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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          <p>
            <s xml:id="echoid-s1419" xml:space="preserve">
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            tubus cylindricus ad annulum ex hyperbola, ſic pa-
              <lb/>
            rallelogrammum P C, ad parabolam A O C.</s>
            <s xml:id="echoid-s1420" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1421" xml:space="preserve">Quod autem probatum fuitdetotis, patet eodem
              <lb/>
            modo probari poſſe de partibus proportionalibus;
              <lb/>
            </s>
            <s xml:id="echoid-s1422" xml:space="preserve">nimirum eodem modo poteſt probari eſſe v. </s>
            <s xml:id="echoid-s1423" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1424" xml:space="preserve">tu-
              <lb/>
            bum cylindricum ex parallelogrammo I B, circa. </s>
            <s xml:id="echoid-s1425" xml:space="preserve">
              <lb/>
            K M, ad partem annuli ex ſegmento hyperbolæ
              <lb/>
            I H B N, circa eandem K M, vt parallelogrammum
              <lb/>
            F N, ad ſegmentum parabolæ I R O N. </s>
            <s xml:id="echoid-s1426" xml:space="preserve">Quare pa-
              <lb/>
            tet propoſitum in omnibus, & </s>
            <s xml:id="echoid-s1427" xml:space="preserve">peromnia.</s>
            <s xml:id="echoid-s1428" xml:space="preserve"/>
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        <div xml:id="echoid-div79" type="section" level="1" n="54">
          <head xml:id="echoid-head65" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s1429" xml:space="preserve">Præſens propoſitio, quæ probata fuit perindiuiſi-
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            bilium methodum breuiorem, probari quoque po-
              <lb/>
            teſt per methodum antiquam prolixiorem. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">Nam
              <lb/>
            cum probatum ſit eſſe armillam circularem T S I.
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            </s>
            <s xml:id="echoid-s1431" xml:space="preserve">ad armillam circularem T H I, vt F I, ad I R; </s>
            <s xml:id="echoid-s1432" xml:space="preserve">& </s>
            <s xml:id="echoid-s1433" xml:space="preserve">cum
              <lb/>
            ſit armilla circularis T S I, ad armillam circularem
              <lb/>
            T H, ſictubus cylindricus ex parallelogrammo S N,
              <lb/>
            circa K M, ad tubum cylindricum ex parallelogram-
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            mo H N, circa eandem K M, quitubus eſt inſcriptus
              <lb/>
            in annulo ex hyperbola; </s>
            <s xml:id="echoid-s1434" xml:space="preserve">& </s>
            <s xml:id="echoid-s1435" xml:space="preserve">cum pariter ſit vt F I, ad
              <lb/>
            I R, ſic parallelogrammum F N, ad parallelogram-
              <lb/>
            mum R N, inſcriptum in parabola: </s>
            <s xml:id="echoid-s1436" xml:space="preserve">ſequitur vt tu-
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            bus ex parallelogrammo S N, ad tubum ex paralle-
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            logrammo H N, ſic eſſe parallelogrammum F N,
              <lb/>
            ad parallelogrammum R N. </s>
            <s xml:id="echoid-s1437" xml:space="preserve">Quare ſi A N, v. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">
              <lb/>
            b@ſſ@caretur, & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">hocidem fieret de eiuſdem </s>
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