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="343" file="0381" n="382" rhead="Conicor. Lib. VII."/>
        </div>
        <div xml:id="echoid-div1035" type="section" level="1" n="327">
          <head xml:id="echoid-head405" xml:space="preserve">PROPOSITIO XXXXI.</head>
          <p>
            <s xml:id="echoid-s11978" xml:space="preserve">IN ellipſi A B C ſit A C axis maior, & </s>
            <s xml:id="echoid-s11979" xml:space="preserve">y O minor, & </s>
            <s xml:id="echoid-s11980" xml:space="preserve">ſint P
              <lb/>
            Q, & </s>
            <s xml:id="echoid-s11981" xml:space="preserve">S T duæ aliæ diametri, ſitque A F erectus ipſius A
              <lb/>
            C, & </s>
            <s xml:id="echoid-s11982" xml:space="preserve">P R erectus ipſius P Q, & </s>
            <s xml:id="echoid-s11983" xml:space="preserve">O f ipſius y O. </s>
            <s xml:id="echoid-s11984" xml:space="preserve">Dico quod
              <lb/>
            C F minor eſt, quàm Q R, & </s>
            <s xml:id="echoid-s11985" xml:space="preserve">Q R, quàm T Z, & </s>
            <s xml:id="echoid-s11986" xml:space="preserve">T Z,
              <lb/>
            quàm y f.</s>
            <s xml:id="echoid-s11987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11988" xml:space="preserve">Ducantur A N, A X ordinatim applicatæ ad diametros P Q, S T,
              <lb/>
            & </s>
            <s xml:id="echoid-s11989" xml:space="preserve">duæ ad axim perpendiculares N M, X V, & </s>
            <s xml:id="echoid-s11990" xml:space="preserve">interceptæ A G, C H.
              <lb/>
            </s>
            <s xml:id="echoid-s11991" xml:space="preserve">Quia quadratum A C ad quadratum y O, nempe A C ad A F eandem,
              <lb/>
              <note position="left" xlink:label="note-0381-01" xlink:href="note-0381-01a" xml:space="preserve">b</note>
            proportionem habet, quàm C G ad G A, ſeu ad C H habebit quadra-
              <lb/>
              <note position="right" xlink:label="note-0381-02" xlink:href="note-0381-02a" xml:space="preserve">Defin. 1.
                <lb/>
              huius.</note>
            tum C A ad quadratum C F ſummæ ipſius C A, eiuſque erecti eandem
              <lb/>
            proportionem, quàm quadratum C G, nempe C G in A H ad quadra-
              <lb/>
            tum G H: </s>
            <s xml:id="echoid-s11992" xml:space="preserve">& </s>
            <s xml:id="echoid-s11993" xml:space="preserve">quadratum A C ad quadratum y O eandem proportionem,
              <lb/>
            habet, quàm G C in C H ad quadratum C H: </s>
            <s xml:id="echoid-s11994" xml:space="preserve">eſtquè quadratum y O ad
              <lb/>
            quadratum ſummæ y f, vt quadra-
              <lb/>
              <figure xlink:label="fig-0381-01" xlink:href="fig-0381-01a" number="452">
                <image file="0381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0381-01"/>
              </figure>
            tum C H ad quadratum H G; </s>
            <s xml:id="echoid-s11995" xml:space="preserve">er-
              <lb/>
            go quadratum A C ad quadratum
              <lb/>
            y f eſt, vt C G in C H minorem
              <lb/>
            ad quadratum H G; </s>
            <s xml:id="echoid-s11996" xml:space="preserve">ſed quadra-
              <lb/>
            tum A C ad quadratum C F ean-
              <lb/>
            dem proportionem habet, quàm.
              <lb/>
            </s>
            <s xml:id="echoid-s11997" xml:space="preserve">G C in maiorem A H ad quadra-
              <lb/>
            tum G H; </s>
            <s xml:id="echoid-s11998" xml:space="preserve">igitur A C ad C F ma-
              <lb/>
            iorem proportionem habet, quàm
              <lb/>
            ad y f: </s>
            <s xml:id="echoid-s11999" xml:space="preserve">& </s>
            <s xml:id="echoid-s12000" xml:space="preserve">propterea C F ſumma,
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s12001" xml:space="preserve">erecti illius minor eſt,
              <lb/>
            quàm y f, quæ eſt ſumma y O, & </s>
            <s xml:id="echoid-s12002" xml:space="preserve">
              <lb/>
            erecti illius. </s>
            <s xml:id="echoid-s12003" xml:space="preserve">Et quoniam C G in,
              <lb/>
            M H, quod minus eſt, quàm C G
              <lb/>
            in A H ad quadratum H G eandem
              <lb/>
            proportionem habet, quàm qua-
              <lb/>
            dratum A C ad quadratum Q R
              <lb/>
            ſummæ diametri, & </s>
            <s xml:id="echoid-s12004" xml:space="preserve">erecti ipſius
              <lb/>
            P Q (16. </s>
            <s xml:id="echoid-s12005" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12006" xml:space="preserve">quare quadratum
              <lb/>
            A C ad quadratnm C F maiorem
              <lb/>
            proportionem babebit, quàm ad
              <lb/>
            quadratum Q R, & </s>
            <s xml:id="echoid-s12007" xml:space="preserve">propterea C F
              <lb/>
            minor erit, quam Q R. </s>
            <s xml:id="echoid-s12008" xml:space="preserve">Et quoniam
              <lb/>
            C G in V H ad quadratum H G eſt vt quadratum A C ad quadratum
              <lb/>
            T Z ad quàm ordinatim applicatur A X (16. </s>
            <s xml:id="echoid-s12009" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12010" xml:space="preserve">erit C F minor quàm
              <lb/>
            T Z: </s>
            <s xml:id="echoid-s12011" xml:space="preserve">cumque C G in H M ad quadratum H G maiorem proportionem,
              <lb/>
            habeat, quàm G C in V H ad quadratum idipſum H G habebit </s>
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