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-s7393" xml:space="preserve">
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            nempe e, f ſunt æquales: </s>
            <s xml:id="echoid-s7394" xml:space="preserve">deinde ducantur V Z, Y a ad axes ordinatæ;
              <lb/>
            </s>
            <s xml:id="echoid-s7395" xml:space="preserve">ergo (propter ſimilitudinem duarum ſectionum) T Z in Z e ad quadra-
              <lb/>
              <note position="right" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">d</note>
            tum Z V eandem proportionem habebit, quam X a in a f ad quadratum
              <lb/>
            a Y, & </s>
            <s xml:id="echoid-s7396" xml:space="preserve">angulus e æqualis eſt angulo f; </s>
            <s xml:id="echoid-s7397" xml:space="preserve">igitur V e T ſimile eſt Y f X, & </s>
            <s xml:id="echoid-s7398" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0234-02" xlink:href="note-0234-02a" xml:space="preserve">Propoſ. 6.
                <lb/>
              pręmiſſ.</note>
            pariter O T R, Q X S; </s>
            <s xml:id="echoid-s7399" xml:space="preserve">& </s>
            <s xml:id="echoid-s7400" xml:space="preserve">propterea O e ad R V eandem proportionem
              <lb/>
            habebit, quàm Q f ad Y S, & </s>
            <s xml:id="echoid-s7401" xml:space="preserve">propter ſimilitudinem duarum ſectionum
              <lb/>
            B I ad I A eſt, vt E K ad K D, & </s>
            <s xml:id="echoid-s7402" xml:space="preserve">A I ad I O, vt D K ad K Q propter
              <lb/>
            ſimilitudinem duorum triangulorum; </s>
            <s xml:id="echoid-s7403" xml:space="preserve">ergo (ex æqualitate, & </s>
            <s xml:id="echoid-s7404" xml:space="preserve">comparan-
              <lb/>
              <note position="left" xlink:label="note-0234-03" xlink:href="note-0234-03a" xml:space="preserve">Lem. 1.
                <lb/>
              lib. 5.</note>
            do antecedentes ad ſummas vel differentias terminorum) erit B I ad B O,
              <lb/>
              <note position="right" xlink:label="note-0234-04" xlink:href="note-0234-04a" xml:space="preserve">e</note>
            vt E K ad E Q, ſed B T ad B I erat, vt X E ad E K (propter ſimilitu-
              <lb/>
            dinem duarum ſectionum)
              <lb/>
              <figure xlink:label="fig-0234-01" xlink:href="fig-0234-01a" number="265">
                <image file="0234-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0234-01"/>
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            ergo ex æqualitate, & </s>
            <s xml:id="echoid-s7405" xml:space="preserve">rurſus
              <lb/>
            comparando antecedẽtes ad
              <lb/>
            ſummas vel differentias ter-
              <lb/>
              <note position="left" xlink:label="note-0234-05" xlink:href="note-0234-05a" xml:space="preserve">Ibldem.</note>
            minorum B T ad T O erit,
              <lb/>
            vt X E ad X Q, cumque T
              <lb/>
            Z in Z e ad quadratum V Z
              <lb/>
              <note position="left" xlink:label="note-0234-06" xlink:href="note-0234-06a" xml:space="preserve">37. lib. 1.</note>
            ſit vt X a in a f ad quadra-
              <lb/>
            tum a Y (39. </s>
            <s xml:id="echoid-s7406" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7407" xml:space="preserve">& </s>
            <s xml:id="echoid-s7408" xml:space="preserve">qua-
              <lb/>
            dratum V Z ad quadratum
              <lb/>
            Z e eſt, vt quadratum a Y ad
              <lb/>
            quadratũ a f erit T Z in Z e,
              <lb/>
            ad quadratũ Z e, nempe T Z
              <lb/>
            ad Z e vt X a in a f ad quadra
              <lb/>
            tum a f nempe G a ad a f, & </s>
            <s xml:id="echoid-s7409" xml:space="preserve">
              <lb/>
            comparãdo antecedentes ad
              <lb/>
            differnntias terminorũ in hy-
              <lb/>
            perbola, & </s>
            <s xml:id="echoid-s7410" xml:space="preserve">ad eorum ſummas
              <lb/>
            in ellipſi, fiet Z T ad T e, nẽ-
              <lb/>
            pe quadratum B T (quod eſt
              <lb/>
            æquale ipſi Z T in T e (39 ex 1.) </s>
            <s xml:id="echoid-s7411" xml:space="preserve">ad quadratnm T e eſt, vt X a ad X f,
              <lb/>
              <note position="left" xlink:label="note-0234-07" xlink:href="note-0234-07a" xml:space="preserve">37. lib. 1.</note>
            nempe a X in X f, quod eſt æquale quadrato E X (39. </s>
            <s xml:id="echoid-s7412" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7413" xml:space="preserve">ad qua-
              <lb/>
            dratum X f; </s>
            <s xml:id="echoid-s7414" xml:space="preserve">ergo B T ad T e potentia eſt, vt E X ad X f; </s>
            <s xml:id="echoid-s7415" xml:space="preserve">& </s>
            <s xml:id="echoid-s7416" xml:space="preserve">propterea
              <lb/>
              <note position="left" xlink:label="note-0234-08" xlink:href="note-0234-08a" xml:space="preserve">Ibidem.</note>
              <figure xlink:label="fig-0234-02" xlink:href="fig-0234-02a" number="266">
                <image file="0234-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0234-02"/>
              </figure>
            </s>
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