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-div105" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s2211" xml:space="preserve">
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            vt numerus parabolæ ad numerum parabolæ vnitate
              <lb/>
            auctum, ſic +℟, ad ℟ 2. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">Erit 2, centrum gra-
              <lb/>
            uitatis duorum ſolidorum mediorum ſimul. </s>
            <s xml:id="echoid-s2213" xml:space="preserve">Sed cum
              <lb/>
            hæc fuerint ſic diſpoſita vt centrum grauitatis vniuſ-
              <lb/>
            cuiuſque ipſorum ſic ſecet illorumaxim; </s>
            <s xml:id="echoid-s2214" xml:space="preserve">ſi ergo axis
              <lb/>
            B D, ſemifufi in prima figura, ſic ſecetur in T, vt
              <lb/>
            B T, ſit ad T D, vt V 2, ad 2 +: </s>
            <s xml:id="echoid-s2215" xml:space="preserve">erit T, cen-
              <lb/>
            trum grauitatis ſemifuſi A B C, orti ex reuolutione
              <lb/>
            ſemiparabolæ A B D, circa baſim B D. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Quod
              <lb/>
            erat reperiendum.</s>
            <s xml:id="echoid-s2217" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div107" type="section" level="1" n="68">
          <head xml:id="echoid-head80" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s2218" xml:space="preserve">Inuentio huius centri grauitatis non continet ali-
              <lb/>
            quam ſeriem ordinatam. </s>
            <s xml:id="echoid-s2219" xml:space="preserve">Verum tamen eſt, quod
              <lb/>
            quilibet numero potert exprimere rationem in qua
              <lb/>
            ſecetur B D, à centrograuitatis tais ſemifuſi, ſi or-
              <lb/>
            dinem obſeruauerit, quem nostenemus in inuentio-
              <lb/>
            ne talis centri in ſemifuſo parabolico quadratico. </s>
            <s xml:id="echoid-s2220" xml:space="preserve">In
              <lb/>
            primo enim ſemifuſo, cum ſit conus, iam patet B D,
              <lb/>
            ſic ſecari vt pars ad B, ſit ad partem ad D, vt 3.
              <lb/>
            </s>
            <s xml:id="echoid-s2221" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s2222" xml:space="preserve">In quadratico verò, conſequenter ad ſupra
              <lb/>
            dicta, ſi B D, ſic ſecetur in S, vt B S, ſit ad
              <lb/>
            S D, vt numerus parabolæ ternario auctus ad nu-
              <lb/>
            merum parabolæ vnitate auctum; </s>
            <s xml:id="echoid-s2223" xml:space="preserve">quarum B D, erit
              <lb/>
            8, talium B S, erit 5, & </s>
            <s xml:id="echoid-s2224" xml:space="preserve">quarum B D, erit 12,
              <lb/>
            talium B S, erit 7, cum dimidia. </s>
            <s xml:id="echoid-s2225" xml:space="preserve">Item ſi ſecetur
              <lb/>
            in I, vt B I, ſit ad I D, vt duplus numerus ter-
              <lb/>
            nario auctus, ad duplum numerum vnitate </s>
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