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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            <s xml:id="echoid-s11699" xml:space="preserve">
              <pb o="334" file="0372" n="373" rhead="Apollonij Pergæi"/>
            Q; </s>
            <s xml:id="echoid-s11700" xml:space="preserve">& </s>
            <s xml:id="echoid-s11701" xml:space="preserve">pariter diameter figuræ P Q minor eſt, quàm diameter figuræ S
              <lb/>
            T. </s>
            <s xml:id="echoid-s11702" xml:space="preserve">Sit iam A C minor quàm A F, & </s>
            <s xml:id="echoid-s11703" xml:space="preserve">eius quadratum non minus dimi-
              <lb/>
              <note position="left" xlink:label="note-0372-01" xlink:href="note-0372-01a" xml:space="preserve">Demonſt.
                <lb/>
              prop. 45.</note>
            dio quadrati exceſſus ipſius A F ſuper A C. </s>
            <s xml:id="echoid-s11704" xml:space="preserve">Et quia A C ad A F ean-
              <lb/>
            dem proportionem habet, quàm A H ad A G; </s>
            <s xml:id="echoid-s11705" xml:space="preserve">ergo duplum quadrati
              <lb/>
            A H non eſt minus quadrato H G; </s>
            <s xml:id="echoid-s11706" xml:space="preserve">ergo M H in H A bis ſumptum ma-
              <lb/>
            ius eſt quadrato H G, & </s>
            <s xml:id="echoid-s11707" xml:space="preserve">addatur communiter duplum G A in A H fiet
              <lb/>
            duplum ſummæ G A, M H, vel C M in A H maius quàm duplum G A
              <lb/>
            in A H cum quadrato H G, ſeu quàm quadratum G A cum quadrato A
              <lb/>
              <figure xlink:label="fig-0372-01" xlink:href="fig-0372-01a" number="442">
                <image file="0372-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0372-01"/>
              </figure>
            H: </s>
            <s xml:id="echoid-s11708" xml:space="preserve">quare duplum C M in M A ad duplum C M in A H, ſeu M A ad
              <lb/>
            A H minorem proportionem habet, quàm duplum C M in M A ad qua-
              <lb/>
            dratum G A vna cum quadrato A H: </s>
            <s xml:id="echoid-s11709" xml:space="preserve">& </s>
            <s xml:id="echoid-s11710" xml:space="preserve">componendo habebit M H ad
              <lb/>
            H A, ſeu M H in H A ad quadratum A H minorem proportionem quàm
              <lb/>
            duplum C M in M A cum duobus quadratis ipſarum G A, & </s>
            <s xml:id="echoid-s11711" xml:space="preserve">A H (quæ
              <lb/>
            omnia ſimul æqualia ſunt quadrato M G cum quadrato M H) ad qua-
              <lb/>
            dratum A G cum quadrato A H: </s>
            <s xml:id="echoid-s11712" xml:space="preserve">& </s>
            <s xml:id="echoid-s11713" xml:space="preserve">permutando M H in H A ad qua-
              <lb/>
            dratum G M cum quadrato M H (nempe quadratum A C ad duo qua-
              <lb/>
            drata laterum figuræ P Q) ſiue ad quadratum diametri figuræ P Q (17.
              <lb/>
            </s>
            <s xml:id="echoid-s11714" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11715" xml:space="preserve">minorem proportionem habebit, quàm quadratum H A ad qua-
              <lb/>
            dratum A G cum quadrato A H, ſeu quàm quadratum A C ad quadra-
              <lb/>
            tum diametri figuræ eius; </s>
            <s xml:id="echoid-s11716" xml:space="preserve">igitur quadratum A C ad diametrum figuræ
              <lb/>
            P Q minorem proportionem habet, quàm ad diametrum figuræ A C: </s>
            <s xml:id="echoid-s11717" xml:space="preserve">& </s>
            <s xml:id="echoid-s11718" xml:space="preserve">
              <lb/>
            ideo diameter figuræ P Q maior erit diametro figuræ A C. </s>
            <s xml:id="echoid-s11719" xml:space="preserve">Præterea,
              <lb/>
            quia duplum quadrati M H maius eſt quadrato H G; </s>
            <s xml:id="echoid-s11720" xml:space="preserve">ergo V H in M H
              <lb/>
            bis maius erit, quàm quadratum H G: </s>
            <s xml:id="echoid-s11721" xml:space="preserve">& </s>
            <s xml:id="echoid-s11722" xml:space="preserve">oſtendetur (quemadmodum
              <lb/>
            diximus) quod diameter figuræ S T maior ſit quàm diameter figuræ P Q.</s>
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