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-div208" type="section" level="1" n="73">
          <p style="it">
            <s xml:id="echoid-s2339" xml:space="preserve">
              <pb o="50" file="0088" n="88" rhead="Apollonij Pergæi"/>
            K G eandem propor-
              <lb/>
            tionem habebit ad R
              <lb/>
              <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a" number="65">
                <image file="0088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0088-01"/>
              </figure>
            G, atque ad M K,
              <lb/>
            vnde R G æqualis e-
              <lb/>
            rit M K, vel F D,
              <lb/>
            quare eadem E I ad
              <lb/>
            K M, vel C D ad
              <lb/>
            D F, ſiue I C ad C
              <lb/>
            S eandem proportio-
              <lb/>
            nem habebit, quam
              <lb/>
            eadem E I ad R G,
              <lb/>
            vel I T ad B G (pro-
              <lb/>
            pter ſimilitudinem
              <lb/>
            triangulorum I E T,
              <lb/>
            & </s>
            <s xml:id="echoid-s2340" xml:space="preserve">G R B) ergo com-
              <lb/>
            parando homologo-
              <lb/>
            rum ſummas in elli-
              <lb/>
            pſi, vel differentias
              <lb/>
              <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">Lem. 4.</note>
            in hyperbola C T ad
              <lb/>
            B O, vel C H ad H
              <lb/>
            O (propter ſimilitu-
              <lb/>
            dinem triangulorum
              <lb/>
            C H T, & </s>
            <s xml:id="echoid-s2341" xml:space="preserve">O H B)
              <lb/>
            eandem proportionẽ
              <lb/>
            habebit, quàm I C
              <lb/>
            ad C S, vel C D ad
              <lb/>
            D F, & </s>
            <s xml:id="echoid-s2342" xml:space="preserve">diuidendo
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s2343" xml:space="preserve">cõ-
              <lb/>
            ponendo in ellipſi C O ad O H eandem proportionem habebit, quàm C F ad F D,
              <lb/>
            ſiue quàm habet latus tranſuerſum ad rectum; </s>
            <s xml:id="echoid-s2344" xml:space="preserve">& </s>
            <s xml:id="echoid-s2345" xml:space="preserve">propterea B H eſt breuiſsima
              <lb/>
              <note position="left" xlink:label="note-0088-02" xlink:href="note-0088-02a" xml:space="preserve">9. 10.
                <lb/>
              huius.</note>
            linearum ex B ad axim cadentium.</s>
            <s xml:id="echoid-s2346" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2347" xml:space="preserve">Deinde educatur quilibet ramus E V ſupra, velinfr a breuiſecantem E B, qui
              <lb/>
            productus ſecet rectam I C in X, & </s>
            <s xml:id="echoid-s2348" xml:space="preserve">C A in Z, atque S M in γ, & </s>
            <s xml:id="echoid-s2349" xml:space="preserve">educatur ex
              <lb/>
            V recta V e perpendicularis ad axim, ſecans D F in c, & </s>
            <s xml:id="echoid-s2350" xml:space="preserve">S M in e, atque
              <lb/>
            contingentem ſectionem in puncto B, ſcilicet ipſam B a ſecet in d. </s>
            <s xml:id="echoid-s2351" xml:space="preserve">Et quia (vt
              <lb/>
            modo oſtenſum eſt) rectangulum F S æquale eſt rectangulo B G M, ſuntque pa-
              <lb/>
            riter oſtenſæ O C, A C, C a proportionales; </s>
            <s xml:id="echoid-s2352" xml:space="preserve">ergo C a eſt quinta proportionalis poſt
              <lb/>
            quatuor præcedentes F C, N C, O C, A C continuè proportionales; </s>
            <s xml:id="echoid-s2353" xml:space="preserve">& </s>
            <s xml:id="echoid-s2354" xml:space="preserve">ideo F C ad
              <lb/>
            C O eſt, vt C O ad C a; </s>
            <s xml:id="echoid-s2355" xml:space="preserve">ergo comparando homologorum differentias tam in hyper-
              <lb/>
              <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">Lem. 3.</note>
            bola, quàm in ellipſi erit, F O ad O a, vt F C ad C O: </s>
            <s xml:id="echoid-s2356" xml:space="preserve">eſt autem G B ad B O,
              <lb/>
            vt F C ad C O, vt antea oſtenſum eſt; </s>
            <s xml:id="echoid-s2357" xml:space="preserve">ergo G B ad B O erit, vt F O ad O a; </s>
            <s xml:id="echoid-s2358" xml:space="preserve">ſed
              <lb/>
            propter ſimilitudinem triangulorum B G b, B O a eſt G B ad B O, vt G b ad O a;
              <lb/>
            </s>
            <s xml:id="echoid-s2359" xml:space="preserve">ergo F O, ſeu M G ad O a eandem proportionem habet, quàm G b ad eandem O a; </s>
            <s xml:id="echoid-s2360" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s2361" xml:space="preserve">propterea M G æqualis eſt G b; </s>
            <s xml:id="echoid-s2362" xml:space="preserve">cumque M b ſecetur æqualiter in G, & </s>
            <s xml:id="echoid-s2363" xml:space="preserve">inæqua-
              <lb/>
            liter in e (ex lemmate 6. </s>
            <s xml:id="echoid-s2364" xml:space="preserve">huius) G b ad e b, ſeu B G, ad d e, propter ſimilitu-
              <lb/>
            dinem triangulorum B G b, & </s>
            <s xml:id="echoid-s2365" xml:space="preserve">B O a, & </s>
            <s xml:id="echoid-s2366" xml:space="preserve">multo magis B G ad V e portionem
              <lb/>
            ipſius d e habebit maiorem proportionem, quàm, e M ad G M; </s>
            <s xml:id="echoid-s2367" xml:space="preserve">ergo </s>
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    </echo>
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