Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of Notes

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            bebit rationem
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            quàm idem qua-
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              <figure xlink:label="fig-0031-01" xlink:href="fig-0031-01a" number="7">
                <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0031-01"/>
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            dratum E A ad
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            rectangulum A E
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            B, & </s>
            <s xml:id="echoid-s539" xml:space="preserve">quatuor qua-
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            drata E A, ſiue
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            vnicum quadra-
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            tum A D, ad qua-
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            tuor quadrata A
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            H, ſiue ad vnicum
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            quadratum A B
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            minorem habebit
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            rationem quàm
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            quadratum E A
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            ad rectangulum
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            A E B, ſed quadratum A D ad A B eſt vt quadratum C D ad F B, & </s>
            <s xml:id="echoid-s540" xml:space="preserve">qua-
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            dratum E A ad rectangulum A E B eſt vt quadratum E D ad rectangu-
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            lum B E D, cum ſit A E æqualis E D, vel vt recta E D ad rectam E B,
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            vel vt quadratum C D ad quadratum G B, quare quadratum C D
              <note symbol="a" position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">20. pri-
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              mi conic.</note>
            F B minorem habebit rationem quàm idem quadratum C D ad quadra-
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            tum G B, ergo quadratum F B maius eſt quadrato G B, vnde punctum F
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            cadit extra Parabolen, & </s>
            <s xml:id="echoid-s541" xml:space="preserve">ſic de quolibet alio puncto rectæ A C F, præ-
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            ter C. </s>
            <s xml:id="echoid-s542" xml:space="preserve">Quare ducta eſt per datum punctum C recta A C F Parabolen
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            contingens. </s>
            <s xml:id="echoid-s543" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s544" xml:space="preserve"/>
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          <head xml:id="echoid-head30" xml:space="preserve">ALITER.</head>
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            <s xml:id="echoid-s545" xml:space="preserve">POſitis ijſdem. </s>
            <s xml:id="echoid-s546" xml:space="preserve">Dico iterum, vt ſupra.</s>
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          <p>
            <s xml:id="echoid-s548" xml:space="preserve">Sumatur enim poſt D A, A B tertia proportionalis A H, erit ag-
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              <figure xlink:label="fig-0031-02" xlink:href="fig-0031-02a" number="8">
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            gregatum extremarum
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            A D, A H maius quàm
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            duplum mediæ A B,
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            ſiue maius quàm du-
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            plum A E cum E B,
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            ſed eſt A D dupla ad
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            A E, ergo A H erit
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            maior quàm dupla E
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            B, ſed eſt A D dupla
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            D E, ergo A D ad D
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            E minorem habet ra-
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            tionem quàm A H ad
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            E B, & </s>
            <s xml:id="echoid-s549" xml:space="preserve">permutando D
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            A ad A H minorem
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            habet rationem quàm D E ad E B, ſed D A ad A H, eſt vt quadratum
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            D A ad quadratum A B, vel vt quadratum D C ad quadratum B F, & </s>
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              <lb/>
            D E ad E B, eſt vt quadratum D C ad quadratum B G, ergo
              <note symbol="b" position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">ibidem.</note>
            tum D C ad quadratum B F minorem habet rationem quàm idem </s>
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