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-s1182" xml:space="preserve">QVoniam enim probatum eſt in propoſit. </s>
            <s xml:id="echoid-s1183" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">ſo-
              <lb/>
            lidum C B k L, æquari cylindro B S, & </s>
            <s xml:id="echoid-s1185" xml:space="preserve">
              <lb/>
            cono G E M; </s>
            <s xml:id="echoid-s1186" xml:space="preserve">ergo cylindrus A L, ad hæc ſoli-
              <lb/>
            da habebit eandem rationem. </s>
            <s xml:id="echoid-s1187" xml:space="preserve">At cylindrus A L,
              <lb/>
            ad cylindrum B S, & </s>
            <s xml:id="echoid-s1188" xml:space="preserve">ad conum G E M, eſt vt qua-
              <lb/>
            dratum E A, ad quadratum E B, cum tertia parte
              <lb/>
            rectanguli K A B. </s>
            <s xml:id="echoid-s1189" xml:space="preserve">Quare &</s>
            <s xml:id="echoid-s1190" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1191" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1192" xml:space="preserve">Aſſumptum patebit ſic. </s>
            <s xml:id="echoid-s1193" xml:space="preserve">Cylindrus A L, ad cy-
              <lb/>
            lindrum B S, eſt vt quadratum A F, ad quadratum
              <lb/>
            E B. </s>
            <s xml:id="echoid-s1194" xml:space="preserve">Pariter idem cylindrus A L, ad conum GEM,
              <lb/>
            eſt vt quadratum C F, ſeù vt idem quadratum A E,
              <lb/>
            ad tertiam partem quadrati G F. </s>
            <s xml:id="echoid-s1195" xml:space="preserve">Ergo colligendo
              <lb/>
            ambo conſequentia, erit cylindrus A L, ad cylin-
              <lb/>
            drum B S, cum cono G E M, nempe ad ſolidum
              <lb/>
            C B k L, vt quadratum A E, ad quadratum E B,
              <lb/>
            cum tertia parte quadrati F G. </s>
            <s xml:id="echoid-s1196" xml:space="preserve">At tertia pars qua-
              <lb/>
            drati F G, eſt æqualis tertiæ parti rectanguli k A B.
              <lb/>
            </s>
            <s xml:id="echoid-s1197" xml:space="preserve">Nam quadratum E A, diuiditur in quadratum E B,
              <lb/>
            & </s>
            <s xml:id="echoid-s1198" xml:space="preserve">in rectangulum k A B: </s>
            <s xml:id="echoid-s1199" xml:space="preserve">pariter quadratum idem
              <lb/>
            E A, ſeù F C, diuiditur in quadratum F G, & </s>
            <s xml:id="echoid-s1200" xml:space="preserve">in
              <lb/>
            rectangulum C G L, ſeù M C G. </s>
            <s xml:id="echoid-s1201" xml:space="preserve">Ergo quadra-
              <lb/>
            tum E B, cum rectangulo K A B, erit æquale qua-
              <lb/>
            drato F G, & </s>
            <s xml:id="echoid-s1202" xml:space="preserve">rectangulo M C G. </s>
            <s xml:id="echoid-s1203" xml:space="preserve">Sed ex ſec. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">co-
              <lb/>
            nic. </s>
            <s xml:id="echoid-s1205" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">rectangulum M C G, eſt æquale
              <lb/>
            quadrato B E. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">Quare reliquum rectangulum k A B,
              <lb/>
            erit æquale reliquo quadrato F G. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">Quare etiam il-
              <lb/>
            lorum tertiæ partes erunt æquales. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">Ergo cylindrus
              <lb/>
            A L, erit ad ſolidum C B k L, vt quadratum E </s>
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