiat
              <lb/>
            E K ad K D in eadẽ
              <lb/>
            proportione figuræ,
              <lb/>
            & </s>
            <s xml:id="echoid-s2201" xml:space="preserve">ex E, K educamus
              <lb/>
            rectas E I, K S pa-
              <lb/>
            rallelas axi A C D,
              <lb/>
            ſecantes I C, & </s>
            <s xml:id="echoid-s2202" xml:space="preserve">L F
              <lb/>
            parallelas ipſi E D
              <lb/>
            in I, S, L, & </s>
            <s xml:id="echoid-s2203" xml:space="preserve">M.
              <lb/>
            </s>
            <s xml:id="echoid-s2204" xml:space="preserve">Immutaui poſtremã
              <lb/>
            partem conſtructio-
              <lb/>
            nis, vt manifeſte er-
              <lb/>
            roneã in textu Ara-
              <lb/>
            bico; </s>
            <s xml:id="echoid-s2205" xml:space="preserve">Si enim I C ad
              <lb/>
            libitum ſumpta ſeca-
              <lb/>
            tur in S in ratione
              <lb/>
            C F ad F D non ca-
              <lb/>
            det neceſſariò E L
              <lb/>
            parallela C D ſuper
              <lb/>
            punctum I.</s>
            <s xml:id="echoid-s2206" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2207" xml:space="preserve">Et interponamus
              <lb/>
              <note position="right" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve">c</note>
            inter F C, C A du-
              <lb/>
            as C N, C O pro-
              <lb/>
            portionales illis duabus, &</s>
            <s xml:id="echoid-s2208" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2209" xml:space="preserve">Textum corruptum ſic reſtituo: </s>
            <s xml:id="echoid-s2210" xml:space="preserve">Interponamus in-
              <lb/>
            ter F C, & </s>
            <s xml:id="echoid-s2211" xml:space="preserve">A C duas medias proportionales, itaut F C, N C, C O, C A ſint continuè
              <lb/>
            proportionales, quod fieri poſſe conſtat ex lemmate 7. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">huius librt.</s>
            <s xml:id="echoid-s2213" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2214" xml:space="preserve">Et ponamus proportionem lineæ alicuius, vt eſt Q compoſitam, &</s>
            <s xml:id="echoid-s2215" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Vo-
              <lb/>
              <note position="right" xlink:label="note-0084-03" xlink:href="note-0084-03a" xml:space="preserve">d</note>
            catur Trutina in hyperbola, & </s>
            <s xml:id="echoid-s2217" xml:space="preserve">ellipſi linea recta Q, quæ ad B O compoſitam propor-
              <lb/>
            tionem habet ex C D ad D F, & </s>
            <s xml:id="echoid-s2218" xml:space="preserve">ex ratione F O ad O C.</s>
            <s xml:id="echoid-s2219" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2220" xml:space="preserve">Producatur priùs E B ſecans axim in H, &</s>
            <s xml:id="echoid-s2221" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2222" xml:space="preserve">Producatur priùs E B ſecans
              <lb/>
              <note position="right" xlink:label="note-0084-04" xlink:href="note-0084-04a" xml:space="preserve">e</note>
            axim in H, & </s>
            <s xml:id="echoid-s2223" xml:space="preserve">rectam S K in R, nec non rectam I C in puncto T.</s>
            <s xml:id="echoid-s2224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2225" xml:space="preserve">Ergo E D ad B O, quæ componitur ex E D ad D K, &</s>
            <s xml:id="echoid-s2226" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2227" xml:space="preserve">Nam poſita inter-
              <lb/>
              <note position="right" xlink:label="note-0084-05" xlink:href="note-0084-05a" xml:space="preserve">f</note>
            media D K, proportio E D ad B O compoſita erit ex ratione E D ad D K, & </s>
            <s xml:id="echoid-s2228" xml:space="preserve">ex ra-
              <lb/>
            tione D K ad B O; </s>
            <s xml:id="echoid-s2229" xml:space="preserve">eſt verò I C ad C S, vt E D ad D K (propter parallelas I E, S K,
              <lb/>
            C D) atque D K eſt æqualis G O in parallelogrammo G D; </s>
            <s xml:id="echoid-s2230" xml:space="preserve">ergo proportio E D ad B O
              <lb/>
            componitur ex ratione I C ad C S, & </s>
            <s xml:id="echoid-s2231" xml:space="preserve">ex ratione G O ad O B.</s>
            <s xml:id="echoid-s2232" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2233" xml:space="preserve">Sed E D ad D K eſt, vt CD ad DF, quia quælibet earum vt proportio
              <lb/>
              <note position="right" xlink:label="note-0084-06" xlink:href="note-0084-06a" xml:space="preserve">g</note>
            </s>
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