Angeli, Stefano degli, Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna
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          <head xml:id="echoid-head121" xml:space="preserve">PROPOSITIO LIII.</head>
          <p style="it">
            <s xml:id="echoid-s3434" xml:space="preserve">Datam A D, taliter producere in B, vt B D, ſit ad
              <lb/>
            exceſſum D A, ſupra dimidiam A B, in
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            data proportione.</s>
            <s xml:id="echoid-s3435" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3436" xml:space="preserve">DAta ratio ſit, quam habet AD, ad H, & </s>
            <s xml:id="echoid-s3437" xml:space="preserve">ſic ſece-
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            tur A D, in E, vt ſit A E, ad E D, vt H, ad dimi-
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            diam A D, & </s>
            <s xml:id="echoid-s3438" xml:space="preserve">ipſi D E, fiat ęqualis D B, Ergo ſi A B,
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              <figure xlink:label="fig-0198-01" xlink:href="fig-0198-01a" number="82">
                <image file="0198-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0198-01"/>
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            diuidatur bifariam in C, punctum C, cadet inter
              <lb/>
            A, D. </s>
            <s xml:id="echoid-s3439" xml:space="preserve">Sit ergo A B, diuiſa bifariam in C. </s>
            <s xml:id="echoid-s3440" xml:space="preserve">Quo-
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            niam A E, eſt æqualis A B, minus E B, ergo etiam
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            dimidia A E, erit æqualis dimidiæ A B, minus dimi-
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            dia E B. </s>
            <s xml:id="echoid-s3441" xml:space="preserve">Sed C B, eſt dimidia A B, & </s>
            <s xml:id="echoid-s3442" xml:space="preserve">B D, eſt
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            dimidia E B; </s>
            <s xml:id="echoid-s3443" xml:space="preserve">ergo dimidia A E, erit æqualis C B,
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            minus D B; </s>
            <s xml:id="echoid-s3444" xml:space="preserve">nempe C D. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">Tunc, quoniam factum
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            fuit vt H, ad dimidiam A D, ſic A E, ad E D;
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            </s>
            <s xml:id="echoid-s3446" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3447" xml:space="preserve">ad conſequentium dupla. </s>
            <s xml:id="echoid-s3448" xml:space="preserve">Ergo vt H, ad
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            A D, ſic A E, ad E B. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">Et conuertendo, vt A D,
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            ad H, ſic B E, ad E A. </s>
            <s xml:id="echoid-s3450" xml:space="preserve">Sed vt B E, ad E A, ita
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            B D, dimidia B E, ad dimidiam A E, nempe ad
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            C D, ei æqualem. </s>
            <s xml:id="echoid-s3451" xml:space="preserve">Ergo vt A D, ad H, ſic B </s>
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