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-div583" type="section" level="1" n="191">
          <p>
            <s xml:id="echoid-s6104" xml:space="preserve">
              <pb o="156" file="0194" n="194" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0194-01" xlink:href="fig-0194-01a" number="210">
                <image file="0194-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0194-01"/>
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            A B ſimilis eſt figuræ ſectionis E F, erit quadratum H E ad H b in H F,
              <lb/>
            vt quadratum A C ad C a in C B; </s>
            <s xml:id="echoid-s6105" xml:space="preserve">& </s>
            <s xml:id="echoid-s6106" xml:space="preserve">b H in H F ad quadratum H F,
              <lb/>
            vt a C in C B ad quadratum C B (nam poſuimus H F ad F b, vt C B ad
              <lb/>
            B a) ergo ex æqualitate, quadratũ E H ad quadratũ H F eſt, vt quadra-
              <lb/>
            tum A C ad quadratum C B: </s>
            <s xml:id="echoid-s6107" xml:space="preserve">& </s>
            <s xml:id="echoid-s6108" xml:space="preserve">propterea E Z ad H F eſt vt A S ad C
              <lb/>
            B; </s>
            <s xml:id="echoid-s6109" xml:space="preserve">Atque ſic oſtendetur, quod X Y ad N F ſit vt Q R ad L B, & </s>
            <s xml:id="echoid-s6110" xml:space="preserve">T V
              <lb/>
            ad M F ſit vt O P ad K B; </s>
            <s xml:id="echoid-s6111" xml:space="preserve">ergo proportiones ordinationum axis vnius
              <lb/>
            earum ad ſua abſciſſa ſunt eædem rationibus aliarum ordinationum axis
              <lb/>
            ad ſua abſciſſa, & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">alternatiuè. </s>
            <s xml:id="echoid-s6113" xml:space="preserve">Quare duæ ſectiones ſunt ſimiles.</s>
            <s xml:id="echoid-s6114" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Defin. 2.
            <lb/>
          huius.</note>
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            <s xml:id="echoid-s6115" xml:space="preserve">E contra oſtendetur, quod
              <lb/>
            ſi duæ ſectiones fuerint ſimi-
              <lb/>
              <figure xlink:label="fig-0194-02" xlink:href="fig-0194-02a" number="211">
                <image file="0194-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0194-02"/>
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            les, earũ figuræ ſimiles quo-
              <lb/>
            que erunt. </s>
            <s xml:id="echoid-s6116" xml:space="preserve">Quia eſt A C ad
              <lb/>
              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">Ex def. 2.
                <lb/>
              buius.</note>
            C B, vt E H ad H F, & </s>
            <s xml:id="echoid-s6117" xml:space="preserve">ean-
              <lb/>
            dem proportionem habent
              <lb/>
            earum quadrata, atque
              <lb/>
            quadratum H F ad H F in
              <lb/>
            H b eſt, vt quadratum C B
              <lb/>
            ad C B in C a (eo quod
              <lb/>
            H F ad F b poſita fuit, vt
              <lb/>
            C B ad B a); </s>
            <s xml:id="echoid-s6118" xml:space="preserve">ergo ex æ-
              <lb/>
            qualitate quadratum E H ad
              <lb/>
            b H in H F, nempe I F
              <lb/>
            ad F b (20. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6120" xml:space="preserve">eſt, vt quadratum A C ad a C in C B, nempe vt
              <lb/>
              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">21. lib. 1.
                <lb/>
              Ibidem.</note>
            D B ad B a (20. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s6122" xml:space="preserve">; </s>
            <s xml:id="echoid-s6123" xml:space="preserve">quare figuræ duarum ſectionum ſunt ſimiles.
              <lb/>
            </s>
            <s xml:id="echoid-s6124" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s6125" xml:space="preserve"/>
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        <div xml:id="echoid-div586" type="section" level="1" n="192">
          <head xml:id="echoid-head246" xml:space="preserve">PROPOSITIO XIII.</head>
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            <s xml:id="echoid-s6126" xml:space="preserve">PArabola non eſt ſimilis hyperbolæ, neque ellipſi.</s>
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          </p>
          <p>
            <s xml:id="echoid-s6128" xml:space="preserve">Hyperbolæ, ſeu ellipſis A B ſit axis B C, & </s>
            <s xml:id="echoid-s6129" xml:space="preserve">inclinatus, ſeu tranſuerſus
              <lb/>
            B a, & </s>
            <s xml:id="echoid-s6130" xml:space="preserve">E F ſit ſectio parabolæ, cuius axis F H. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">Dico, quod ſectio E F
              <lb/>
            non eſt ſimilis ſectioni A B hyperbolicæ, aut ellipticæ, alioquin ſit </s>
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