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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[31.] PROPOSITIO XV.
[32.] SCHOLIVM.
[33.] PROPOSITIO XVI.
[34.] SCHOLIVM.
[35.] PROPOSITIO XVII. Segmenti fupradicti conoidis hyperbolici centrum grauitatis reperire.
[36.] SCHOLIVM.
[37.] PROPOSITIO XVIII.
[38.] SCHOLIVM I.
[39.] SCHOLIVM II.
[40.] SCHOLIVM III.
[41.] PROPOSITIO XIX.
[42.] SCHOLIVM I.
[43.] SCHOLIVM II.
[44.] PROPOSITIO XX.
[45.] SCHOLIVM.
[46.] PROPOSITIO XXI.
[47.] PROPOSITIO XXII.
[48.] SCHOLIVMI.
[49.] SCHOLIVM II.
[50.] PROPOSITIO XXIII.
[51.] PROPOSITIO XXIV.
[52.] PROPOSITIO XXV.
[53.] PROPOSITIO XXVI.
[54.] SCHOLIVM I.
[55.] SCHOLIVM II.
[56.] SCHOLIVM III.
[57.] PROPOSITIO XXVII.
[58.] ALITER.
[59.] PROPOSITIO XXVIII.
[60.] SCHOLIVMI.
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          <head xml:id="echoid-head70" xml:space="preserve">PROPOSITIO XXVIII.</head>
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            <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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            <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-
              <lb/>
            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
              <lb/>
            ad rectangulum M R V, vt quadratum D B, </s>
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