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-div684" type="section" level="1" n="228">
          <pb o="200" file="0238" n="238" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s7502" xml:space="preserve">Educamus itaque N A ad O ex B L, & </s>
            <s xml:id="echoid-s7503" xml:space="preserve">P D ad Q ex M E, quia B G
              <lb/>
              <note position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">b</note>
            ad B I eſt, vt H E ad E K, & </s>
            <s xml:id="echoid-s7504" xml:space="preserve">B G ad B L eſt vt H E ad E M; </s>
            <s xml:id="echoid-s7505" xml:space="preserve">ergo L B
              <lb/>
            ad B I, nempe L N ad A I (19. </s>
            <s xml:id="echoid-s7506" xml:space="preserve">ex 1. </s>
            <s xml:id="echoid-s7507" xml:space="preserve">(nempe L O ad O I eſt vt M E
              <lb/>
            ad E K, nempe P M ad D K, nempe M Q ad Q K; </s>
            <s xml:id="echoid-s7508" xml:space="preserve">& </s>
            <s xml:id="echoid-s7509" xml:space="preserve">contra O L ad L
              <lb/>
            I, vt V M ad M K, &</s>
            <s xml:id="echoid-s7510" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7511" xml:space="preserve">Addenda non nulla verba, quæ deficiunt, & </s>
            <s xml:id="echoid-s7512" xml:space="preserve">reliqua
              <lb/>
            reſtituenda cenſui, vt in textu leguntur. </s>
            <s xml:id="echoid-s7513" xml:space="preserve">Zuoniam B G ad B I eſt vt H E ad
              <lb/>
            E K, & </s>
            <s xml:id="echoid-s7514" xml:space="preserve">B L ad B G eſt vt M E ad E H; </s>
            <s xml:id="echoid-s7515" xml:space="preserve">ergo, ex æqualitate, L B ad B I
              <lb/>
            eandem proportionem habet, quàm M E ad E K, ſed quadratum N L ad qua-
              <lb/>
            dratum A I eſt in parabola, vt abſcißa L B ad B I; </s>
            <s xml:id="echoid-s7516" xml:space="preserve">pariterque quadratum P
              <lb/>
              <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">20. lib. 1.</note>
            M ad quadratum D K eſt, vt M E ad E K: </s>
            <s xml:id="echoid-s7517" xml:space="preserve">& </s>
            <s xml:id="echoid-s7518" xml:space="preserve">propterea quadratum N L ad
              <lb/>
            quadratum A I eandem proportionem habebit quàm quadratum P M ad quadra-
              <lb/>
            tum D K; </s>
            <s xml:id="echoid-s7519" xml:space="preserve">igitur N L ad A I eandem proportionem habebit, quàm P M ad D
              <lb/>
              <figure xlink:label="fig-0238-01" xlink:href="fig-0238-01a" number="271">
                <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-01"/>
              </figure>
            K; </s>
            <s xml:id="echoid-s7520" xml:space="preserve">ſed vt N L ad A I ita eſt L O ad O I (propter parallelas A I, N L, & </s>
            <s xml:id="echoid-s7521" xml:space="preserve">ſimi-
              <lb/>
            litudinem triangulorũ A I O, & </s>
            <s xml:id="echoid-s7522" xml:space="preserve">O N L) pariterg; </s>
            <s xml:id="echoid-s7523" xml:space="preserve">vt P M ad D K ita eſt M
              <lb/>
            Z ad Z K (propter ſimilitudinem triangulorum Q M P, & </s>
            <s xml:id="echoid-s7524" xml:space="preserve">Q K D) igitur
              <lb/>
            L O ad O I eandem proportionem habebit, quàm M Q ad Q K; </s>
            <s xml:id="echoid-s7525" xml:space="preserve">& </s>
            <s xml:id="echoid-s7526" xml:space="preserve">compa-
              <lb/>
            rando antecedentes ad differentias, vel ſummas terminorum O L ad L I eandem
              <lb/>
            proportionem habebit, quàm Q M ad M K.</s>
            <s xml:id="echoid-s7527" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7528" xml:space="preserve">Et B L ad L N eſt vt E M ad M P (propter ſimilitudinem duorum
              <lb/>
            ſegmentorum) ergo ex æqualitate O L ad L N, &</s>
            <s xml:id="echoid-s7529" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7530" xml:space="preserve">Sequitur quidem hoc
              <lb/>
              <note position="right" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">c</note>
            non propter ſimilitudinem ſegmentorum, quandoquidem ſegmenta ſimilia non
              <lb/>
            ſupponuntur ſed quia ſemper parabolæ ſunt ſimiles, & </s>
            <s xml:id="echoid-s7531" xml:space="preserve">in eis poſitæ ſunt axium
              <lb/>
            abſciſſæ L B, & </s>
            <s xml:id="echoid-s7532" xml:space="preserve">M E proportionales lateribus rectis B G, & </s>
            <s xml:id="echoid-s7533" xml:space="preserve">E H, propterea
              <lb/>
              <note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">11. huius.</note>
            (vt in prop. </s>
            <s xml:id="echoid-s7534" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7535" xml:space="preserve">huius oſtenſum eſt ) B L ad L N eandem proportionem habebit
              <lb/>
            quàm E M ad M P; </s>
            <s xml:id="echoid-s7536" xml:space="preserve">ſed prius L B ad B I erat vt M E ad E K, ergo comparã-
              <lb/>
            do differentias terminorum ad antecedentes erit I L ad L B vt K M ad M E,
              <lb/>
            eſtq; </s>
            <s xml:id="echoid-s7537" xml:space="preserve">oſtenſa O L ad L I vt Q M ad M K, ergo ex æquali ordinata O L ad L B
              <lb/>
            erit vt Q M ad M E.</s>
            <s xml:id="echoid-s7538" xml:space="preserve"/>
          </p>
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