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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            dratorum duorum laterum figuræ eius; </s>
            <s xml:id="echoid-s12406" xml:space="preserve">igitur quadratum A C ad diffe-
              <lb/>
            rentiam quadratorum duorum laterum figuræ I L minorem proportionem
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            habet, in prima ellipſi, & </s>
            <s xml:id="echoid-s12407" xml:space="preserve">maiorem in reliquis, quam ad differentiam
              <lb/>
            quadratorum duorum laterum figuræ A C; </s>
            <s xml:id="echoid-s12408" xml:space="preserve">ergo differentia quadratorum
              <lb/>
            duorum laterum figuræ A C minor eſt in prima ellipſi, & </s>
            <s xml:id="echoid-s12409" xml:space="preserve">maior in cæ-
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            teris, quàm differentia quadratorum duorum laterum figuræ I L. </s>
            <s xml:id="echoid-s12410" xml:space="preserve">Præte-
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            rea M H ad H E minorem proportionem, aut maiorem habet, quàm M
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            G ad G E: </s>
            <s xml:id="echoid-s12411" xml:space="preserve">& </s>
            <s xml:id="echoid-s12412" xml:space="preserve">ponamus in ellipſi Y D æqualem D M, oſtendeturquè
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              <figure xlink:label="fig-0398-01" xlink:href="fig-0398-01a" number="469">
                <image file="0398-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0398-01"/>
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            quod M H in H A minus ſit in prima ellipſi, & </s>
            <s xml:id="echoid-s12413" xml:space="preserve">maior in cæteris, quàm
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            duarum M G, M H ſumma in earum differentiam M Y: </s>
            <s xml:id="echoid-s12414" xml:space="preserve">& </s>
            <s xml:id="echoid-s12415" xml:space="preserve">oſtendetur
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            quemadmodum dictum eſt, quod differentia quadratorum duorum late-
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            rum figuræ I L maior eſt, quàm differentia quadratorum duorum late-
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            rum figuræ P Q.</s>
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            <s xml:id="echoid-s12417" xml:space="preserve">Deinde in hyperbola ponamus I K erectum ipſius I L, erit differentia
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            quadratorum duarum I L, I K (quæ eſt æqualis K L in ſummam L I, I
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            K) maior illa, quàm I L in L K, quod eſt æquale differentiæ quadrari
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            I L, & </s>
            <s xml:id="echoid-s12418" xml:space="preserve">eius figuræ, nempe differentiæ quadrati A C, & </s>
            <s xml:id="echoid-s12419" xml:space="preserve">eius figuræ
              <lb/>
            (29. </s>
            <s xml:id="echoid-s12420" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12421" xml:space="preserve">& </s>
            <s xml:id="echoid-s12422" xml:space="preserve">non eſt maior in prima, quàm duplum, & </s>
            <s xml:id="echoid-s12423" xml:space="preserve">in ſecunda ma-
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            ior duplo, & </s>
            <s xml:id="echoid-s12424" xml:space="preserve">hoc eſt propoſitum.</s>
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Impressum