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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[31.] PROPOSITIO XV.
[32.] SCHOLIVM.
[33.] PROPOSITIO XVI.
[34.] SCHOLIVM.
[35.] PROPOSITIO XVII. Segmenti fupradicti conoidis hyperbolici centrum grauitatis reperire.
[36.] SCHOLIVM.
[37.] PROPOSITIO XVIII.
[38.] SCHOLIVM I.
[39.] SCHOLIVM II.
[40.] SCHOLIVM III.
[41.] PROPOSITIO XIX.
[42.] SCHOLIVM I.
[43.] SCHOLIVM II.
[44.] PROPOSITIO XX.
[45.] SCHOLIVM.
[46.] PROPOSITIO XXI.
[47.] PROPOSITIO XXII.
[48.] SCHOLIVMI.
[49.] SCHOLIVM II.
[50.] PROPOSITIO XXIII.
[51.] PROPOSITIO XXIV.
[52.] PROPOSITIO XXV.
[53.] PROPOSITIO XXVI.
[54.] SCHOLIVM I.
[55.] SCHOLIVM II.
[56.] SCHOLIVM III.
[57.] PROPOSITIO XXVII.
[58.] ALITER.
[59.] PROPOSITIO XXVIII.
[60.] SCHOLIVMI.
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            bolici contento inter duo plana baſi parallela, ad
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            ipſum.</s>
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          <head xml:id="echoid-head41" xml:space="preserve">PROPOSITIO XV.</head>
          <p style="it">
            <s xml:id="echoid-s743" xml:space="preserve">Si ſegmento conoidis hyperbolici reſecti plano baſi parallelo,
              <lb/>
            ſit circumſcriptus cylindrus. </s>
            <s xml:id="echoid-s744" xml:space="preserve">Erit bic ad ipſum ſegmen-
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            tum, vt rectangulum ſub compoſita ex latere tranſuer-
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            ſo, & </s>
            <s xml:id="echoid-s745" xml:space="preserve">ex diametro conoidis, & </s>
            <s xml:id="echoid-s746" xml:space="preserve">ſub diametro, ad re-
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            ctangulum ſub eadem compoſita, & </s>
            <s xml:id="echoid-s747" xml:space="preserve">ſub diametro co-
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            noidis ad verticem, vna cum rectangulo ſub compoſi-
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            ta ex dimidio lateris tranſuerſi, & </s>
            <s xml:id="echoid-s748" xml:space="preserve">ex tertia parte dia-
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            metri fruſti, & </s>
            <s xml:id="echoid-s749" xml:space="preserve">ſub eadem tertia parte.</s>
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            <s xml:id="echoid-s751" xml:space="preserve">COnoides hyperbolicum cuius baſis A C, ver-
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            tex B, diameter D B, latus tranſuerſum.
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            </s>
            <s xml:id="echoid-s752" xml:space="preserve">G B, intelligatur ſectum plano H K I, A C, pa-
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            rallelo, & </s>
            <s xml:id="echoid-s753" xml:space="preserve">ipſi ſit circumſcriptus cylindricus L C. </s>
            <s xml:id="echoid-s754" xml:space="preserve">Di-
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            co hunc eſſe ad ſegmentum conoidis, vt rectangu-
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            lum G D B, ad rectangulum ſub G D, in B k,
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            vna cum rectangulo ſub compoſita ex dimidia G B,
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            & </s>
            <s xml:id="echoid-s755" xml:space="preserve">tertia parte D k, & </s>
            <s xml:id="echoid-s756" xml:space="preserve">ſub tertia parte D k.</s>
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            <s xml:id="echoid-s758" xml:space="preserve">Segmento A H I C, intelligatur inſcriptum ſeg.
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            </s>
            <s xml:id="echoid-s759" xml:space="preserve">mentum E N O F, conoidis parabolici cuius ver-
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            tex B, conditionis ſupra ſæpe expoſitæ; </s>
            <s xml:id="echoid-s760" xml:space="preserve">& </s>
            <s xml:id="echoid-s761" xml:space="preserve">in talibus
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            ſegmentis intelligantur ſegmenta conorum inſcri-
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            ptorum in integris conoidibus, quæ ſint A P Q C,
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            E R S F. </s>
            <s xml:id="echoid-s762" xml:space="preserve">Quoniam fruſtum A H I C, conſtat ex
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            fruſto parabolico, & </s>
            <s xml:id="echoid-s763" xml:space="preserve">ex differentia fruſtorum </s>
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