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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            <s xml:id="echoid-s2235" xml:space="preserve">
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            erit 24; </s>
            <s xml:id="echoid-s2236" xml:space="preserve">IS, erit 1; </s>
            <s xml:id="echoid-s2237" xml:space="preserve">& </s>
            <s xml:id="echoid-s2238" xml:space="preserve">B S, 15. </s>
            <s xml:id="echoid-s2239" xml:space="preserve">Et qualium B D,
              <lb/>
            erit 48, talium I S, erit 2, & </s>
            <s xml:id="echoid-s2240" xml:space="preserve">BS, 30. </s>
            <s xml:id="echoid-s2241" xml:space="preserve">Sed qualium
              <lb/>
            IS, erat 2, talium S T, erat 3. </s>
            <s xml:id="echoid-s2242" xml:space="preserve">Ergo qualium B D,
              <lb/>
            erit 48, talium B T, erit 33, & </s>
            <s xml:id="echoid-s2243" xml:space="preserve">T D, 15. </s>
            <s xml:id="echoid-s2244" xml:space="preserve">Ergo
              <lb/>
            centrum grauitatis ſemifuſi parabolici quadratici ſic
              <lb/>
            diuidit B D, in T, vt B T, ſit ad T D, vt 33, ad
              <lb/>
            15; </s>
            <s xml:id="echoid-s2245" xml:space="preserve">& </s>
            <s xml:id="echoid-s2246" xml:space="preserve">ſubtriplando terminos, vt 11, ad 5.</s>
            <s xml:id="echoid-s2247" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2248" xml:space="preserve">Sed non ſolum ſupradicta methodo reperiemus
              <lb/>
            centrum grauitatis ſemifuſi parabolici, ſed etiam ex-
              <lb/>
            ceſſus cylindri ipſi circumſcripti ſupra ipſum; </s>
            <s xml:id="echoid-s2249" xml:space="preserve">nem-
              <lb/>
            pe centrum grauitatis ſolidi ex trilineo E B A, in pri-
              <lb/>
            ma figura, reuoluto circa baſim ſemiparabolæ B D.
              <lb/>
            </s>
            <s xml:id="echoid-s2250" xml:space="preserve">Cum autem tale centrum facilius inuen@atur
              <unsure/>
            alio mo-
              <lb/>
            do, ideo hunc experiemur in parabola quadratica in
              <lb/>
            numeris. </s>
            <s xml:id="echoid-s2251" xml:space="preserve">Supponamus ergo BD, ſectam bifariam
              <lb/>
            in S, & </s>
            <s xml:id="echoid-s2252" xml:space="preserve">in T, ſic vt BT, ſit ad T D, vt 11, ad 5. </s>
            <s xml:id="echoid-s2253" xml:space="preserve">
              <lb/>
            adeo vt T, ſit centrum grauitatis ſemifuſi A B C. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">Er-
              <lb/>
            go quarum BD, erit 16, talium ST, erit 3, & </s>
            <s xml:id="echoid-s2255" xml:space="preserve">
              <lb/>
            B S, 8. </s>
            <s xml:id="echoid-s2256" xml:space="preserve">Ergo qualium B D, erit 37, cum tertia par-
              <lb/>
            te, talium ST, erit 7, & </s>
            <s xml:id="echoid-s2257" xml:space="preserve">BS, 18, cum duobus ter-
              <lb/>
            tijs. </s>
            <s xml:id="echoid-s2258" xml:space="preserve">Cum autem ex ſchol. </s>
            <s xml:id="echoid-s2259" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s2260" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2261" xml:space="preserve">14. </s>
            <s xml:id="echoid-s2262" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2263" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2264" xml:space="preserve">
              <lb/>
            ſit exceſſus cylindri circumſcripti ſemifuſo ad ipſum
              <lb/>
            vt 7, ad 8, & </s>
            <s xml:id="echoid-s2265" xml:space="preserve">ſi fiat vt talis exceſſus ad ſemifuſum,
              <lb/>
            ſic reriprocè T S, ad S I, ſit 1, centrum grauitatis
              <lb/>
            prædicti exceſlus; </s>
            <s xml:id="echoid-s2266" xml:space="preserve">erit SI, 8, qualium BS, eſt 18,
              <lb/>
            cum duobus tertijs. </s>
            <s xml:id="echoid-s2267" xml:space="preserve">Ergo talium reliqua BI, erit
              <lb/>
            10, cum duobus tertijs. </s>
            <s xml:id="echoid-s2268" xml:space="preserve">Qualium ergo BD, eſt
              <lb/>
            37, cum tertia parte, erit BI, 10, cum duabus
              <lb/>
            tertijs partibus, & </s>
            <s xml:id="echoid-s2269" xml:space="preserve">reliqua DI, 26, cum duo bus </s>
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