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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        <div xml:id="echoid-div185" type="section" level="1" n="121">
          <pb o="197" file="0209" n="209"/>
          <p>
            <s xml:id="echoid-s3635" xml:space="preserve">Sed notetur, in ſemifuſis, B D, ſecari in F, ali-
              <lb/>
            qua continuata ſerie, nempe ſic vt B F, ſit ad F D,
              <lb/>
            vt vnitas ad duplum numerum fuſi. </s>
            <s xml:id="echoid-s3636" xml:space="preserve">Nempe in pri-
              <lb/>
            mo vt 1, ad 2. </s>
            <s xml:id="echoid-s3637" xml:space="preserve">In ſecundo vt 1, ad 4. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">In tertio vt 1,
              <lb/>
            ad 6. </s>
            <s xml:id="echoid-s3639" xml:space="preserve">& </s>
            <s xml:id="echoid-s3640" xml:space="preserve">ſic in infinitum. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">Quod enim in primo ſe-
              <lb/>
            mifuſo, nempe in cono ſit vt 1, ad 2, patet ex dictis.
              <lb/>
            </s>
            <s xml:id="echoid-s3642" xml:space="preserve">In alijs ſic patebit. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">Nam cum ſit E F, ad F B, com-
              <lb/>
            ponendo, vt numerus parabolæ ad vnitatem; </s>
            <s xml:id="echoid-s3644" xml:space="preserve">erit
              <lb/>
            conuertendo F B, ad F E, vt vnitas ad numerum
              <lb/>
            parabolæ. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">Et ad D F, duplam F E, vt vnitas ad
              <lb/>
            duplum numerum parabolæ, ſeù ſemifuſi.</s>
            <s xml:id="echoid-s3646" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div186" type="section" level="1" n="122">
          <head xml:id="echoid-head134" xml:space="preserve">PROPOSITIO LXII.</head>
          <p style="it">
            <s xml:id="echoid-s3647" xml:space="preserve">Minimum trianguium circumſcriptum cuilibet infinitarum
              <lb/>
            p@rabolarum, eſt illud cuius latera tangunt baſim maximi
              <lb/>
            triangu
              <gap/>
            in parabola in ſcripti.</s>
            <s xml:id="echoid-s3648" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3649" xml:space="preserve">ESto ſemiparabola quælibet A B C, cuius dia-
              <lb/>
            meter B C, & </s>
            <s xml:id="echoid-s3650" xml:space="preserve">in ipſa ſit in ſcriptum maximum
              <lb/>
            trianguium E C F (quod enim dicetur de dimidia
              <lb/>
            intelligetur etiam de tota) ſitque ei circumſcriptum
              <lb/>
            triangulum G E I C. </s>
            <s xml:id="echoid-s3651" xml:space="preserve">Dico hoc eſſe minimum om-
              <lb/>
            nium circumſcriptibilium ſemiparabolæ. </s>
            <s xml:id="echoid-s3652" xml:space="preserve">Si non,
              <lb/>
            ſit minimum H O k C, & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">per punctum E, duca-
              <lb/>
            tur L E M, parallela K H. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Patet manifeſtè trian-
              <lb/>
            gulum L M C, minus eſſe triangulo k O H C, cum
              <lb/>
            L M, ſecet, k H, vero tangat parabolam. </s>
            <s xml:id="echoid-s3655" xml:space="preserve">Quoniam
              <lb/>
            autem ex ſuperioribus, triangulum E F C, eſt </s>
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