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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          <p>
            <s xml:id="echoid-s2175" xml:space="preserve">
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            analogum cum figura A B C, conſtante ex duabus
              <lb/>
            ſemiparabolis. </s>
            <s xml:id="echoid-s2176" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2177" xml:space="preserve">quatuor ſolida ſecundæ fi-
              <lb/>
            guræ ſimul erunt proportionaliter analoga cum fi-
              <lb/>
            gura A B C. </s>
            <s xml:id="echoid-s2178" xml:space="preserve">Sed ex ſchol. </s>
            <s xml:id="echoid-s2179" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2180" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2182" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">cen-
              <lb/>
            trum grauitatis figuræ A B C, ſic diuidit B D, vt
              <lb/>
            pars terminata ad B, ſit ad partem terminatam ad
              <lb/>
            D, vt numerus parabolæ ternario auctus ad nume-
              <lb/>
            rum parabolæ vnitate auctum. </s>
            <s xml:id="echoid-s2185" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2186" xml:space="preserve">centrum gra-
              <lb/>
            uitatis quatuor ſolidorum ſecundæ figuræ ſimul ſic
              <lb/>
            ſecabit V X, vt pars terminata ad V, ſit ad partem
              <lb/>
            terminatam ad X, vt numerus parabolæ ternario
              <lb/>
            auctus ad numerum parabolæ vnitate auctum. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">Sup-
              <lb/>
            ponatur à perito geometra, ſic diuiſa in ℟. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Item ex
              <lb/>
            propoſit. </s>
            <s xml:id="echoid-s2189" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2191" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">de infin. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">parab. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">conſtat centrum
              <lb/>
            grauitatis ſolidi ex ſemiparabola D B C, in prima
              <lb/>
            figura circa C F, ſic diuidere F C, vt pars termi-
              <lb/>
            nata ad F, ſit ad partem terminatam ad C, vt
              <lb/>
            duplus numerus parabolæ ternario auctus, ad du-
              <lb/>
            plum numerum vnitate auctum. </s>
            <s xml:id="echoid-s2195" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2196" xml:space="preserve">centrum
              <lb/>
            grauitatis ſolidorum extremorum in ſecunda figura,
              <lb/>
            ſic ſecabunt lineas circa quas ſemiparabolæ intelli-
              <lb/>
            guntur reuolutæ. </s>
            <s xml:id="echoid-s2197" xml:space="preserve">Cum ergo talia ſolida ſint ex inſti-
              <lb/>
            tuto ſic diſpoſita, vt commune amborum centrum
              <lb/>
            grauitatis cadat in V X: </s>
            <s xml:id="echoid-s2198" xml:space="preserve">ſi ergo V X, ſic diuida-
              <lb/>
            tur in +, vt V +, ſit ad + X, vt duplus nume-
              <lb/>
            rus parabolæ ternario auctus, ad duplum numerum
              <lb/>
            parabolæ vnitate auctum; </s>
            <s xml:id="echoid-s2199" xml:space="preserve">+ erit centrum grauita-
              <lb/>
            tis illorum ſolidorum ſimul. </s>
            <s xml:id="echoid-s2200" xml:space="preserve">Cum ergo in VX, ſit
              <lb/>
            centrum grauitatis tam quatuor ſolidorum </s>
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