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-div945" type="section" level="1" n="297">
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            <s xml:id="echoid-s11121" xml:space="preserve">
              <pb o="311" file="0349" n="350" rhead="Conicor. Lib. VII."/>
            I L ad L O, ſeu quàm A m ad m R; </s>
            <s xml:id="echoid-s11122" xml:space="preserve">& </s>
            <s xml:id="echoid-s11123" xml:space="preserve">A C ad eandem A R minorem pro-
              <lb/>
            portionem habet quàm A m; </s>
            <s xml:id="echoid-s11124" xml:space="preserve">ideoque A C minor erit, quàm A m, & </s>
            <s xml:id="echoid-s11125" xml:space="preserve">A m
              <lb/>
              <note position="right" xlink:label="note-0349-01" xlink:href="note-0349-01a" xml:space="preserve">Lem. 2.
                <lb/>
              Lib. 5.</note>
            minor quàm m R, ſicuti I L minor eſt, quàm L O ; </s>
            <s xml:id="echoid-s11126" xml:space="preserve">& </s>
            <s xml:id="echoid-s11127" xml:space="preserve">propterea ſecta A R
              <lb/>
            bifariam in n in vtroq; </s>
            <s xml:id="echoid-s11128" xml:space="preserve">caſu C n ſemidifferentia maximè, & </s>
            <s xml:id="echoid-s11129" xml:space="preserve">minimè ſcilicet
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s11130" xml:space="preserve">C R maior erit, quàm m n ſemidifferentia inæqualium intermedia-
              <lb/>
            rum A m, & </s>
            <s xml:id="echoid-s11131" xml:space="preserve">R m: </s>
            <s xml:id="echoid-s11132" xml:space="preserve">ſuntque duo quaarata ex A C, & </s>
            <s xml:id="echoid-s11133" xml:space="preserve">ex C R æqualia qua-
              <lb/>
            dratis ex R n, & </s>
            <s xml:id="echoid-s11134" xml:space="preserve">ex C n bis ſumptis, atquè quadrata ex A m, & </s>
            <s xml:id="echoid-s11135" xml:space="preserve">ex R m
              <lb/>
            æqualia ſunt quadratis ex R n, & </s>
            <s xml:id="echoid-s11136" xml:space="preserve">ex m n bis ſumptis, ſed duplum quadrati
              <lb/>
            n C cum duplo quadrati n R maiora ſunt duplo quadrati n m cum duplo qua-
              <lb/>
            drati n R (cum n R ſit communis, & </s>
            <s xml:id="echoid-s11137" xml:space="preserve">n C maior ſit n m); </s>
            <s xml:id="echoid-s11138" xml:space="preserve">igitur in vtroque
              <lb/>
            caſu duo quadrata ex maxima, & </s>
            <s xml:id="echoid-s11139" xml:space="preserve">ex minima, ſcilicet quadratum A C vna
              <lb/>
            cum quadrato C R maiora ſunt quadrato A m, & </s>
            <s xml:id="echoid-s11140" xml:space="preserve">quadrato m R ſimul ſum-
              <lb/>
            ptis: </s>
            <s xml:id="echoid-s11141" xml:space="preserve">& </s>
            <s xml:id="echoid-s11142" xml:space="preserve">quadratum A R minorem proportionem habet ad ſummam quadrato-
              <lb/>
            rum ex A C, & </s>
            <s xml:id="echoid-s11143" xml:space="preserve">ex C R, quàm ad ſummam quadrati A m, & </s>
            <s xml:id="echoid-s11144" xml:space="preserve">quadrati m
              <lb/>
            R; </s>
            <s xml:id="echoid-s11145" xml:space="preserve">ſed quadratum I O ad quadratum I L vna cum quadraio L O eandem pro-
              <lb/>
            portionem habet, quàm quadratum A R ad ſummam duorum quadratorum ex
              <lb/>
            A m, & </s>
            <s xml:id="echoid-s11146" xml:space="preserve">ex m R (propterea quod A R, & </s>
            <s xml:id="echoid-s11147" xml:space="preserve">I O diuiduntur proportionaliter in
              <lb/>
            m, & </s>
            <s xml:id="echoid-s11148" xml:space="preserve">L): </s>
            <s xml:id="echoid-s11149" xml:space="preserve">igitur quadratum A R ad ſummam quadrati A C vna cum qua-
              <lb/>
            drato C R minorem proportionem habet, quàm quadratum IO ad ſummam qua-
              <lb/>
            drati I L cum quadrato L O.</s>
            <s xml:id="echoid-s11150" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11151" xml:space="preserve">Non ſecus oſtendetur, quod quadratum ſumme I L, & </s>
            <s xml:id="echoid-s11152" xml:space="preserve">N O ad quadrati ex
              <lb/>
            I L, & </s>
            <s xml:id="echoid-s11153" xml:space="preserve">quadrati ex N O ſummam habet minorem proportionem, quàm qua-
              <lb/>
            dratum ſumme S T, & </s>
            <s xml:id="echoid-s11154" xml:space="preserve">V X ad quadratorum ex S T, atquè ex V X ſum-
              <lb/>
              <note position="right" xlink:label="note-0349-02" xlink:href="note-0349-02a" xml:space="preserve">ex 22.
