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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          <p>
            <s xml:id="echoid-s11525" xml:space="preserve">
              <pb o="326" file="0364" n="365" rhead="Apollonij Pergæi"/>
            camus perpendicularem, & </s>
            <s xml:id="echoid-s11526" xml:space="preserve">diametrum. </s>
            <s xml:id="echoid-s11527" xml:space="preserve">Dico, quod P Q æ-
              <lb/>
            qualis eſt trienti ipſius P R.</s>
            <s xml:id="echoid-s11528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11529" xml:space="preserve">Educamus inter P Q, A C diametrum I L, & </s>
            <s xml:id="echoid-s11530" xml:space="preserve">educamus C B ei æ-
              <lb/>
            quidiſtantem, & </s>
            <s xml:id="echoid-s11531" xml:space="preserve">perpendicularem B E, & </s>
            <s xml:id="echoid-s11532" xml:space="preserve">ſecemus E l æqualem E A
              <lb/>
            erit ſumma ipſarum G E, & </s>
            <s xml:id="echoid-s11533" xml:space="preserve">E H æqualis C l; </s>
            <s xml:id="echoid-s11534" xml:space="preserve">eſtque H E minor quam
              <lb/>
            M H, quæ quarta pars eſt ipſius C m; </s>
            <s xml:id="echoid-s11535" xml:space="preserve">ergo ſumma ipſarum M G, H E
              <lb/>
            in M H quater ſumptum minus eſt quadrato C m: </s>
            <s xml:id="echoid-s11536" xml:space="preserve">auferatur communi-
              <lb/>
            ter M G, H E in M E quater ſumptum remanebit quadruplum ſummæ
              <lb/>
            M G, H E in H E minus quàm quadratum C l (quia M G, H E ſimul
              <lb/>
            ſumptæ, nempe M C vna cum A E in M E quater ſumptum æquale eſt
              <lb/>
            quadrato l m; </s>
            <s xml:id="echoid-s11537" xml:space="preserve">quod eſt duplum M E, & </s>
            <s xml:id="echoid-s11538" xml:space="preserve">aggregatum C E, A E, nem-
              <lb/>
            pe C l in l m bis ſumptum ) igitur aggregatum M G, & </s>
            <s xml:id="echoid-s11539" xml:space="preserve">H E in M E
              <lb/>
            quater ſumptum ad aggregatum M G, H E in H E quater ſumptum, nẽ-
              <lb/>
            pe G E ad H E maiorem proportionem habebit, quàm ad quadratum l
              <lb/>
            C. </s>
            <s xml:id="echoid-s11540" xml:space="preserve">& </s>
            <s xml:id="echoid-s11541" xml:space="preserve">componendo M H ad H E, ſeu M H in H A ad E H in H A
              <lb/>
            habebit maiorem proportionem, quàm M G, H E in M E quater ſum-
              <lb/>
            ptum cum quadrato l C (quæ æqualia ſunt quadrato C m) ad quadra-
              <lb/>
            tum l C: </s>
            <s xml:id="echoid-s11542" xml:space="preserve">& </s>
            <s xml:id="echoid-s11543" xml:space="preserve">permutando erit M H in H A ad quadratum C m, nempe
              <lb/>
            ad quadratum ſummæ ipſarum M G, & </s>
            <s xml:id="echoid-s11544" xml:space="preserve">M H, ſeu quadratum A C ad
              <lb/>
            quadratum ſummæ ipſarum P Q, P R (17. </s>
            <s xml:id="echoid-s11545" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11546" xml:space="preserve">maiorem proportio-
              <lb/>
            nem habebit, quàm E H in H A ad quadratum l C (quod eſt æquale
              <lb/>
            quadrato ſummæ ipſarum G E, E H ) quod erit vt quadratum A C ad
              <lb/>
            quadratum aggregati ipſarum I L, I K: </s>
            <s xml:id="echoid-s11547" xml:space="preserve">quapropter A C ad duo latera
              <lb/>
            figuræ P Q maiorem proportionem habet, quàm ad duo latera figuræ I
              <lb/>
            L. </s>
            <s xml:id="echoid-s11548" xml:space="preserve">Et propterea duo latera figuræ P Q minora ſunt, quàm duo latera
              <lb/>
              <figure xlink:label="fig-0364-01" xlink:href="fig-0364-01a" number="432">
                <image file="0364-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0364-01"/>
              </figure>
            </s>
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