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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            <s xml:id="echoid-s12509" xml:space="preserve">
              <pb o="366" file="0404" n="405" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0404-01" xlink:href="fig-0404-01a" number="478">
                <image file="0404-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0404-01"/>
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            nem, quàm ad minorem D E, & </s>
            <s xml:id="echoid-s12510" xml:space="preserve">componendo H M ad M D minorem propor-
              <lb/>
            tionem habebit, quàm H E ad E D, & </s>
            <s xml:id="echoid-s12511" xml:space="preserve">ideo differentia quadratorum ex P Q,
              <lb/>
            & </s>
            <s xml:id="echoid-s12512" xml:space="preserve">ex P R maior erit, quàm differentia quadratorum ex I L, & </s>
            <s xml:id="echoid-s12513" xml:space="preserve">ex I K, ſeu
              <lb/>
              <note position="left" xlink:label="note-0404-01" xlink:href="note-0404-01a" xml:space="preserve">Lem. 17.
                <lb/>
              huius.</note>
            maior quàm differentia quadratorum ex A C, & </s>
            <s xml:id="echoid-s12514" xml:space="preserve">ex A F.</s>
            <s xml:id="echoid-s12515" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12516" xml:space="preserve">Rurſus quia rectangulum C A F maius eſt quadrato A F, (propterea quod
              <lb/>
            rectangulum illud medium proportionale eſt inter maius quadratum ex A C, & </s>
            <s xml:id="echoid-s12517" xml:space="preserve">
              <lb/>
            quadratum minus ex A F), ergo differentia quadrati A C à rectangulo C A
              <lb/>
            F, ſcilicet difſerentia ſpatiorum maximi, & </s>
            <s xml:id="echoid-s12518" xml:space="preserve">intermedij, minor erit, quàm
              <lb/>
            differentia inter quadratum maximum A C, & </s>
            <s xml:id="echoid-s12519" xml:space="preserve">minimum A F, ſed differen-
              <lb/>
            tia quadratorum ex A C, & </s>
            <s xml:id="echoid-s12520" xml:space="preserve">ex A F minor oſtenſa eſt, quàm differentia qua-
              <lb/>
            dratorum ex I L, & </s>
            <s xml:id="echoid-s12521" xml:space="preserve">ex I K, ergo multo magis differentia quadrati A C à re-
              <lb/>
            ctangulo C A F minor erit, quàm differentia quadratorum ex I L, & </s>
            <s xml:id="echoid-s12522" xml:space="preserve">ex I K.</s>
            <s xml:id="echoid-s12523" xml:space="preserve"/>
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            <s xml:id="echoid-s12524" xml:space="preserve">Tandem quia quadratum A C ad ſemidifferentiam quadratorum ex I L, & </s>
            <s xml:id="echoid-s12525" xml:space="preserve">
              <lb/>
            ex I K eandem proportionem habet, quàm rectangulum E H A ad ſemifferen-
              <lb/>
              <note position="left" xlink:label="note-0404-02" xlink:href="note-0404-02a" xml:space="preserve">Prop. 20
                <lb/>
              huius.</note>
            tiam quadratorum ex E H, & </s>
            <s xml:id="echoid-s12526" xml:space="preserve">ex E G, vel ad ſemiſſem rectanguli ex E X in
              <lb/>
            G H, vel potius ad rectanguluw ſub E D, & </s>
            <s xml:id="echoid-s12527" xml:space="preserve">ſub G H; </s>
            <s xml:id="echoid-s12528" xml:space="preserve">ſed quadrati A C à
              <lb/>
              <note position="left" xlink:label="note-0404-03" xlink:href="note-0404-03a" xml:space="preserve">Lem.
                <lb/>
              16. huius.</note>
            rectangulo C A F differentia ad quadratum ipſum A G, ſeu differentia A C,
              <lb/>
            & </s>
            <s xml:id="echoid-s12529" xml:space="preserve">A F ad A C eandem proportionem habet, quàm H G ad H A, ſeu quàm
              <lb/>
            rectangulum E H G ad rectangulum E H A, igitur ex æquali differentia qua-
              <lb/>
              <note position="left" xlink:label="note-0404-04" xlink:href="note-0404-04a" xml:space="preserve">ex Def. 2.
                <lb/>
              huius.</note>
            drati A C à rectangulo C A F ad ſemidifferentiam quadratorum ex I L, & </s>
            <s xml:id="echoid-s12530" xml:space="preserve">ex
              <lb/>
            I K eandem proportionem habebit, quàm rectangulũ E H G ad rectangulum ſub
              <lb/>
            E D, & </s>
            <s xml:id="echoid-s12531" xml:space="preserve">G H, eſtq; </s>
            <s xml:id="echoid-s12532" xml:space="preserve">primũ rectangulũ reliquo rectangulo æquè alto maius, cum eius
              <lb/>
            baſis E H maior ſit, quàm E D, igitur differentia quadrati A C à rectangulo
              <lb/>
            C A F maior erit, quàm ſemidifferentia quadratorum ex I L, & </s>
            <s xml:id="echoid-s12533" xml:space="preserve">ex I K.</s>
            <s xml:id="echoid-s12534" xml:space="preserve"/>
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