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-div1170" type="section" level="1" n="383">
          <p>
            <s xml:id="echoid-s13698" xml:space="preserve">
              <pb o="413" file="0451" n="452" rhead="Aſſumpt. Liber."/>
            tũ O B, ſiue X S in parabola
              <lb/>
              <figure xlink:label="fig-0451-01" xlink:href="fig-0451-01a" number="526">
                <image file="0451-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0451-01"/>
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              <note position="right" xlink:label="note-0451-01" xlink:href="note-0451-01a" xml:space="preserve">Prop. 11.
                <lb/>
              lib. 1.</note>
            æquale eſt rectangulo S FN,
              <lb/>
            ergo AO ad A C eſt vt qua-
              <lb/>
            dratum E B ad quadratum
              <lb/>
            O B, & </s>
            <s xml:id="echoid-s13699" xml:space="preserve">propterea parallele-
              <lb/>
            pipedum, cuius baſis quadra-
              <lb/>
            tum O B, altitudo O A æ-
              <lb/>
            quale erit parallelepipedo ba-
              <lb/>
            ſe quadrato E B, altitudine
              <lb/>
            A C contento, quod erat
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s13700" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13701" xml:space="preserve">Ex hiſce propoſitionibus de-
              <lb/>
            ducit inſuper Eutocius aliqua,
              <lb/>
            quæ non omnino firma, & </s>
            <s xml:id="echoid-s13702" xml:space="preserve">cer-
              <lb/>
            ta mihi videntur, nam ex eo
              <lb/>
            quod recta linea vt I X tangit
              <lb/>
            vtramq; </s>
            <s xml:id="echoid-s13703" xml:space="preserve">coniſectionem (hyper-
              <lb/>
            bolen ſcilicet B X, & </s>
            <s xml:id="echoid-s13704" xml:space="preserve">parabo-
              <lb/>
            len F X) in eodem puncto X
              <lb/>
            concludit hyperbolen interius
              <lb/>
            contingere parabolen quàm de-
              <lb/>
            inceps non ſecat ad eaſdem par-
              <lb/>
            tes axis illius. </s>
            <s xml:id="echoid-s13705" xml:space="preserve">Hoc autem omnino
              <lb/>
            neceſſarium nõ
              <unsure/>
            eſt ex demonſtra-
              <lb/>
            tis à me in prop. </s>
            <s xml:id="echoid-s13706" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13707" xml:space="preserve">21. </s>
            <s xml:id="echoid-s13708" xml:space="preserve">& </s>
            <s xml:id="echoid-s13709" xml:space="preserve">
              <lb/>
            22. </s>
            <s xml:id="echoid-s13710" xml:space="preserve">Adàit. </s>
            <s xml:id="echoid-s13711" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13712" xml:space="preserve">6. </s>
            <s xml:id="echoid-s13713" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s13714" xml:space="preserve">fieri
              <lb/>
            enim poteſt vt Parabole exte-
              <lb/>
            rius hyperbolen tangat in X, & </s>
            <s xml:id="echoid-s13715" xml:space="preserve">
              <lb/>
            poſtea hinc inde eam ſecet. </s>
            <s xml:id="echoid-s13716" xml:space="preserve">Poteſt inſuper hyperbole ſecare eandem parabolam
              <lb/>
            in eodem puncto X, licet ambo in eodem puncto tangantur ab aliqua recta li-
              <lb/>
            nea, vt eſt I X; </s>
            <s xml:id="echoid-s13717" xml:space="preserve">quod quidem adnotaſſe fuit operepretium.</s>
            <s xml:id="echoid-s13718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1172" type="section" level="1" n="384">
          <head xml:id="echoid-head476" xml:space="preserve">FINIS.</head>
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