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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            ad D C, exceſſum D A, ſupra A C, dimidiam A B.
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            <s xml:id="echoid-s3452" xml:space="preserve">Quod erat faciendum.</s>
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        <div xml:id="echoid-div172" type="section" level="1" n="110">
          <head xml:id="echoid-head122" xml:space="preserve">PROPOSITIO LIV.</head>
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            <s xml:id="echoid-s3454" xml:space="preserve">Sidiameter cuiuslibet infinitarum parabolarum ſic produca
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            tur vt pars exterior producta, ſit ad exceſſum diametrì
              <lb/>
            ſupra dimidiam compoſitæ ex diametro, & </s>
            <s xml:id="echoid-s3455" xml:space="preserve">ex producta
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            vt numerus parabolæ vnitate minor, ad vnitatem.
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            <s xml:id="echoid-s3456" xml:space="preserve">Triangulum inſcripium in parabold, cums baſis bißecet
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            illam compoſitam, erit omnium maximum in ipſa inſcri-
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            ptibilium.</s>
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          </p>
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            <s xml:id="echoid-s3458" xml:space="preserve">DB, diameter parabolæ cuiuſcunque A B C, ſic
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            producatur in E, vt E B, ſit ad B F, exceſſum
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            B D, ſupra D F, medietatem D E, vt numerus pa-
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            rabolæ vnitate minutus, ad vnitatem, & </s>
            <s xml:id="echoid-s3459" xml:space="preserve">fiat triangu-
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            lum G D H. </s>
            <s xml:id="echoid-s3460" xml:space="preserve">Dico hoc eſſe maximum omnium in-
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            ſcriptibilium in A B C. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">Ducantur E G K, E H L.
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            </s>
            <s xml:id="echoid-s3462" xml:space="preserve">Ergo ex propoſit. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">50. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">erunt tangentes parabolam, & </s>
            <s xml:id="echoid-s3465" xml:space="preserve">
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            triangulum K E L, erit parabolæ circumſcriptum. </s>
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            Si ergo triangulum G D H, non eſt maximum para-
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            bolæ inſcrip um, ſit hoc triangulum, cuius baſis
              <lb/>
            O P, infra, velſupra G H, quæ producatur vſque
              <lb/>
            ad triangulum in M, & </s>
            <s xml:id="echoid-s3467" xml:space="preserve">N; </s>
            <s xml:id="echoid-s3468" xml:space="preserve">& </s>
            <s xml:id="echoid-s3469" xml:space="preserve">pariter intelligatur
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            triangulum M D N, cuius baſis M N. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">Cum D E,
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            ſecta ſit bifariam in F; </s>
            <s xml:id="echoid-s3471" xml:space="preserve">ergo triangulum G D H, erit
              <lb/>
            maximum inſcriptibilium intra triangulum K E L. </s>
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            Ergo erit maius triangulo cuius baſis M N. </s>
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