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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          <p>
            <s xml:id="echoid-s10674" xml:space="preserve">
              <pb o="293" file="0331" n="332" rhead="Conicor. Lib. VII."/>
            differentia I L, & </s>
            <s xml:id="echoid-s10675" xml:space="preserve">N O maior ſit, quàm differentia quarumlibet duarum
              <lb/>
            coniugatarum ab axi remotiorum. </s>
            <s xml:id="echoid-s10676" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s10677" xml:space="preserve"/>
          </p>
          <figure number="384">
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        <div xml:id="echoid-div904" type="section" level="1" n="281">
          <head xml:id="echoid-head351" xml:space="preserve">Notæ in Propoſit. XII.</head>
          <p style="it">
            <s xml:id="echoid-s10678" xml:space="preserve">IN eiſdem figuris, quia quadratum A C ad quadratum ſui coniugati in
              <lb/>
              <note position="left" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">a</note>
            propoſitione 12. </s>
            <s xml:id="echoid-s10679" xml:space="preserve">& </s>
            <s xml:id="echoid-s10680" xml:space="preserve">25. </s>
            <s xml:id="echoid-s10681" xml:space="preserve">nempe A C ad A F erectum ipſius eſt vt præ-
              <lb/>
            ſecta C G ad Interceptam G A, ſeu C H: </s>
            <s xml:id="echoid-s10682" xml:space="preserve">ergo quadratum A C in hy-
              <lb/>
            perbola ad differentiam quadratorum axium ipſius, & </s>
            <s xml:id="echoid-s10683" xml:space="preserve">in ellipſi ad illo-
              <lb/>
            rum ſnmmam eſt, vt C G ad H G, &</s>
            <s xml:id="echoid-s10684" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10685" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s10686" xml:space="preserve">Quia quadratum A C ad
              <lb/>
            quadratum axis ei coniugati Q R, ſiue C A ad eius erectum A F eandem pro-
              <lb/>
              <note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Defin. 1.
                <lb/>
              & 2.
                <lb/>
              huius.</note>
            portionem habet, quàm præſecta C G ad Interceptam G A, vel ad C H, & </s>
            <s xml:id="echoid-s10687" xml:space="preserve">
              <lb/>
            comparando antecedentes ad terminorum differentias in hyperbola, & </s>
            <s xml:id="echoid-s10688" xml:space="preserve">ad ter-
              <lb/>
            minorum ſummas in ellipſi, quadratum C A ad differentiam quadratorum ex axi
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s10689" xml:space="preserve">ex axi Q R habebit in hyperbola eandem proportionem, quàm C G
              <lb/>
            ad differentiam inter C G, & </s>
            <s xml:id="echoid-s10690" xml:space="preserve">C H: </s>
            <s xml:id="echoid-s10691" xml:space="preserve">in ellipſi verò quadratum A C ad ſum-
              <lb/>
            mam quadratorum ex A C, & </s>
            <s xml:id="echoid-s10692" xml:space="preserve">ex Q R eandem proportionem habebit, quàm
              <lb/>
            C G ad ſummam ipſius C G cum C H.</s>
            <s xml:id="echoid-s10693" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10694" xml:space="preserve">Et quia iam demonſtratum eſt, quod quadratum C A ad quadratum
              <lb/>
              <note position="left" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">b</note>
            I L ſit, vt C G ad E H, &</s>
            <s xml:id="echoid-s10695" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">Relicta abſtruſa complicatione propoſitionum
              <lb/>
            Arabici Interpretis diſtinctiori methodo, ſicuti in præcedenti ſectione factum eſt
              <lb/>
              <note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">6. huius.</note>
            propoſitiones declarabimus. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">Quoniam in hyperbola quadratum I L ad quadra-
              <lb/>
            tum N O eandem proportionem habet, quàm H E ad E G comparando antece-
              <lb/>
            dentes ad terminorum differentias, quadratum I L ad differentiam quadrati
              <lb/>
            I L à quadrato N O eandem proportionem habebit, quàm H E ad ipſarum H
              <lb/>
            E, & </s>
            <s xml:id="echoid-s10698" xml:space="preserve">E G differentiam; </s>
            <s xml:id="echoid-s10699" xml:space="preserve">ſed quadratum A C ad quadratum I L eſt vt C G
              <lb/>
            ad H E (veluti in propoſitione 8. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">oſtenſum eſt) ergo ex æqualitate quadratum
              <lb/>
            A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10701" xml:space="preserve">ex N O differentiam eandem </s>
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