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-div1112" type="section" level="1" n="352">
          <p>
            <s xml:id="echoid-s13001" xml:space="preserve">
              <pb o="388" file="0426" n="427" rhead="Archimedis"/>
            quas confecimus de rectangulis. </s>
            <s xml:id="echoid-s13002" xml:space="preserve">Et quia
              <lb/>
              <figure xlink:label="fig-0426-01" xlink:href="fig-0426-01a" number="490">
                <image file="0426-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0426-01"/>
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            in triangulo G A C linea B E educta eſt
              <lb/>
            parallela baſi, & </s>
            <s xml:id="echoid-s13003" xml:space="preserve">iam educta eſt ex D
              <lb/>
            ſemipartitione baſis linea D A ſeca ns
              <lb/>
            parallelam in F, erit B F æqualis ipſi F
              <lb/>
            E, & </s>
            <s xml:id="echoid-s13004" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13005" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1114" type="section" level="1" n="353">
          <head xml:id="echoid-head445" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
          <p>
            <s xml:id="echoid-s13006" xml:space="preserve">DIcit Doctor: </s>
            <s xml:id="echoid-s13007" xml:space="preserve">Quod autem C D ſit æqualis ipſi D G, vti remittit ad
              <lb/>
            ſuum librum de propoſitionibus rectangulorum, eo quod duo angu-
              <lb/>
            li D C B, D B C æquales ſunt propter æqualitatem D B, D C, & </s>
            <s xml:id="echoid-s13008" xml:space="preserve">an-
              <lb/>
            gulus D B C cum augulo D B G eſt rectus, & </s>
            <s xml:id="echoid-s13009" xml:space="preserve">ſimiliter angulus D C B
              <lb/>
            cum angulo C G B: </s>
            <s xml:id="echoid-s13010" xml:space="preserve">neceſſe eſt, vt ſint duo anguli D G B, D B G æqua-
              <lb/>
            les etiam, ergo duo latera D B, D G ſunt æqualia.</s>
            <s xml:id="echoid-s13011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13012" xml:space="preserve">Rurſus ſi dicatur quod proportio C D ad D B ſit vt proportio D B ad
              <lb/>
            D G, & </s>
            <s xml:id="echoid-s13013" xml:space="preserve">D C æqualis ipſi D B, ergo D B æqualis eſt D G, eſſet para-
              <lb/>
            bola. </s>
            <s xml:id="echoid-s13014" xml:space="preserve">Dicit, quod vero B F ſit æqualis F E, hoc conſtat ex eo quod
              <lb/>
            caſus A D ſuper duas lineas B E, G C parallelas in triangulo A G C,
              <lb/>
            exigit eorum ſectio in eadem proportione, & </s>
            <s xml:id="echoid-s13015" xml:space="preserve">id quidem, quia A D ad
              <lb/>
            A F eandem proportionem habet, quam G D ad B F, & </s>
            <s xml:id="echoid-s13016" xml:space="preserve">quam D C ad
              <lb/>
            E F, ergo G D ad B F eſt vt D C ad E F, & </s>
            <s xml:id="echoid-s13017" xml:space="preserve">permutando G D ad ei æ-
              <lb/>
            qualem D C, eſt vt B F ad E F, & </s>
            <s xml:id="echoid-s13018" xml:space="preserve">propterea ipſæ etiam ſunt æquales.</s>
            <s xml:id="echoid-s13019" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1115" type="section" level="1" n="354">
          <head xml:id="echoid-head446" xml:space="preserve">Notæ in Propoſ. II.</head>
          <p style="it">
            <s xml:id="echoid-s13020" xml:space="preserve">HVius ſecundæ propoſitionis expoſitio, & </s>
            <s xml:id="echoid-s13021" xml:space="preserve">demonſtratio inſigniter deformata
              <lb/>
            eſt; </s>
            <s xml:id="echoid-s13022" xml:space="preserve">in propoſitione enim ſupponuntur duæ rectæ D C, D B tangere cir-
              <lb/>
            culum tantummodo, non autem conſtituere angulum rectum, & </s>
            <s xml:id="echoid-s13023" xml:space="preserve">ſolummodo re-
              <lb/>
            cta linea B E perpendicularis ducitur ad diametrum A C, quare male in de-
              <lb/>
            monſtratione pronunciatur quadrilaterum B D C E parallelogrammum rectan-
              <lb/>
            gulum, cum ferè ſemper ſit Trapetium: </s>
            <s xml:id="echoid-s13024" xml:space="preserve">pariterque errat, quando ait rectam
              <lb/>
            B D perpendicularem eſſe ſuper C G, quæ nunquam vera ſunt, niſi in vnico caſu,
              <lb/>
            quando ſcilicet B E cadit perpendiculariter ſuper centrum circuli.</s>
            <s xml:id="echoid-s13025" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13026" xml:space="preserve">Interim notandum eſt hanc elegantem
              <lb/>
              <figure xlink:label="fig-0426-02" xlink:href="fig-0426-02a" number="491">
                <image file="0426-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0426-02"/>
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            propoſitionem, inſignem vſum habere pro
              <lb/>
            inueſtigatione menſuræ circuli, & </s>
            <s xml:id="echoid-s13027" xml:space="preserve">recta-
              <lb/>
            rum in eo ſubtenſarum; </s>
            <s xml:id="echoid-s13028" xml:space="preserve">deduci namque
              <lb/>
            poßunt non contemnenda problemata; </s>
            <s xml:id="echoid-s13029" xml:space="preserve">Si
              <lb/>
            enim quis cupiat circulo adſcribere duas
              <lb/>
            figuras or dinatas ſimiles, quarum circum-
              <lb/>
            ſcripta ſuperet inſcriptam exceſſu minori
              <lb/>
            quolibet dato, facile problema </s>
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