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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            hyperbolici diuerſus ab illis, quos tradidimus ſupra
              <lb/>
            in propoſit. </s>
            <s xml:id="echoid-s2884" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2885" xml:space="preserve">& </s>
            <s xml:id="echoid-s2886" xml:space="preserve">14. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">nolumus ipſum omittere, ſed
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            præmittenda eſt ſequens propoſitio eius manifeſta-
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            tioni.</s>
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          <head xml:id="echoid-head101" xml:space="preserve">PROPOSITIO XLIII.</head>
          <p style="it">
            <s xml:id="echoid-s2889" xml:space="preserve">Differentia ſupradictorum conoideorum, est ad conoides hy-
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            perboluum vt ſexta pars diametri ad tertiam partem
              <lb/>
            ciuſdem, vna cum dimidio lateris tranſuerſi.</s>
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            <s xml:id="echoid-s2891" xml:space="preserve">IN ſchemate ſuperiori. </s>
            <s xml:id="echoid-s2892" xml:space="preserve">Dico exceſſum conoidis
              <lb/>
            parabolici A F B C, ſupra conoides hyperboli-
              <lb/>
            cum A E B C, eſſe vt ſexta pars D B, ad tertiam
              <lb/>
            partem D B, cum dimidio G B. </s>
            <s xml:id="echoid-s2893" xml:space="preserve">Quoniam enim
              <lb/>
            vt elicitur ex propoſit. </s>
            <s xml:id="echoid-s2894" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2895" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2896" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2897" xml:space="preserve">conoides paraboli-
              <lb/>
            cum eſt ſeſquialterum coni A B C; </s>
            <s xml:id="echoid-s2898" xml:space="preserve">ergo erit ad ip-
              <lb/>
            ſum vt G D, ad duo tertia G D; </s>
            <s xml:id="echoid-s2899" xml:space="preserve">nempe vt dimi-
              <lb/>
            dium G D, ad tertiam partem G D. </s>
            <s xml:id="echoid-s2900" xml:space="preserve">Rurſum cum
              <lb/>
            ex propoſit.</s>
            <s xml:id="echoid-s2901" xml:space="preserve">, 5 7. </s>
            <s xml:id="echoid-s2902" xml:space="preserve">& </s>
            <s xml:id="echoid-s2903" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ſit cylindrus conoidi hyper-
              <lb/>
            bolico circumſcriptus, ad ipſum, vt G D, ad dimi-
              <lb/>
            diam G B, cum tertia parte D B; </s>
            <s xml:id="echoid-s2905" xml:space="preserve">erit conus A B C,
              <lb/>
            tertia pars cylindri, ad conoides hyperbolicum, vt
              <lb/>
            tertia pars G D, ad dimidiam G B cum tertia par-
              <lb/>
            te D B Quare ex quali, erit conoides paraboli-
              <lb/>
            cum ad conoides hyperbolicum vt dimidium G D,
              <lb/>
            ad dimidium G B, cum tertia parte B D. </s>
            <s xml:id="echoid-s2906" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2907" xml:space="preserve">
              <lb/>
            diuidendo, erit differentia conoideorum ad </s>
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