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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            ſimile factum ſub H B, & </s>
            <s xml:id="echoid-s3329" xml:space="preserve">ſub eadem poteſtate B G,
              <lb/>
            erit in maiori rationc quam poteſtas D G, eiuſdem
              <lb/>
            gradus cum parabola ad ſimilem poteſtatem G H.
              <lb/>
            </s>
            <s xml:id="echoid-s3330" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">permutando primum factum ad poteſtatem
              <lb/>
            D G, crit in maiori ratione quam fecundum factum
              <lb/>
            ad poteſtatem G H. </s>
            <s xml:id="echoid-s3332" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3333" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3334" xml:space="preserve">factum ſub D B, in qua-
              <lb/>
            dratum B G, habebit ad cubum D G, maiorem ra-
              <lb/>
            tionem, quam factum ſub H B, & </s>
            <s xml:id="echoid-s3335" xml:space="preserve">ſub quadrato B G,
              <lb/>
            ad cubum H G. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">Quod implicat, quia factum ſub
              <lb/>
            D B, & </s>
            <s xml:id="echoid-s3337" xml:space="preserve">ſub poteſtate B G, eſt in minori ratione ad
              <lb/>
            poteſtatem D G, & </s>
            <s xml:id="echoid-s3338" xml:space="preserve">non in maiori. </s>
            <s xml:id="echoid-s3339" xml:space="preserve">Quia ex doctri-
              <lb/>
            na ſcholij anteced. </s>
            <s xml:id="echoid-s3340" xml:space="preserve">factum ſub H B, & </s>
            <s xml:id="echoid-s3341" xml:space="preserve">ſub poteſtate
              <lb/>
            B G, eſt omnium maximum homogeneorum ſub par-
              <lb/>
            tibus H G, non ſic factum ſub D B, & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">ſub poteſta-
              <lb/>
            te B G, eſt maximum homogeneorum ſub partibus
              <lb/>
            D G. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">factum ſub H B, & </s>
            <s xml:id="echoid-s3346" xml:space="preserve">ſub quadrato B G,
              <lb/>
            eſt maximum omnium parallelepipedorum applica-
              <lb/>
            bilium ad partem H G, non ſic eſt maximum factum
              <lb/>
            ſub D B, & </s>
            <s xml:id="echoid-s3347" xml:space="preserve">ſub quadrato B G, applicabilium ad
              <lb/>
            partem D G. </s>
            <s xml:id="echoid-s3348" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s3349" xml:space="preserve"/>
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          <head xml:id="echoid-head116" xml:space="preserve">SCHOLIV M.</head>
          <p>
            <s xml:id="echoid-s3350" xml:space="preserve">Ex dictis facile eliciemus, quod ſi circa diametrum
              <lb/>
            B D, & </s>
            <s xml:id="echoid-s3351" xml:space="preserve">ſuper eadem baſi A D, intelligamus infini-
              <lb/>
            tas ſemiparabolas, & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">accepto in diametro B D, pun-
              <lb/>
            cto H, ducatur H C E F G, parallela A D, ſecans
              <lb/>
            omnes curuas parabolicas, & </s>
            <s xml:id="echoid-s3353" xml:space="preserve">pariter intelligamus
              <lb/>
            infinitas tangentes K E, L F, M G, &</s>
            <s xml:id="echoid-s3354" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3355" xml:space="preserve">eliciemus
              <lb/>
            inquam, triangula infinita C B H, E k H, F L </s>
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