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-div57" type="section" level="1" n="39">
          <p>
            <s xml:id="echoid-s1054" xml:space="preserve">
              <pb o="57" file="0069" n="69"/>
            lum B E K, v.</s>
            <s xml:id="echoid-s1055" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1056" xml:space="preserve">illam, quæ oritur ex rotatione tri-
              <lb/>
            linei B O Q ci ca E F; </s>
            <s xml:id="echoid-s1057" xml:space="preserve">agnoſcemus eius centrum
              <lb/>
            grauitatis ſecare E I, in eadem ratione. </s>
            <s xml:id="echoid-s1058" xml:space="preserve">Quia ta-
              <lb/>
            lis pars eſt proportionaliter an aloga cum cono P E R.
              <lb/>
            </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Cum vero etiam pars annuli orta ex rotatione trape-
              <lb/>
            zij mixti C O Q D, ſit probata proportionaliter
              <lb/>
            analoga ſegmento conico G P R M, & </s>
            <s xml:id="echoid-s1060" xml:space="preserve">cum talis
              <lb/>
            ſegmenti conici ſit in libro cit. </s>
            <s xml:id="echoid-s1061" xml:space="preserve">pluribus modis inuen-
              <lb/>
            tum centrum grauitatis; </s>
            <s xml:id="echoid-s1062" xml:space="preserve">ex dictis ibidem reperie nus
              <lb/>
            in quo puncto I F, ſit centrum grauitatis prædicti
              <lb/>
            ſegmenti annuli.</s>
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        <div xml:id="echoid-div59" type="section" level="1" n="40">
          <head xml:id="echoid-head51" xml:space="preserve">SCHOLIVM III.</head>
          <p>
            <s xml:id="echoid-s1064" xml:space="preserve">Sed paradoxum Galilei, de quo locuti ſumus ſu-
              <lb/>
            pra ſchol. </s>
            <s xml:id="echoid-s1065" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1066" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1067" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1068" xml:space="preserve">poſlumus etiam deducere
              <lb/>
            ex præſenti propoſitione. </s>
            <s xml:id="echoid-s1069" xml:space="preserve">Nam etiam ex hac facto
              <lb/>
            concinno diſcurſu, tandem concludemus, circumfe-
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            rentiam B E k, extremitatem annuli, æqualem fore
              <lb/>
            E, vertici coni.</s>
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        <div xml:id="echoid-div60" type="section" level="1" n="41">
          <head xml:id="echoid-head52" xml:space="preserve">PROPOSITIO XIX.</head>
          <p style="it">
            <s xml:id="echoid-s1071" xml:space="preserve">In ſchem. </s>
            <s xml:id="echoid-s1072" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1074" xml:space="preserve">annulus ſtrictus ex quadrila-
              <lb/>
            tero mixto C B E G, circa E F, eſt æqualis cylindro
              <lb/>
            D K, tam ſecundum totum, quam ſecundum partes
              <lb/>
            proportionales.</s>
            <s xml:id="echoid-s1075" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1076" xml:space="preserve">PAtet faciliter. </s>
            <s xml:id="echoid-s1077" xml:space="preserve">Cum enim in anteced. </s>
            <s xml:id="echoid-s1078" xml:space="preserve">propoſit.
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            </s>
            <s xml:id="echoid-s1079" xml:space="preserve">oſtenſum ſit, annulum latum ex trilineo </s>
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