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-div1009" type="section" level="1" n="319">
          <pb o="335" file="0373" n="374" rhead="Conicor. Lib. VII."/>
        </div>
        <div xml:id="echoid-div1011" type="section" level="1" n="320">
          <head xml:id="echoid-head396" xml:space="preserve">PROPOSITIO XXXXVI.</head>
          <p>
            <s xml:id="echoid-s11724" xml:space="preserve">SIt poſtea quadratum A C minus dimidio quadrati ex differentia ipſa-
              <lb/>
            rum C A, & </s>
            <s xml:id="echoid-s11725" xml:space="preserve">A F; </s>
            <s xml:id="echoid-s11726" xml:space="preserve">erit duplum quadrati A H minus quadrato H G
              <lb/>
            & </s>
            <s xml:id="echoid-s11727" xml:space="preserve">ponamus duplum quadrati M H æquale quadrato H G: </s>
            <s xml:id="echoid-s11728" xml:space="preserve">& </s>
            <s xml:id="echoid-s11729" xml:space="preserve">educamus
              <lb/>
            ad axim perpendicularem N M, & </s>
            <s xml:id="echoid-s11730" xml:space="preserve">iungamus N C; </s>
            <s xml:id="echoid-s11731" xml:space="preserve">& </s>
            <s xml:id="echoid-s11732" xml:space="preserve">ducamus diame-
              <lb/>
            trum P Q parallelã ipſi N C, erit H M ad M G, vt P Q ad P R, & </s>
            <s xml:id="echoid-s11733" xml:space="preserve">pro-
              <lb/>
              <note position="right" xlink:label="note-0373-01" xlink:href="note-0373-01a" xml:space="preserve">6. huius.</note>
            pterea quadratum P Q dimidium erit quadrati exceſſus ipſius P R; </s>
            <s xml:id="echoid-s11734" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0373-02" xlink:href="note-0373-02a" xml:space="preserve">a</note>
            P Q eſt vna æqualium: </s>
            <s xml:id="echoid-s11735" xml:space="preserve">ponatur inſuper inter A, & </s>
            <s xml:id="echoid-s11736" xml:space="preserve">P diameter I L, & </s>
            <s xml:id="echoid-s11737" xml:space="preserve">
              <lb/>
            conſtructio perficiatur, vt prius. </s>
            <s xml:id="echoid-s11738" xml:space="preserve">Et quia duplum quadrati M H æquale
              <lb/>
            eſt quadrato H G, erit duplum M H in H E minus quadrato H G, & </s>
            <s xml:id="echoid-s11739" xml:space="preserve">
              <lb/>
            ponatur communiter duplum G E in E H; </s>
            <s xml:id="echoid-s11740" xml:space="preserve">igitur duplum aggregati M G
              <lb/>
            in E H minus eſt quadrato G E cum quadrato E H; </s>
            <s xml:id="echoid-s11741" xml:space="preserve">& </s>
            <s xml:id="echoid-s11742" xml:space="preserve">oſtendetur que-
              <lb/>
            madmodum diximus antea, quod quadratum diametri figuræ P Q mi-
              <lb/>
            nus ſit quadrato diametri figuræ I L; </s>
            <s xml:id="echoid-s11743" xml:space="preserve">& </s>
            <s xml:id="echoid-s11744" xml:space="preserve">quadratum diametri figuræ I L
              <lb/>
            minus ſit quadrato diametri figure A C.</s>
            <s xml:id="echoid-s11745" xml:space="preserve"/>
          </p>
          <figure number="443">
            <image file="0373-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0373-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s11746" xml:space="preserve">Deindè ducatur diameter inclinata S T extra ſegmentum A P, & </s>
            <s xml:id="echoid-s11747" xml:space="preserve">C X ei
              <lb/>
            parallela, & </s>
            <s xml:id="echoid-s11748" xml:space="preserve">ad axim perpendicularis X V: </s>
            <s xml:id="echoid-s11749" xml:space="preserve">& </s>
            <s xml:id="echoid-s11750" xml:space="preserve">quia duplum quadrati M H
              <lb/>
            æquale eſt quadrato H G erit duplum V H in H M maius quadrato H
              <lb/>
            G: </s>
            <s xml:id="echoid-s11751" xml:space="preserve">ponatur communiter duplum G M in M H, fiet duplum aggregati
              <lb/>
            V G, M H, in M H maius quadrato M G cum quadrato M H: </s>
            <s xml:id="echoid-s11752" xml:space="preserve">quare
              <lb/>
            duplum aggregati V G, & </s>
            <s xml:id="echoid-s11753" xml:space="preserve">M H in M V ad duplum aggregati V G, & </s>
            <s xml:id="echoid-s11754" xml:space="preserve">
              <lb/>
            M H in M H, nempe M V ad M H minorem proportionem habebit,
              <lb/>
            quàm duplum aggregati V G, & </s>
            <s xml:id="echoid-s11755" xml:space="preserve">M H in M V ad quadratum G M cum
              <lb/>
            quadrato M H: </s>
            <s xml:id="echoid-s11756" xml:space="preserve">& </s>
            <s xml:id="echoid-s11757" xml:space="preserve">componendo oſtendetur (quemadmodum antea di-
              <lb/>
            ctum eſt) quod quadratum A C ad diametrum figuræ P Q maiorem pro-
              <lb/>
            portionem habeat, quàm ad diametrum figuræ S T. </s>
            <s xml:id="echoid-s11758" xml:space="preserve">Eadem prorſus cõ-
              <lb/>
            tingent in reliquis omnibus diametris. </s>
            <s xml:id="echoid-s11759" xml:space="preserve">Quapropter diameter figuræ P Q
              <lb/>
            minor eſt diametro figuræ cuiuslibet diametri ad vtraſque eius partes in
              <lb/>
            eadem ſectione exiſtente. </s>
            <s xml:id="echoid-s11760" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s11761" xml:space="preserve"/>
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