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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[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)
[101.] PROPOSITIO XLIX.
Page: 187 (175)
[102.] SCHOLIVM.
Page: 189 (177)
[103.] PROPOSITIO L.
Page: 191 (179)
[104.] SCHOLIV M.
Page: 193 (181)
[105.] PROPOSITIO LI.
Page: 195 (183)
[106.] SCHOLIVM.
Page: 196 (184)
[107.] PROPOSITIO LII.
Page: 196 (184)
[108.] SCHOLIVM.
Page: 197 (185)
[109.] PROPOSITIO LIII.
Page: 198 (186)
[110.] PROPOSITIO LIV.
Page: 199 (187)
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            finitarum parabolarum in diametro, quam inuentio-
              <lb/>
            ni centri æquilibrij infinitarum ſemiparabolarum in
              <lb/>
            baſi. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">At inuenimus centra grauitatis infinitarum.
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            <s xml:id="echoid-s2815" xml:space="preserve">parabolarum in diamctro non adhibendo infinitas
              <lb/>
            parabolas, ſed illas tantum, quarum exponentes
              <lb/>
            ſunt numeri pares. </s>
            <s xml:id="echoid-s2816" xml:space="preserve">E contra verò adhibendo infi-
              <lb/>
            nitas parabolas, non inuenimus centra æquilibrij in
              <lb/>
            baſi infinitarum ſemiparabolarum, ſed illarum tan-
              <lb/>
            tum, quarum exponentes ſunt numeri pares.</s>
            <s xml:id="echoid-s2817" xml:space="preserve"/>
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            <s xml:id="echoid-s2818" xml:space="preserve">Ex cit. </s>
            <s xml:id="echoid-s2819" xml:space="preserve">autem propoſit. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2821" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2822" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2823" xml:space="preserve">& </s>
            <s xml:id="echoid-s2824" xml:space="preserve">ex ſchol eiuſ-
              <lb/>
            dem, poſſumus ex propoſit. </s>
            <s xml:id="echoid-s2825" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s2826" xml:space="preserve">elicere ratio-
              <lb/>
            nem, quam habet cylindrus ex AM, circa E A, ad
              <lb/>
            partem annuli ex APMD, circa E A, cuius expo-
              <lb/>
            nens ſit numerus par. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">Et inſuper centrum æquili-
              <lb/>
            brij in A D, ſegmenti APMD, ſemiparabolæ
              <lb/>
            A B D, cuius exponens itidem ſit numerus par.
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            </s>
            <s xml:id="echoid-s2828" xml:space="preserve">Hæc autem facile patent ex dictis.</s>
            <s xml:id="echoid-s2829" xml:space="preserve"/>
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            <s xml:id="echoid-s2830" xml:space="preserve">Quot igitur ſolidorum manifeſtata ſint centra
              <lb/>
            grauitatis, potuit lector ex dictis cognoſcere. </s>
            <s xml:id="echoid-s2831" xml:space="preserve">Sed
              <lb/>
            nolumus ſub ſilentio relinquere aliqua, quæ nobis
              <lb/>
            ſcitu digna videntur.</s>
            <s xml:id="echoid-s2832" xml:space="preserve"/>
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          <head xml:id="echoid-head97" xml:space="preserve">PROPOSITIO XLI.</head>
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            <s xml:id="echoid-s2833" xml:space="preserve">Si ſuper eadem baſi, & </s>
            <s xml:id="echoid-s2834" xml:space="preserve">circa eandem diametrum ſint ſe-
              <lb/>
            mihyperbola, & </s>
            <s xml:id="echoid-s2835" xml:space="preserve">ſemiparabola. </s>
            <s xml:id="echoid-s2836" xml:space="preserve">Tota ſemihy-
              <lb/>
            perbola cadet intra ſemipar abolam.</s>
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            <s xml:id="echoid-s2838" xml:space="preserve">SInt ſemihy perbola A E B D, & </s>
            <s xml:id="echoid-s2839" xml:space="preserve">ſemiparabola
              <lb/>
            A F B D, quarum eadem baſis A D, </s>
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