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-div174" type="section" level="1" n="111">
          <p>
            <s xml:id="echoid-s3479" xml:space="preserve">
              <pb o="189" file="0201" n="201"/>
            tate minutum eſſe nihil; </s>
            <s xml:id="echoid-s3480" xml:space="preserve">vnde D B, in triangulo non
              <lb/>
            eſt producenda; </s>
            <s xml:id="echoid-s3481" xml:space="preserve">ſed ſupponendo A B C, eſſe trian-
              <lb/>
            gulum, B D, eſt biſlecanda, & </s>
            <s xml:id="echoid-s3482" xml:space="preserve">triangulum G D H,
              <lb/>
            eſt maximum. </s>
            <s xml:id="echoid-s3483" xml:space="preserve">Quod ſic eſſe, probatum eſt ſupra
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">51.</s>
            <s xml:id="echoid-s3485" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div175" type="section" level="1" n="112">
          <head xml:id="echoid-head124" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s3486" xml:space="preserve">Triangulum ergo G D H, maximum inſcriptibi-
              <lb/>
            lium intra parabolam A B C, ſic diuidit D B, in F,
              <lb/>
            vt B F, ſit ad F D, vt vnitas adnumerum parabolæ.
              <lb/>
            </s>
            <s xml:id="echoid-s3487" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3489" xml:space="preserve">in triangulo vt 1, ad 1. </s>
            <s xml:id="echoid-s3490" xml:space="preserve">In parabola quadrati-
              <lb/>
            ca vt 1, ad 2. </s>
            <s xml:id="echoid-s3491" xml:space="preserve">In cubica vt 1, ad 3. </s>
            <s xml:id="echoid-s3492" xml:space="preserve">Et ſic in infini-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s3493" xml:space="preserve">In triangulo enim, patet ex dictis. </s>
            <s xml:id="echoid-s3494" xml:space="preserve">In alijs ſic
              <lb/>
            patebit. </s>
            <s xml:id="echoid-s3495" xml:space="preserve">Quum etenim ſit E B, ad B F, vt numerus
              <lb/>
            parabolæ vnitate minutus, ad vnitatem; </s>
            <s xml:id="echoid-s3496" xml:space="preserve">erit com-
              <lb/>
            ponendo, E F, ad F B, vt numerus parabolæ ad
              <lb/>
            vnitatem. </s>
            <s xml:id="echoid-s3497" xml:space="preserve">Sed F D, eſt æqualis E F. </s>
            <s xml:id="echoid-s3498" xml:space="preserve">Quare patet
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s3499" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div176" type="section" level="1" n="113">
          <head xml:id="echoid-head125" xml:space="preserve">PROPOSITIOLV.</head>
          <p style="it">
            <s xml:id="echoid-s3500" xml:space="preserve">Maximum triangulum inſcriptibile in figura conſtante ex
              <lb/>
            duabus quibuſcunque ſemiparabolis ſic diſpoſitis, vt ſe-
              <lb/>
            mibaſis euadat diameter, eſt æquale maximo inſcripto in
              <lb/>
            parabola.</s>
            <s xml:id="echoid-s3501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3502" xml:space="preserve">MEnte intelligamus ſemiparabolam A B D, du-
              <lb/>
            plicari ad partes A D. </s>
            <s xml:id="echoid-s3503" xml:space="preserve">Dico maximum </s>
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