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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          <head xml:id="echoid-head93" xml:space="preserve">PROPOSITIO XXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s2669" xml:space="preserve">Data cuiuſcunque ſemifigurœ circa diametrum quadratu-
              <lb/>
            ra, dataque ratione cylindri circumſcripti ſolido ex ſe-
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            mifigura reuoluta ſiue circa diametrum, ſiue circa du-
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            ctam diametro parallelam, vel per extremitatem baſis,
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            vel extra figuram. </s>
            <s xml:id="echoid-s2670" xml:space="preserve">Datur ratio cylindri circumſcripti
              <lb/>
            altero dictorum ſolidorum adipſum.</s>
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          <p>
            <s xml:id="echoid-s2672" xml:space="preserve">SIt data quælibet ſemifigura D B C, circa dia-
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            metrum B D, & </s>
            <s xml:id="echoid-s2673" xml:space="preserve">data ſitratio quam habet pa-
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            rallelogrammum B C, ad ipſam figuram; </s>
            <s xml:id="echoid-s2674" xml:space="preserve">inſuper
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            detur ratio, quam habet cylindrus ex B C, in pri-
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            ma figura, reuoluto ſiue circa D B, ſiue circa F C,
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            ad alterum ſolidorum ex ſemifigura D B C, ſiue cir-
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            ca B D, ſiue circa F C: </s>
            <s xml:id="echoid-s2675" xml:space="preserve">vel in ſecunda figura detur
              <lb/>
            vel ratio cylindri E C, ad ſolidum A B C, vel cy-
              <lb/>
            lindri D H, ad ſolidum ex D B C, reuoluta cir-
              <lb/>
            ca T S. </s>
            <s xml:id="echoid-s2676" xml:space="preserve">Dico dari etiam rationem alterius cylindri,
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            ad alterum ſolidum exſemifigura.</s>
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            <s xml:id="echoid-s2678" xml:space="preserve">Probetur prius in prima figura, in qua intelliga-
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            mus parallelogrammum E C, cum figura integra
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            A B C, rotari circa F C. </s>
            <s xml:id="echoid-s2679" xml:space="preserve">Frgo ex propoſit. </s>
            <s xml:id="echoid-s2680" xml:space="preserve">29.
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            <s xml:id="echoid-s2681" xml:space="preserve">cum data ſit ratio ex hypotheſi, parallelogrammi
              <lb/>
            E C, ad figuram A B C, dabitur quoque ratio cy-
              <lb/>
            lindri E G, ad ſohdum A B C H G. </s>
            <s xml:id="echoid-s2682" xml:space="preserve">Sed tale ſoli-
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            dum ex propoſit. </s>
            <s xml:id="echoid-s2683" xml:space="preserve">30. </s>
            <s xml:id="echoid-s2684" xml:space="preserve">æquatur duobus ſolidis ex
              <lb/>
            D B C, circa D B, & </s>
            <s xml:id="echoid-s2685" xml:space="preserve">duobus, ex eadem circa F C.</s>
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