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

Table of contents

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[71.] PROPOSITIO XXXIII.
Page: 140 (128)
[72.] SCHOLIVM.
Page: 142 (130)
[73.] PROPOSITIO XXXIV.
Page: 145 (133)
[74.] SCHOLIVM.
Page: 146 (134)
[75.] PROPOSITIO XXXV.
Page: 148 (136)
[76.] SCHOLIVM.
Page: 148 (136)
[77.] PROPOSITIO XXXVI.
Page: 149 (137)
[78.] SCHOLIVM.
Page: 150 (138)
[79.] PROPOSITIO XXXVII.
Page: 151 (139)
[80.] SCHOLIVM.
Page: 155 (143)
[81.] PROPOSITIO XXXVIII.
Page: 156 (144)
[82.] PROPOSITIO XXXIX.
Page: 160 (148)
[83.] PROPOSITIO XL.
Page: 160 (148)
[84.] SCHOLIVM.
Page: 161 (149)
[85.] PROPOSITIO XLI.
Page: 165 (153)
[86.] SCHOLIVM.
Page: 167 (155)
[87.] PROPOSITIO XLII.
Page: 167 (155)
[88.] SCHOLIVM.
Page: 168 (156)
[89.] PROPOSITIO XLIII.
Page: 169 (157)
[90.] PROPOSITIO XLIV.
Page: 170 (158)
[91.] SCHOLIVM.
Page: 171 (159)
[92.] PROPOSITIO XLV.
Page: 171 (159)
[93.] SCHOLIVM I.
Page: 174 (162)
[94.] SCHOLIVM II.
Page: 174 (162)
[95.] PROPOSITIO XLVI.
Page: 176 (164)
[96.] PROPOSITIO XLVII.
Page: 177 (165)
[97.] SCHOLIVM.
Page: 179 (167)
[98.] PROPOSITIO XLVIII.
Page: 180 (168)
[99.] SCHOLIVM I.
Page: 182 (170)
[100.] SCHOLIVM II.
Page: 184 (172)
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            datis, licet quartum colligere. </s>
            <s xml:id="echoid-s2456" xml:space="preserve">Nempe cèntrum
              <lb/>
            grauitatis figuræ A B C, circa diametrum: </s>
            <s xml:id="echoid-s2457" xml:space="preserve">centrum
              <lb/>
            æquilibrij ſemifiguræ D B C, in D C: </s>
            <s xml:id="echoid-s2458" xml:space="preserve">centrum
              <lb/>
            grauitatis ſolidi A B C, orti ex reuolutione ſemi-
              <lb/>
            figuræ A B D, circa B D: </s>
            <s xml:id="echoid-s2459" xml:space="preserve">& </s>
            <s xml:id="echoid-s2460" xml:space="preserve">centrum grauitatis ſe-
              <lb/>
            miſiguræ D B C, reuolutæ circa F C. </s>
            <s xml:id="echoid-s2461" xml:space="preserve">Nam datis
              <lb/>
            tribus primis, patebit dari quartum ſic. </s>
            <s xml:id="echoid-s2462" xml:space="preserve">Dato cen-
              <lb/>
            tro grauitatis figuræ A B C, datur centrum graui-
              <lb/>
            tatis ſolidi orti ex gyratione A B C, circa C F; </s>
            <s xml:id="echoid-s2463" xml:space="preserve">& </s>
            <s xml:id="echoid-s2464" xml:space="preserve">
              <lb/>
            conſequenter centrum grauitatis quatuor ſolidorum
              <lb/>
            diſpoſitorum in ſecunda figura. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">Secundo dato cen-
              <lb/>
            tro æquilibrij ſemifiguræ D B C, in D C, dabitur
              <lb/>
            ratio ſolidi ex ſemifigura D B C, reuoluta circa D B,
              <lb/>
            ad ſolidum ex eadem reuoluta circa C F; </s>
            <s xml:id="echoid-s2466" xml:space="preserve">ex propo-
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">& </s>
            <s xml:id="echoid-s2471" xml:space="preserve">conſequenter in ſecunda figura dabi-
              <lb/>
            tur ratio duorum ſolidorum mediorum ad duo extre-
              <lb/>
            ma. </s>
            <s xml:id="echoid-s2472" xml:space="preserve">Tertio dato centro grauitatis ſolidi A B C, da-
              <lb/>
            bitur etiam in ſecunda figura centrum duorum ſoli-
              <lb/>
            dorum mediorum ſimul. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">Si ergo ℟, ſit centrum
              <lb/>
            quatuor ſimul, iam datum, & </s>
            <s xml:id="echoid-s2474" xml:space="preserve">2, ſit centrum duo-
              <lb/>
            rum mediorum etiam datum, ſi fiat 2 ℟, ad ℟ +, in
              <lb/>
            ratione data, nempe vt duo ſolida extrema, ad duo
              <lb/>
            media, vel vt vnum ad vnum; </s>
            <s xml:id="echoid-s2475" xml:space="preserve">erit + centrum gra-
              <lb/>
            uitatis duorum extremorum, vel vnius extremi, quod
              <lb/>
            eſt quartum, quod quærebatur. </s>
            <s xml:id="echoid-s2476" xml:space="preserve">Ita ſuppoſitis dari
              <lb/>
            tribus quibuſuis quatuor iam dictorum, patebit ſimi-
              <lb/>
            li diſcurſu, dari quartum. </s>
            <s xml:id="echoid-s2477" xml:space="preserve">His animaduerſis.</s>
            <s xml:id="echoid-s2478" xml:space="preserve"/>
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