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-s325" xml:space="preserve">
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            quadratum A D, ad tertiam partem ſui; </s>
            <s xml:id="echoid-s326" xml:space="preserve">& </s>
            <s xml:id="echoid-s327" xml:space="preserve">ad co-
              <lb/>
            num E B F, vtidem quadratum A D, ad tertiam
              <lb/>
            partem quadrati E D; </s>
            <s xml:id="echoid-s328" xml:space="preserve">ſequitur eſſe ad differentiam
              <lb/>
            conorum vt idem quadratum A D, ad tertiam par-
              <lb/>
            tem differentiæ quadratorum A D, D E, nempe
              <lb/>
            ad tertiam partem rectanguli A E C. </s>
            <s xml:id="echoid-s329" xml:space="preserve">Cum verò ex
              <lb/>
            hypotheſi, ſit quadratum A D, ad quadratum E D,
              <lb/>
            vt D G, ad G B; </s>
            <s xml:id="echoid-s330" xml:space="preserve">ergo per conuerſionem rationis,
              <lb/>
            erit quadratum A D, ad rectangulum A E C, vt
              <lb/>
            G D, ad D B. </s>
            <s xml:id="echoid-s331" xml:space="preserve">Et quadratum A D, erit ad ter-
              <lb/>
            tiam partem rectanguli A E C, vt G D, ad ter-
              <lb/>
            tiam partem D B. </s>
            <s xml:id="echoid-s332" xml:space="preserve">Quare etiam cylindrus Q C, erit
              <lb/>
            ad differentiam conorum, & </s>
            <s xml:id="echoid-s333" xml:space="preserve">conſequenter ad diffe-
              <lb/>
            rentiam conoideorum, vt G D, ad tertiam partem
              <lb/>
            D B. </s>
            <s xml:id="echoid-s334" xml:space="preserve">Pariter ratio cylindri Q C, ad conoides E B F,
              <lb/>
            eſt eadem cum ratione quadrati A D, ad dimidium
              <lb/>
            quadrati E D. </s>
            <s xml:id="echoid-s335" xml:space="preserve">Quia cum ſit ad cylindrum T F, vt
              <lb/>
            quadratum A D, ad quadratum E D; </s>
            <s xml:id="echoid-s336" xml:space="preserve">& </s>
            <s xml:id="echoid-s337" xml:space="preserve">cum co-
              <lb/>
            noides E B F, ſit dimidium cylindri T F, vt ſæpe
              <lb/>
            probatum eſt in noſtris lib. </s>
            <s xml:id="echoid-s338" xml:space="preserve">de inſinit. </s>
            <s xml:id="echoid-s339" xml:space="preserve">parab. </s>
            <s xml:id="echoid-s340" xml:space="preserve">Ergo
              <lb/>
            cylindrus Q C, erit ad conoides E B F, vt quadra-
              <lb/>
            tum A D, ad dimidium quadrati E D; </s>
            <s xml:id="echoid-s341" xml:space="preserve">nempe ex
              <lb/>
            hypotheſi, vt D G, ad dimidiam G B. </s>
            <s xml:id="echoid-s342" xml:space="preserve">Ergo colli-
              <lb/>
            gendo conſequentia, erit cylindrus Q C, ad conoi-
              <lb/>
            des, & </s>
            <s xml:id="echoid-s343" xml:space="preserve">ad differentiam conoideorum, nempe ad co-
              <lb/>
            noides hyperbolicum A B C, vt G D, ad dimi-
              <lb/>
            diam G B, cum tertia parte B D. </s>
            <s xml:id="echoid-s344" xml:space="preserve">Quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s345" xml:space="preserve"/>
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