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-div922" type="section" level="1" n="289">
          <p>
            <s xml:id="echoid-s10867" xml:space="preserve">
              <pb o="301" file="0339" n="340" rhead="Conicor. Lib. VII."/>
            in ſecunda ellipſi minorem, quàm C G ad G M, nempe quàm quadra-
              <lb/>
            tum A C ad figuram ipſius S T ( 18. </s>
            <s xml:id="echoid-s10868" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10869" xml:space="preserve">) ergo figura ipſius A C eſt
              <lb/>
            minor; </s>
            <s xml:id="echoid-s10870" xml:space="preserve">in ſecunda verò maior quàm figura ipſius I L; </s>
            <s xml:id="echoid-s10871" xml:space="preserve">& </s>
            <s xml:id="echoid-s10872" xml:space="preserve">ſimiliter figura
              <lb/>
            ipſius I L maior, aut minor eſt figura S T. </s>
            <s xml:id="echoid-s10873" xml:space="preserve">Et hoc eſt propoſitum.</s>
            <s xml:id="echoid-s10874" xml:space="preserve"/>
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        <div xml:id="echoid-div924" type="section" level="1" n="290">
          <head xml:id="echoid-head361" xml:space="preserve">PROPOSITIO XXXXII.</head>
          <p>
            <s xml:id="echoid-s10875" xml:space="preserve">
              <emph style="sc">In</emph>
            hyperbole, & </s>
            <s xml:id="echoid-s10876" xml:space="preserve">ellipſi sũ-
              <lb/>
              <figure xlink:label="fig-0339-01" xlink:href="fig-0339-01a" number="394">
                <image file="0339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0339-01"/>
              </figure>
            ma duorum axium minor eſt
              <lb/>
            ſumma quarumlibet duarum cõ-
              <lb/>
            iugatarum diametrorum eiuſdẽ
              <lb/>
            ſectionis.</s>
            <s xml:id="echoid-s10877" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10878" xml:space="preserve">XXXXIII. </s>
            <s xml:id="echoid-s10879" xml:space="preserve">Et planum ab eis
              <lb/>
            contentũ minus eſt plano à dua-
              <lb/>
            bus coniugatis contento, & </s>
            <s xml:id="echoid-s10880" xml:space="preserve">
              <lb/>
            planum à proximioribus axi
              <lb/>
            coniugatis contentum minus
              <lb/>
            eſt plano à remotioribus con-
              <lb/>
            tento.</s>
            <s xml:id="echoid-s10881" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10882" xml:space="preserve">Iiſdem figuris manentibus, quia in hyperbole A C minor eſt quàm I
              <lb/>
            L, & </s>
            <s xml:id="echoid-s10883" xml:space="preserve">I L, quàm S T; </s>
            <s xml:id="echoid-s10884" xml:space="preserve">& </s>
            <s xml:id="echoid-s10885" xml:space="preserve">ſiquidem
              <lb/>
              <figure xlink:label="fig-0339-02" xlink:href="fig-0339-02a" number="395">
                <image file="0339-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0339-02"/>
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            A C æqualis fuerit Q R, erit quo-
              <lb/>
            que I L æqualis N O, & </s>
            <s xml:id="echoid-s10886" xml:space="preserve">S T æqua-
              <lb/>
            lis V X ( 21. </s>
            <s xml:id="echoid-s10887" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10888" xml:space="preserve">) ergo ſumma
              <lb/>
            ipſorum A C, Q R minor eſt, quã
              <lb/>
            ſumma I L, N O, & </s>
            <s xml:id="echoid-s10889" xml:space="preserve">quàm S T,
              <lb/>
            V X: </s>
            <s xml:id="echoid-s10890" xml:space="preserve">ſi verò A C non fuerit æqua-
              <lb/>
            lis ipſi Q R, vtique differentia duo-
              <lb/>
              <note position="right" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">12. 13.
                <lb/>
              huius.</note>
            rum quadratorum A C, Q R æqua-
              <lb/>
            lis erit differentiæ quadratorum I L,
              <lb/>
            N O: </s>
            <s xml:id="echoid-s10891" xml:space="preserve">& </s>
            <s xml:id="echoid-s10892" xml:space="preserve">propterea ſumma ipſorum
              <lb/>
              <note position="left" xlink:label="note-0339-02" xlink:href="note-0339-02a" xml:space="preserve">d</note>
            A C, Q R minor erit, quàm ſum-
              <lb/>
            ma I L, N O: </s>
            <s xml:id="echoid-s10893" xml:space="preserve">& </s>
            <s xml:id="echoid-s10894" xml:space="preserve">hæc ſumma ex
              <lb/>
            hac eadem demonſtratione minor
              <lb/>
            etiam erit, quàm ſumma duarum
              <lb/>
            S T, V X. </s>
            <s xml:id="echoid-s10895" xml:space="preserve">At in ellipſi; </s>
            <s xml:id="echoid-s10896" xml:space="preserve">quia A
              <lb/>
            C ad Q R maiorem proportionem
              <lb/>
              <note position="left" xlink:label="note-0339-03" xlink:href="note-0339-03a" xml:space="preserve">e</note>
            habet, quàm I L ad N O ( 28. </s>
            <s xml:id="echoid-s10897" xml:space="preserve">ex
              <lb/>
            7. </s>
            <s xml:id="echoid-s10898" xml:space="preserve">) habebit quadratum ex ſumma
              <lb/>
            A C, Q R ad earundem duarum
              <lb/>
            ſummam quadratorum maiorem
              <lb/>
            proportionem, quàm quadratum
              <lb/>
            ſummæ I L, N O ad </s>
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