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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              <pb o="411" file="0449" n="450" rhead="Aſſumpt. Liber."/>
            gulum A D E, erit in primo caſu D O maior, quàm C D, in ſecundo
              <lb/>
            vero minor; </s>
            <s xml:id="echoid-s13661" xml:space="preserve">& </s>
            <s xml:id="echoid-s13662" xml:space="preserve">propterea A O minor erit, quàm A C in vtroque caſu.
              <lb/>
            </s>
            <s xml:id="echoid-s13663" xml:space="preserve">Et quia quadratum C B ad rectangulum A D E eſt vt C D ad D O, igi-
              <lb/>
            tur ſolida parallelepipeda reciproca erunt æqualia, ſcilicet ſolidum qua-
              <lb/>
              <figure xlink:label="fig-0449-01" xlink:href="fig-0449-01a" number="524">
                <image file="0449-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0449-01"/>
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            drato C B in D O ducto æquale erit ſolido, cuius baſis rectangulum A
              <lb/>
            D E, altitudo vero C D, ſeu potius æquale erit ſolido, cuius baſis re-
              <lb/>
            ctangulum E D C, altitudo vero A D, & </s>
            <s xml:id="echoid-s13664" xml:space="preserve">propterea vt quadratum B C
              <lb/>
            ad rectangulum E D C, ita erit reciproce A D ad D O, & </s>
            <s xml:id="echoid-s13665" xml:space="preserve">comparando
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            antecedentes ad terminorum differentias in primo caſu, & </s>
            <s xml:id="echoid-s13666" xml:space="preserve">ad eorundem
              <lb/>
            ſummas in ſecundo caſu, erit quadratum B C ad quadratum D B vt A
              <lb/>
            D ad A O, & </s>
            <s xml:id="echoid-s13667" xml:space="preserve">denuo ſolidum parallelepipedum rectangulum contentum
              <lb/>
            ſub quadrato B C in A O æquale erit ei, cuius baſis quadratum D B,
              <lb/>
            altitudo vero A D: </s>
            <s xml:id="echoid-s13668" xml:space="preserve">Eſt vero A O oſtenſa minor, quàm A C in vtroque
              <lb/>
            caſu, igitur parallelepipedum, cuius baſis quadratum B C, altitudo A
              <lb/>
            C maius eſt eo, cuius baſis eſt idem quadratum B C, altitudo A O;
              <lb/>
            </s>
            <s xml:id="echoid-s13669" xml:space="preserve">ideoque parallelepipedum, cuius baſis quadratum B C, altitudo A C
              <lb/>
            maius eſt quolibet parallelepipedo, cuius baſis quadratum B D, altitudo
              <lb/>
            A D: </s>
            <s xml:id="echoid-s13670" xml:space="preserve">quare patet propoſitum.</s>
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          <head xml:id="echoid-head475" xml:space="preserve">PROPOSITIO XVII.</head>
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            <s xml:id="echoid-s13672" xml:space="preserve">SIt A B tripla ipſius A E, maior vero quàm tripla alterius C A,
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            ſecari debet eadem A B citra, & </s>
            <s xml:id="echoid-s13673" xml:space="preserve">vltra E, in O, ita vt
              <lb/>
            parallelepipedum, cuius baſis quadratum O B, altitudo O A
              <lb/>
            æquale ſit parallelepipedo, cuius baſis quadratum E B, altitu-
              <lb/>
            do A C.</s>
            <s xml:id="echoid-s13674" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13675" xml:space="preserve">Fiat rectangulum A C B F, & </s>
            <s xml:id="echoid-s13676" xml:space="preserve">producantur latera C A, F B, & </s>
            <s xml:id="echoid-s13677" xml:space="preserve">fiat
              <lb/>
            rectangulum C F N æquale quadrato E B, & </s>
            <s xml:id="echoid-s13678" xml:space="preserve">ducta diametro C E G </s>
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