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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            centrum ℟. </s>
            <s xml:id="echoid-s2428" xml:space="preserve">Item ex prop. </s>
            <s xml:id="echoid-s2429" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2430" xml:space="preserve">& </s>
            <s xml:id="echoid-s2431" xml:space="preserve">14. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">habemus centrum
              <lb/>
            grauitatis conoidis hyperbolici, & </s>
            <s xml:id="echoid-s2433" xml:space="preserve">conſequenter
              <lb/>
            duorum conoideorum diſpoſitorum vt in ſecunda fi-
              <lb/>
            gura. </s>
            <s xml:id="echoid-s2434" xml:space="preserve">Sit hoc 2. </s>
            <s xml:id="echoid-s2435" xml:space="preserve">Pariter, quoniam ex propoſit. </s>
            <s xml:id="echoid-s2436" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s2437" xml:space="preserve">habemus centrum æquilibrij ſemihyperbolæ D B C,
              <lb/>
            in D C; </s>
            <s xml:id="echoid-s2438" xml:space="preserve">habebimus etiam ex propoſit. </s>
            <s xml:id="echoid-s2439" xml:space="preserve">4 lib 3. </s>
            <s xml:id="echoid-s2440" xml:space="preserve">ra-
              <lb/>
            tionem quam habent ſolida ex ſemihyperbola D B C,
              <lb/>
            reuoluta circa B D, & </s>
            <s xml:id="echoid-s2441" xml:space="preserve">F C, ad inuicem; </s>
            <s xml:id="echoid-s2442" xml:space="preserve">& </s>
            <s xml:id="echoid-s2443" xml:space="preserve">conſe-
              <lb/>
            quenter habebimus rationem, quam habent in ſe-
              <lb/>
            cunda figura duo ſolida extrema ad duo media. </s>
            <s xml:id="echoid-s2444" xml:space="preserve">Si er-
              <lb/>
            go fiat vt duo ſolida extrema ad duo media ſic reci-
              <lb/>
            procè 2 ℟, ad ℟ +. </s>
            <s xml:id="echoid-s2445" xml:space="preserve">Erit +, centrum grauitatis
              <lb/>
            duorum annulorum ſimul. </s>
            <s xml:id="echoid-s2446" xml:space="preserve">Vndè patet quomodo
              <lb/>
            poſſimus habere centrum grauitatis vnius annuli ſoli
              <lb/>
            ex ſemihyperbola. </s>
            <s xml:id="echoid-s2447" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s2448" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2449" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div117" type="section" level="1" n="74">
          <head xml:id="echoid-head86" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s2450" xml:space="preserve">Habito centro grauitatis annuli, non ignorabitur
              <lb/>
            centrum grauitatis conici hyperbolici B C H; </s>
            <s xml:id="echoid-s2451" xml:space="preserve">pro
              <lb/>
            quare conſideretur ſcholium antecedentis propoſi-
              <lb/>
            tionis, diſcurſuſque in ipſo expoſitus imitetur.</s>
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          </p>
          <p>
            <s xml:id="echoid-s2453" xml:space="preserve">Q oniam autem ex doctrinis ſuperius traditis li-
              <lb/>
            cet nobis colligere centra grauitatis aliquorum ſoli-
              <lb/>
            dorum, de quibus nunquam geometria locuta eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s2454" xml:space="preserve">ideo vt hoc expeditius fiat, opere pretium ducimus
              <lb/>
            doctrinas ſuperius traditas aptius ordinare, regulam
              <lb/>
            quandam generalem exponendo. </s>
            <s xml:id="echoid-s2455" xml:space="preserve">Sciendum ergo
              <lb/>
            eſt, quatuor eſſe centra grauitatis, quorum </s>
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