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-div114" type="section" level="1" n="72">
          <p>
            <s xml:id="echoid-s2392" xml:space="preserve">
              <pb o="133" file="0145" n="145"/>
            ta V X, eſt 25; </s>
            <s xml:id="echoid-s2393" xml:space="preserve">V 2, 14; </s>
            <s xml:id="echoid-s2394" xml:space="preserve">& </s>
            <s xml:id="echoid-s2395" xml:space="preserve">2 X, 11; </s>
            <s xml:id="echoid-s2396" xml:space="preserve">talium V ℟,
              <lb/>
            erit 12, cum dimidia; </s>
            <s xml:id="echoid-s2397" xml:space="preserve">& </s>
            <s xml:id="echoid-s2398" xml:space="preserve">℟ 2, 1, cum dimidia. </s>
            <s xml:id="echoid-s2399" xml:space="preserve">Cum
              <lb/>
            ergo ex ſecunda parte propoſit. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">15, lib. </s>
            <s xml:id="echoid-s2401" xml:space="preserve">ſecun. </s>
            <s xml:id="echoid-s2402" xml:space="preserve">ſit di-
              <lb/>
            uidendo conicus B C H, ad annulum vt 2, ad 10,
              <lb/>
            ſeù vt 1, ad 5; </s>
            <s xml:id="echoid-s2403" xml:space="preserve">& </s>
            <s xml:id="echoid-s2404" xml:space="preserve">ſi fiat reciprocè vt conicus,
              <lb/>
            ad annulum, nempe vt 1, ad 5, ſic 2 ℟, ad ℟ +, ſit
              <lb/>
            +, centrum grauitatis conici; </s>
            <s xml:id="echoid-s2405" xml:space="preserve">& </s>
            <s xml:id="echoid-s2406" xml:space="preserve">cum ſit vt 1, ad 5,
              <lb/>
            ſic vnum cum dimidio ad 7, cum dimidio. </s>
            <s xml:id="echoid-s2407" xml:space="preserve">Ergo
              <lb/>
            + ℟, erit 7, cum dimidio. </s>
            <s xml:id="echoid-s2408" xml:space="preserve">Quare reliqua V +, erit
              <lb/>
            5, & </s>
            <s xml:id="echoid-s2409" xml:space="preserve">+ X, 20. </s>
            <s xml:id="echoid-s2410" xml:space="preserve">Ergo V X, ſic ſecatur in +, & </s>
            <s xml:id="echoid-s2411" xml:space="preserve">F C,
              <lb/>
            v. </s>
            <s xml:id="echoid-s2412" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">in N, à centro grauitatis conici B C H, vt
              <lb/>
            C N, ſit ad N F, vt 20, ad 5, ſeù vt 4. </s>
            <s xml:id="echoid-s2414" xml:space="preserve">ad 1.</s>
            <s xml:id="echoid-s2415" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div116" type="section" level="1" n="73">
          <head xml:id="echoid-head85" xml:space="preserve">PROPOSITIO XXXIV.</head>
          <p style="it">
            <s xml:id="echoid-s2416" xml:space="preserve">Annuli stricti orti ex reuolutione ſemihyperbolæ, vt in an-
              <lb/>
            teced. </s>
            <s xml:id="echoid-s2417" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2418" xml:space="preserve">ſuppoſita hyperbolæ quadratura, poſſumus
              <lb/>
            centrum grauitatis aſſignare.</s>
            <s xml:id="echoid-s2419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2420" xml:space="preserve">SEd ſupponamus D B C, eſſe ſemihyperbolam,
              <lb/>
            &</s>
            <s xml:id="echoid-s2421" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2422" xml:space="preserve">Dico etiam nos poſſe aſſignare centrum
              <lb/>
            grauitatis annuli ſtricti ex ſemihyperbola D B C,
              <lb/>
            circa F C. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">Reuoluta enim hyperbola A B C, tota
              <lb/>
            circa F C, vt fiat annulus A B C H G, cum hic ſit
              <lb/>
            æqualis quatuor ſolidis diſpoſicis vt in ſecunda figu-
              <lb/>
            ra, vt ſæpe dictum eſt; </s>
            <s xml:id="echoid-s2424" xml:space="preserve">ergo ex propoſit. </s>
            <s xml:id="echoid-s2425" xml:space="preserve">22. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">in qua
              <lb/>
            aſſignatur centrum grauitatis in B D, hyperbolæ
              <lb/>
            A B C, habebimus etiam centrum grauitatis qua-
              <lb/>
            tuor illorum ſolidorum ſimul diſpoſitorum. </s>
            <s xml:id="echoid-s2427" xml:space="preserve">Sit </s>
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