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-s10370" xml:space="preserve">
              <pb o="282" file="0320" n="320" rhead="Apollonij Pergæi"/>
            ſecet axim in M, & </s>
            <s xml:id="echoid-s10371" xml:space="preserve">I S ad axim perpendicularem, ſeu ordinatim applica-
              <lb/>
            tam, eum ſecans in S. </s>
            <s xml:id="echoid-s10372" xml:space="preserve">Et quia trianguli A C B duo latera A C, A B ſecan-
              <lb/>
            tur proportionaliter, ſcilicet bifariam in D, & </s>
            <s xml:id="echoid-s10373" xml:space="preserve">K; </s>
            <s xml:id="echoid-s10374" xml:space="preserve">ergo I D parallela eſt baſi
              <lb/>
            C B: </s>
            <s xml:id="echoid-s10375" xml:space="preserve">eſtquè tangens I M parallela ipſi B A, cum ambo ad diametrum I L ſint
              <lb/>
              <note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">Prop. 5.
                <lb/>
              lib. 2.</note>
            ordinatim applicatæ; </s>
            <s xml:id="echoid-s10376" xml:space="preserve">pariterquè I S parallela eſt B E ( cum ſint ad axim per-
              <lb/>
            pendiculares ) igitur triangula M I S, A B E ſimilia erunt; </s>
            <s xml:id="echoid-s10377" xml:space="preserve">pariterquè trian-
              <lb/>
            gula D I S, C B E erunt ſimilia: </s>
            <s xml:id="echoid-s10378" xml:space="preserve">& </s>
            <s xml:id="echoid-s10379" xml:space="preserve">ideo M S ad S I erit vt A E ad E B, & </s>
            <s xml:id="echoid-s10380" xml:space="preserve">
              <lb/>
            S I ad S D erit, vt B E ad E C: </s>
            <s xml:id="echoid-s10381" xml:space="preserve">quarè ex æquali ordinata M S ad S D ean-
              <lb/>
            dem proportionem habebit, quàm A E ad E C: </s>
            <s xml:id="echoid-s10382" xml:space="preserve">eſtquè quadratum I M ad qua-
              <lb/>
            dratum N D, vt M S ad S D; </s>
            <s xml:id="echoid-s10383" xml:space="preserve">ergo quadratum I M ad quadratum N D eſt,
              <lb/>
              <note position="left" xlink:label="note-0320-02" xlink:href="note-0320-02a" xml:space="preserve">Prop. 4.
                <lb/>
              huius.</note>
            vt A E ad E C, &</s>
            <s xml:id="echoid-s10384" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10385" xml:space="preserve"/>
          </p>
          <figure number="372">
            <image file="0320-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0320-01"/>
          </figure>
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        <div xml:id="echoid-div879" type="section" level="1" n="269">
          <head xml:id="echoid-head337" xml:space="preserve">SECTIO TERTIA</head>
          <head xml:id="echoid-head338" xml:space="preserve">Continens Propoſit. Apollonij VIII. IX. X.
            <lb/>
          XI. XV. XIX. XVI. XVIII.
            <lb/>
          XVII. & XX.</head>
          <p>
            <s xml:id="echoid-s10386" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s10387" xml:space="preserve">IN hyperbola, vel ellipſi quadratum axis inclinati, ſiue
              <lb/>
            tranſuerſi ad quadratum ſummæ duarum diametrorum
              <lb/>
            coniugatarum eiuſdem ſectionis habebit eandem proportionem,
              <lb/>
            quàm productum præſectæ axis in ſuam interceptam compara-
              <lb/>
            tam ad quadratum ſummæ ſuæ interceptæ, & </s>
            <s xml:id="echoid-s10388" xml:space="preserve">potentis compa-
              <lb/>
            ratarum.</s>
            <s xml:id="echoid-s10389" xml:space="preserve"/>
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