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-s565" xml:space="preserve">
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            ptus cylindrus O C. </s>
            <s xml:id="echoid-s566" xml:space="preserve">Dico hunc eſſe ad illud vt E D,
              <lb/>
            ad dimidiam E B, cum tertia parte B D. </s>
            <s xml:id="echoid-s567" xml:space="preserve">Sit F,
              <lb/>
            centrum hyperbolæ genitricis, & </s>
            <s xml:id="echoid-s568" xml:space="preserve">F G, F H, ſint
              <lb/>
            eius aſymptoti, & </s>
            <s xml:id="echoid-s569" xml:space="preserve">per B, ſit ducta I B, parallela
              <lb/>
            G D; </s>
            <s xml:id="echoid-s570" xml:space="preserve">intelligamuſque ex reuolutione trapezij
              <lb/>
            G I B D, circa B D, genitum eſſe fruſtum conicum
              <lb/>
            G I K H, cui ſit circumſcriptus cylindrus N H, & </s>
            <s xml:id="echoid-s571" xml:space="preserve">
              <lb/>
            inſcriptus I M. </s>
            <s xml:id="echoid-s572" xml:space="preserve">Quoniam linea G H, diuiſa eſt ſe-
              <lb/>
            cundum conditiones propoſit. </s>
            <s xml:id="echoid-s573" xml:space="preserve">9. </s>
            <s xml:id="echoid-s574" xml:space="preserve">nam ex propoſit.
              <lb/>
            </s>
            <s xml:id="echoid-s575" xml:space="preserve">10. </s>
            <s xml:id="echoid-s576" xml:space="preserve">2. </s>
            <s xml:id="echoid-s577" xml:space="preserve">conic. </s>
            <s xml:id="echoid-s578" xml:space="preserve">rectangulum G A H, eſt æquale qua-
              <lb/>
            drato I B, ſeù quadrato L D. </s>
            <s xml:id="echoid-s579" xml:space="preserve">Ergo rectangulum
              <lb/>
            G L H, erit æquale quadrato A D. </s>
            <s xml:id="echoid-s580" xml:space="preserve">Ergo etiam ar-
              <lb/>
            milla circularis G L H, quæ eſt baſis tubi cylindrici
              <lb/>
            N L P, erit æqualis circulo A C, baſi cylindri O C. </s>
            <s xml:id="echoid-s581" xml:space="preserve">
              <lb/>
            Cum ergo ex propoſit. </s>
            <s xml:id="echoid-s582" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s583" xml:space="preserve">exceſſus fruſti coni
              <lb/>
            G I k H, ſupra cylindrum I M, ſit æqualis conoidi
              <lb/>
            hyperbolico A B C. </s>
            <s xml:id="echoid-s584" xml:space="preserve">Ergo tubus cylindricus N L P,
              <lb/>
            ad illum exceſſum, & </s>
            <s xml:id="echoid-s585" xml:space="preserve">cylindrus O C, ad conoides
              <lb/>
            erunt in eadem ratione. </s>
            <s xml:id="echoid-s586" xml:space="preserve">At ex propoſit. </s>
            <s xml:id="echoid-s587" xml:space="preserve">8. </s>
            <s xml:id="echoid-s588" xml:space="preserve">tubus eſt
              <lb/>
            ad exceſſum vt E D, ad F B, cum tertia parte D B. </s>
            <s xml:id="echoid-s589" xml:space="preserve">
              <lb/>
            Quare patet propoſitum.</s>
            <s xml:id="echoid-s590" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s591" xml:space="preserve">Oſten ſa ergo proportione cylindri circumſcripti
              <lb/>
            conoidi hyperbolico ad ipſum, facile docebimus in
              <lb/>
            qua linea diametro parallela ſit centrum grauitatis
              <lb/>
            ſemihyperbolæ. </s>
            <s xml:id="echoid-s592" xml:space="preserve">Sit ergo.</s>
            <s xml:id="echoid-s593" xml:space="preserve"/>
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