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-div932" type="section" level="1" n="293">
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            <s xml:id="echoid-s10956" xml:space="preserve">
              <pb o="305" file="0343" n="344" rhead="Conicor. Lib. VII."/>
            erit quadratum A C ad quadratum differentię ipſarum A C, A F, vt
              <lb/>
            quadratum H A ad quadratum H G, at ad quadratum differentię ipſa-
              <lb/>
            rum I L, I K eſt, vt E H in H A ad quadratum H G (19. </s>
            <s xml:id="echoid-s10957" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10958" xml:space="preserve">ad
              <lb/>
            quadratum verò differentię S T, S Z eſt, vt H M in H A ad quadratum
              <lb/>
            H G (19. </s>
            <s xml:id="echoid-s10959" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10960" xml:space="preserve">eſt verò M H in H A maius quàm E H in H A, atque
              <lb/>
            E H in H A maius quàm quadratum H A; </s>
            <s xml:id="echoid-s10961" xml:space="preserve">igitur A C ad differentiam
              <lb/>
            ipſarum A C, A F minorem proportionem habet, quàm ad differentiam
              <lb/>
            ipſarum I L, I K, & </s>
            <s xml:id="echoid-s10962" xml:space="preserve">ad differentiam earundem I L, I K minorem pro-
              <lb/>
            portionem habet, quam ad differentiam ipſarum S T, S Z; </s>
            <s xml:id="echoid-s10963" xml:space="preserve">igitur diffe-
              <lb/>
            rentia ipſarum A C, A F maior eſt, quàm differentia ipſarum I L, I K,
              <lb/>
            atquè differentia earundem I L, I K maior eſt quàm differentia S T, S
              <lb/>
            Z. </s>
            <s xml:id="echoid-s10964" xml:space="preserve">Quod erat propoſitum.</s>
            <s xml:id="echoid-s10965" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div935" type="section" level="1" n="294">
          <head xml:id="echoid-head365" xml:space="preserve">Notę in Propoſit. XXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s10966" xml:space="preserve">S It in primis figuris axis A C maior, quàm axis Q R. </s>
            <s xml:id="echoid-s10967" xml:space="preserve">Quia quadratum
              <lb/>
              <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">ex 15. 16.
                <lb/>
              lib. 1.
                <lb/>
              Defin. 1.
                <lb/>
              huius.</note>
            A C ad quadratum Q R eandem proportionem habet, quàm H A ad A G:
              <lb/>
            </s>
            <s xml:id="echoid-s10968" xml:space="preserve">eſtque G A minor quàm G E; </s>
            <s xml:id="echoid-s10969" xml:space="preserve">ergo H G ad G A maiorem proportionem habet
              <lb/>
            quàm ad G E: </s>
            <s xml:id="echoid-s10970" xml:space="preserve">& </s>
            <s xml:id="echoid-s10971" xml:space="preserve">componendo in hyperbola, & </s>
            <s xml:id="echoid-s10972" xml:space="preserve">diuidendo in ellipſi H A ad A
              <lb/>
            G maiorem proportionem habet, quàm H E ad E G; </s>
            <s xml:id="echoid-s10973" xml:space="preserve">ſed H E ad E G eandem
              <lb/>
              <note position="right" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">6. & 7.
                <lb/>
              huius.</note>
              <figure xlink:label="fig-0343-01" xlink:href="fig-0343-01a" number="401">
                <image file="0343-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0343-01"/>
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            proportionem habet, quàm quadratum
              <lb/>
            I L ad quadratum N O; </s>
            <s xml:id="echoid-s10974" xml:space="preserve">ergo quadra-
              <lb/>
            tum A C ad quadratum Q R maiorem
              <lb/>
            proportionem habet, quàm quadratum
              <lb/>
            I L ad quadratum N O : </s>
            <s xml:id="echoid-s10975" xml:space="preserve">& </s>
            <s xml:id="echoid-s10976" xml:space="preserve">propterea
              <lb/>
            A C ad Q R maiorem proportionem
              <lb/>
            habet, quàm I L ad N O : </s>
            <s xml:id="echoid-s10977" xml:space="preserve">& </s>
            <s xml:id="echoid-s10978" xml:space="preserve">ſunt
              <lb/>
            quoquè earundem proportionum dupli-
              <lb/>
            catę pariter inęquales, nimirum axis
              <lb/>
              <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">ex 15. 16.
                <lb/>
              huius.</note>
            A C ad eius latus rectum A F maio-
              <lb/>
            rem proportionem habebit, quàm dia-
              <lb/>
            meter I L ad eius latus rectum I K.
              <lb/>
            </s>
            <s xml:id="echoid-s10979" xml:space="preserve">Secundò quia G E minor eſt, quàm
              <lb/>
            G M ; </s>
            <s xml:id="echoid-s10980" xml:space="preserve">ergo H G ad G E maiorem pro-
              <lb/>
            portionem habet, quàm ad G M ; </s>
            <s xml:id="echoid-s10981" xml:space="preserve">& </s>
            <s xml:id="echoid-s10982" xml:space="preserve">componendo in hyperbola, & </s>
            <s xml:id="echoid-s10983" xml:space="preserve">diuidendo in
              <lb/>
            ellipſi H E ad E G maiorem proportionem habebit, quàm H M ad M G, & </s>
            <s xml:id="echoid-s10984" xml:space="preserve">
              <lb/>
            quadratum I L ad quadratum N O habet eandem proportionem, quàm H E ad
              <lb/>
            E G ; </s>
            <s xml:id="echoid-s10985" xml:space="preserve">nec non quadratum S T ad quadratum V X eandem proportionem habet,
              <lb/>
              <note position="right" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">6. & 7.
                <lb/>
              huius.</note>
            quàm H M ad M G ; </s>
            <s xml:id="echoid-s10986" xml:space="preserve">ergo quadratum I L ad quadratum N O maiorem pro-
              <lb/>
            portionem habet, quàm quadratum S T ad quadratum V X, & </s>
            <s xml:id="echoid-s10987" xml:space="preserve">I L ad N O
              <lb/>
            maiorem proportionem habebit, quàm S T ad V X, & </s>
            <s xml:id="echoid-s10988" xml:space="preserve">earundem proportio-
              <lb/>
            num duplicatę inęquales quoque erunt, ſcilicet I L ad eius latus rectum maio-
              <lb/>
            rem proportionem habebit, quàm S T ad eius latus rectum. </s>
            <s xml:id="echoid-s10989" xml:space="preserve">Deindè in ſecun-
              <lb/>
            dis figuris ſit axis A C minor quàm Q R. </s>
            <s xml:id="echoid-s10990" xml:space="preserve">Quia H A minor eſt, quàm H E;</s>
            <s xml:id="echoid-s10991" xml:space="preserve"/>
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