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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            parallelas eidem armillæ N L P, vt omnès lineæ pa-
              <lb/>
            rallelogrammi C E, parallelæ D B, ad omnes lineas
              <lb/>
            parabolæ itidem parallelas D B. </s>
            <s xml:id="echoid-s2980" xml:space="preserve">Quare etiam tu-
              <lb/>
            bus ad exceſſum, erit vt parallelogrammum ad pa-
              <lb/>
            rabolam.</s>
            <s xml:id="echoid-s2981" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2982" xml:space="preserve">Hoc autem quod probatum fuit de totis, patet eo-
              <lb/>
            dem modo probari poſſe de partibus proportionali-
              <lb/>
            bus. </s>
            <s xml:id="echoid-s2983" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2984" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2985" xml:space="preserve">codem modo probare poterimus, partem
              <lb/>
            tubi K Z, eſſe ad partem exceſſus inter plana k M,
              <lb/>
            Q Z, contentam, vt parallelogrammum A H, ad
              <lb/>
            portionem A G F. </s>
            <s xml:id="echoid-s2986" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s2987" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div145" type="section" level="1" n="93">
          <head xml:id="echoid-head105" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s2988" xml:space="preserve">Cum ergo ex ſchol. </s>
            <s xml:id="echoid-s2989" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s2990" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2992" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2993" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">ſit
              <lb/>
            parallelogrammum E C, ſeſquialterum parabolæ,
              <lb/>
            etiam tubus erit ſeſquialter prædicti exceſſus. </s>
            <s xml:id="echoid-s2995" xml:space="preserve">l@mo ex
              <lb/>
            propoſitionibus varijs eiuſdem lib. </s>
            <s xml:id="echoid-s2996" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s2997" xml:space="preserve">habebimus
              <lb/>
            varias rationes partium tubi contentarum inter pla-
              <lb/>
            na plano A C, parallela. </s>
            <s xml:id="echoid-s2998" xml:space="preserve">Quæ autem hæ ſint re-
              <lb/>
            linquimus lectori conſiderare ex illis propoſitioni-
              <lb/>
            bus, in quibus aſſignantur rationes variarum par-
              <lb/>
            tium parallelogrammi C E, ad varia ſegmenta pa-
              <lb/>
            rabolæ.</s>
            <s xml:id="echoid-s2999" xml:space="preserve"/>
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        <div xml:id="echoid-div146" type="section" level="1" n="94">
          <head xml:id="echoid-head106" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s3000" xml:space="preserve">Ad modum ergo perſæpe rememoratorum, poſſu-
              <lb/>
            mus deducere, exceſſum portionis A B C, </s>
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