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-s667" xml:space="preserve">
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            ſecetur in P, vt Q P, ſit ad P L, vt dimidia G B, ad
              <lb/>
            tertiam partem B D. </s>
            <s xml:id="echoid-s668" xml:space="preserve">Dico P, eſſe centrum graui-
              <lb/>
            tatis conoidis hyperbolici A B C. </s>
            <s xml:id="echoid-s669" xml:space="preserve">Inſcribantur co-
              <lb/>
            noides parabolicum E B F, & </s>
            <s xml:id="echoid-s670" xml:space="preserve">coni, vt factum eſt ſu-
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            pra. </s>
            <s xml:id="echoid-s671" xml:space="preserve">Quoniam ex ſchol. </s>
            <s xml:id="echoid-s672" xml:space="preserve">2. </s>
            <s xml:id="echoid-s673" xml:space="preserve">propoſit 4. </s>
            <s xml:id="echoid-s674" xml:space="preserve">Q, eſt cen-
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            trum grauitatis tam differentiæ conorum, quam dif-
              <lb/>
            ferentiæ conoideorum, & </s>
            <s xml:id="echoid-s675" xml:space="preserve">vt oſtenditur à multis, & </s>
            <s xml:id="echoid-s676" xml:space="preserve">
              <lb/>
            etiam à nobis lib. </s>
            <s xml:id="echoid-s677" xml:space="preserve">4. </s>
            <s xml:id="echoid-s678" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s679" xml:space="preserve">14, L, eſt centrum
              <lb/>
            grauitatis conoidis parabolici E B F; </s>
            <s xml:id="echoid-s680" xml:space="preserve">ergo ſi L Q, ſic
              <lb/>
            diuidatur in P, vt ſit reciprocè Q P, ad P L, vt co-
              <lb/>
            noides E B F, ad differentiam conoideorum, erit P,
              <lb/>
            centrũ grauitatistotius conoidis hyperbolici A B C.
              <lb/>
            </s>
            <s xml:id="echoid-s681" xml:space="preserve">Sed vt conoides E B F, ad differentiam conoi-
              <lb/>
            deorum, ſic dimidia G B, ad tertiam partem D B,
              <lb/>
            vt ſtatim patebit. </s>
            <s xml:id="echoid-s682" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s683" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s684" xml:space="preserve">Aſſumptum vero patet ex dictis. </s>
            <s xml:id="echoid-s685" xml:space="preserve">Quia facile pa-
              <lb/>
            tebit conoides E B F, eſſe ad differentiam conoi-
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            deorum, ſeù ad differentiam conorum, vt dimidium
              <lb/>
            quadrati D E, ad tertiam partem rectanguli A E C.
              <lb/>
            </s>
            <s xml:id="echoid-s686" xml:space="preserve">Sed cum ex data hypotheſi, ſit diuidendo, & </s>
            <s xml:id="echoid-s687" xml:space="preserve">con-
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            uertendo, quadratum D E, ad rectangulum A E C,
              <lb/>
            vt G B, ad B D. </s>
            <s xml:id="echoid-s688" xml:space="preserve">Erit & </s>
            <s xml:id="echoid-s689" xml:space="preserve">vt dimidium quadrati D E,
              <lb/>
            ad tertiam partem rectanguli A E C, ſic dimidia
              <lb/>
            G B, ad tertiam partem B D.</s>
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        <div xml:id="echoid-div40" type="section" level="1" n="28">
          <head xml:id="echoid-head38" xml:space="preserve">SCHOLIV M.</head>
          <p>
            <s xml:id="echoid-s691" xml:space="preserve">Siquis verò ſcire cupiat, in qua proportione ſece-
              <lb/>
            tur tota B D, à centro grauitatis P, hoc tali </s>
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