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-div958" type="section" level="1" n="301">
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            <s xml:id="echoid-s11288" xml:space="preserve">
              <pb o="316" file="0354" n="355" rhead="Apollonij Pergæi"/>
            Simili modo oſtendetur quod I K minor ſit, quam P R: </s>
            <s xml:id="echoid-s11289" xml:space="preserve">etenim ſi pona-
              <lb/>
            tur linea f æqualis ſummæ M G, G E: </s>
            <s xml:id="echoid-s11290" xml:space="preserve">cum G E non ſit maior duplo E
              <lb/>
            H, & </s>
            <s xml:id="echoid-s11291" xml:space="preserve">f maior ſit duplo G E; </s>
            <s xml:id="echoid-s11292" xml:space="preserve">igitur f in E H maius eſt quadrato G E.
              <lb/>
            </s>
            <s xml:id="echoid-s11293" xml:space="preserve">Poſtea oſtendetur (quemadmodum antea dictum eſt) quod M H ad H
              <lb/>
            E, nempe M H in H A ad E H in H A minorem proportionem habet
              <lb/>
              <figure xlink:label="fig-0354-01" xlink:href="fig-0354-01a" number="420">
                <image file="0354-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0354-01"/>
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            quàm quadratum M G ad quadratum G E; </s>
            <s xml:id="echoid-s11294" xml:space="preserve">& </s>
            <s xml:id="echoid-s11295" xml:space="preserve">permutando M H in H A
              <lb/>
            ad quadratum M G, ſeu quadratum A C ad quadratum P R(15. </s>
            <s xml:id="echoid-s11296" xml:space="preserve">ex 7.)
              <lb/>
            </s>
            <s xml:id="echoid-s11297" xml:space="preserve">minorem proportionem habebit, quàm E H in H A ad quadratum G E,
              <lb/>
            nempe quàm quadratum A C ad quadratum I K: </s>
            <s xml:id="echoid-s11298" xml:space="preserve">& </s>
            <s xml:id="echoid-s11299" xml:space="preserve">propterea A C ad
              <lb/>
            P R minorem proportionem habebit, quàm ad I K; </s>
            <s xml:id="echoid-s11300" xml:space="preserve">ideoquè I K minor
              <lb/>
            eſt, quàm P R: </s>
            <s xml:id="echoid-s11301" xml:space="preserve">& </s>
            <s xml:id="echoid-s11302" xml:space="preserve">pariter P R minor, quàm S Z.</s>
            <s xml:id="echoid-s11303" xml:space="preserve"/>
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          <head xml:id="echoid-head375" xml:space="preserve">PROPOSITIO XXXV. &
            <lb/>
          XXXVI.</head>
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            <s xml:id="echoid-s11304" xml:space="preserve">S It poſtea A C minor dimidio A F; </s>
            <s xml:id="echoid-s11305" xml:space="preserve">erit A G maior duplo A H, & </s>
            <s xml:id="echoid-s11306" xml:space="preserve">
              <lb/>
            ideo H G maior eſt, quàm H A: </s>
            <s xml:id="echoid-s11307" xml:space="preserve">ponatur iam H M æqualis H G,
              <lb/>
            ducaturque ad axim perpendicularis N M ; </s>
            <s xml:id="echoid-s11308" xml:space="preserve">iungaturque N C, & </s>
            <s xml:id="echoid-s11309" xml:space="preserve">educa-
              <lb/>
            tur diameter P Q parallela N C. </s>
            <s xml:id="echoid-s11310" xml:space="preserve">Et quia M H medietas eſt ipſius M G,
              <lb/>
            erit P Q dimidium ipſius P R (6. </s>
            <s xml:id="echoid-s11311" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11312" xml:space="preserve">Inter duas diametros P Q, A C
              <lb/>
            ducatur diameter I I.</s>
            <s xml:id="echoid-s11313" xml:space="preserve">, & </s>
            <s xml:id="echoid-s11314" xml:space="preserve">C B ei parallela, & </s>
            <s xml:id="echoid-s11315" xml:space="preserve">ad axim perpendicularis
              <lb/>
            B E. </s>
            <s xml:id="echoid-s11316" xml:space="preserve">Quoniam M H in H E minus eſt quadrato H G; </s>
            <s xml:id="echoid-s11317" xml:space="preserve">addito </s>
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