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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            <s xml:id="echoid-s3375" xml:space="preserve">
              <pb o="183" file="0195" n="195"/>
            eſſe H B, vt pars vltra B, ſit ad B H, vt numerus
              <lb/>
            parabolæ vnitate minutus, nempe vt nihil, ad vnita-
              <lb/>
            tem. </s>
            <s xml:id="echoid-s3376" xml:space="preserve">Ergo H B, non eſt producenda, ſed à puncto
              <lb/>
            B, ad C, ducenda eſt linea, quæ vtique quodam-
              <lb/>
            modo poteſt dici tangere triangulum, quia ipſum
              <lb/>
            non ſecat.</s>
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        <div xml:id="echoid-div166" type="section" level="1" n="105">
          <head xml:id="echoid-head117" xml:space="preserve">PROPOSITIO LI.</head>
          <p style="it">
            <s xml:id="echoid-s3378" xml:space="preserve">Maximum triangulum inſcriptum in quolibet triangulo, eſt
              <lb/>
            cutus baſis bifariam diuidit diametrum
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            circum ſcripti.</s>
            <s xml:id="echoid-s3379" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3380" xml:space="preserve">ESto triangulum A B C, cuius diameter B D,
              <lb/>
            quæ ſecetur in F, bifariam à baſe E O, trian-
              <lb/>
            guli E D O. </s>
            <s xml:id="echoid-s3381" xml:space="preserve">Dico triangulum E D O, eſſe maxi-
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            mum omnium inſcriptibilium in triangulo A B C.
              <lb/>
            </s>
            <s xml:id="echoid-s3382" xml:space="preserve">Quoniam enim triangulum A B C, ad triangulum
              <lb/>
            E D O, habet rationem compoſitam ex ratione
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            A C, ad E O (nempe ex ratione D B, ad B F) & </s>
            <s xml:id="echoid-s3383" xml:space="preserve">
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            ex ratione B D, ad D F; </s>
            <s xml:id="echoid-s3384" xml:space="preserve">& </s>
            <s xml:id="echoid-s3385" xml:space="preserve">hæ duæ rationes com-
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            ponunt rationem quadrati B D, ad rectangulum
              <lb/>
            B F D. </s>
            <s xml:id="echoid-s3386" xml:space="preserve">Ergo triangulum A B C, erit ad E D O,
              <lb/>
            vt quadratum D B, ad rectangulum B F D. </s>
            <s xml:id="echoid-s3387" xml:space="preserve">Sed
              <lb/>
            rectangulum B F D, eſt maximum omnium rectan-
              <lb/>
            gulorum factibilium ex partibus B D, in puncto di-
              <lb/>
            uifæ. </s>
            <s xml:id="echoid-s3388" xml:space="preserve">Ergo etiam triangulum E D O, erit ma-
              <lb/>
            ximum omnium inſcriptibilium intra A B C. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">Quod
              <lb/>
            &</s>
            <s xml:id="echoid-s3390" xml:space="preserve">c.</s>
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