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-head70" xml:space="preserve">PROPOSITIO XXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s1619" xml:space="preserve">Exceſſus cylindri circumſ@ripti conoidi hyperbolico ſupra
              <lb/>
            cylindrum circumſcriptum conoidi parabolico ſæpe ex-
              <lb/>
            plicato, est ad differentiam conoideorum, vt paralle-
              <lb/>
            logrammum circumſcriptum trilineo quadratico ad ip-
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            ſum, tam ſecundum totum, quam ſecundum partes
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            proportionales; </s>
            <s xml:id="echoid-s1620" xml:space="preserve">ſi diametri trilinei, & </s>
            <s xml:id="echoid-s1621" xml:space="preserve">conoidis ſecentur
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            proportionaliter.</s>
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          <p>
            <s xml:id="echoid-s1623" xml:space="preserve">SInt ergo conoidea hyperbolicum A B C, & </s>
            <s xml:id="echoid-s1624" xml:space="preserve">pa-
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            rabolicum E B F, vt ſæpe dictum eſt, cum cir-
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            cumſcriptis cylindris Q C, T F, & </s>
            <s xml:id="echoid-s1625" xml:space="preserve">inſuper ſit ſe-
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            miparabola B C O, cuius diameter O B, baſis
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            O C, & </s>
            <s xml:id="echoid-s1626" xml:space="preserve">parallelogrammum ei circumſcriptum ſit
              <lb/>
            D O, adeovt D B C, ſit trilineum quadraticum, cu-
              <lb/>
            ius diameter D B. </s>
            <s xml:id="echoid-s1627" xml:space="preserve">Dico tubum cylindricum
              <lb/>
            Q E L C, eſſe ad differentiam conoideorum, vt pa-
              <lb/>
            rallelogrammum D O, ad trilineum B D C, tam
              <lb/>
            ſecundum totum, quam fecundum partes propor-
              <lb/>
            tionales. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Sumatur in D B, diametro arbitrariè pun-
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            ctum G, per quod in ſolidis intelligatur tranfire pla-
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            num H K, plano A C, parallelum, ſecans tubum
              <lb/>
            in P, conoides hyperbolicum in M, & </s>
            <s xml:id="echoid-s1629" xml:space="preserve">paraboli-
              <lb/>
            cum in R: </s>
            <s xml:id="echoid-s1630" xml:space="preserve">item in parallelogrammo ducatur GK,
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            parallela D C, ſecans curuam parabolicam in S.
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            </s>
            <s xml:id="echoid-s1631" xml:space="preserve">Quoniam ex propoſit. </s>
            <s xml:id="echoid-s1632" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1633" xml:space="preserve">rectangulum A E C, eſt
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            ad rectangulum M R V, vt quadratum D B, </s>
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