                <lb/>
              huius.</note>
            mam: </s>
            <s xml:id="echoid-s11155" xml:space="preserve">& </s>
            <s xml:id="echoid-s11156" xml:space="preserve">ideo I L cum N O minores erunt, quàm S T cum V X.</s>
            <s xml:id="echoid-s11157" xml:space="preserve"/>
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        <div xml:id="echoid-div949" type="section" level="1" n="298">
          <head xml:id="echoid-head369" xml:space="preserve">Notæ in Propoſit. XXXXIII.</head>
          <note position="left" xml:space="preserve">f</note>
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            <s xml:id="echoid-s11158" xml:space="preserve">R Emanet A C in Q R minus quàm I L in N O, & </s>
            <s xml:id="echoid-s11159" xml:space="preserve">pariter I L in N
              <lb/>
              <note position="left" xlink:label="note-0349-04" xlink:href="note-0349-04a" xml:space="preserve">f</note>
            O minus quàm S T in V X, &</s>
            <s xml:id="echoid-s11160" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11161" xml:space="preserve">Quia ſi ex quadrato ſummæ A C,
              <lb/>
              <figure xlink:label="fig-0349-01" xlink:href="fig-0349-01a" number="414">
                <image file="0349-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0349-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s11162" xml:space="preserve">Q R quferantur duo quadrata ex
              <lb/>
            C A, & </s>
            <s xml:id="echoid-s11163" xml:space="preserve">ex Q R ſimul ſumpta, re-
              <lb/>
            manent duo rectangula ſub C A, & </s>
            <s xml:id="echoid-s11164" xml:space="preserve">
              <lb/>
            Q R contenta: </s>
            <s xml:id="echoid-s11165" xml:space="preserve">pariterque duplum re-
              <lb/>
            ctanguli ex I L in N O eſt rcſiduum
              <lb/>
            quadrati ex ſumma ipſarum I L, & </s>
            <s xml:id="echoid-s11166" xml:space="preserve">
              <lb/>
            N O deſcripti, poſtquàm ablata ſunt
              <lb/>
            quadratum ex I L, & </s>
            <s xml:id="echoid-s11167" xml:space="preserve">quadratum ex
              <lb/>
              <note position="right" xlink:label="note-0349-05" xlink:href="note-0349-05a" xml:space="preserve">Prop. 22.
                <lb/>
              huius.</note>
            N O ſimul; </s>
            <s xml:id="echoid-s11168" xml:space="preserve">ſed bina quadrata vtrinq;
              <lb/>
            </s>
            <s xml:id="echoid-s11169" xml:space="preserve">ablata ſunt æqualia inter ſe in ellipſi; </s>
            <s xml:id="echoid-s11170" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s11171" xml:space="preserve">ſumma A C, Q R minor eſt quàm
              <lb/>
              <note position="right" xlink:label="note-0349-06" xlink:href="note-0349-06a" xml:space="preserve">Prop 42.
                <lb/>
              huius.</note>
            ſumma I L, N O; </s>
            <s xml:id="echoid-s11172" xml:space="preserve">Ergo duplum re-
              <lb/>
            ctanguli ſub C A & </s>
            <s xml:id="echoid-s11173" xml:space="preserve">ſub Q R mi-
              <lb/>
            nus eſt duplo rectanguli I L in N O,
              <lb/>
            & </s>
            <s xml:id="echoid-s11174" xml:space="preserve">rectangulum ſub A C, & </s>
            <s xml:id="echoid-s11175" xml:space="preserve">Q R minus eſt rectangulo ſub I L, & </s>
            <s xml:id="echoid-s11176" xml:space="preserve">N O.</s>
            <s xml:id="echoid-s11177" xml:space="preserve"/>
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