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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[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.
[61.] SCHOLIVM II.
[62.] PROPOSITIO XXIX.
[63.] SCHOLIV M.
[64.] PROPOSITIO XXX.
[65.] SCHOLIVM I.
[66.] SCHOLIVM II.
[67.] PROPOSITIO XXXI. Semifuſi parabolici cuiuſcunque, centrum grauitatis reperire.
[68.] SCHOLIVM.
[69.] PROPOSITIO XXXII.
[70.] SCHOLIV M.
[71.] PROPOSITIO XXXIII.
[72.] SCHOLIVM.
[73.] PROPOSITIO XXXIV.
[74.] SCHOLIVM.
[75.] PROPOSITIO XXXV.
[76.] SCHOLIVM.
[77.] PROPOSITIO XXXVI.
[78.] SCHOLIVM.
[79.] PROPOSITIO XXXVII.
[80.] SCHOLIVM.
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            nes lineas trilinei C D B, parallelas itidem D C;
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            <s xml:id="echoid-s1642" xml:space="preserve">nempe vt tubus ad differentiam, ſic parallelogram-
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            mum ad trilineum.</s>
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            <s xml:id="echoid-s1644" xml:space="preserve">Cum vero quod oſtenſum eſt de totis, pateat poſ-
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            ſe eodem modo probari de partibus proportionali-
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            bus, ideo patet propoſitum.</s>
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        <div xml:id="echoid-div88" type="section" level="1" n="60">
          <head xml:id="echoid-head71" xml:space="preserve">SCHOLIVMI.</head>
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            <s xml:id="echoid-s1646" xml:space="preserve">Patet ergo quomodo adhibito etiam alio ſolido
              <lb/>
            hyperbolico, nempe differentia conoideorum, poſſi-
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            mus quadrare parabolam. </s>
            <s xml:id="echoid-s1647" xml:space="preserve">Cum enim ex propoſit.
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            </s>
            <s xml:id="echoid-s1648" xml:space="preserve">anteced. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">tubus cylindricus Q E L C, ſit triplus dif-
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            ferentiæ conoideorum; </s>
            <s xml:id="echoid-s1650" xml:space="preserve">etiam parallelogrammum
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            triplum erit trilinei; </s>
            <s xml:id="echoid-s1651" xml:space="preserve">& </s>
            <s xml:id="echoid-s1652" xml:space="preserve">conſequenter ſeſquialterum
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            femiparabolæ.</s>
            <s xml:id="echoid-s1653" xml:space="preserve"/>
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            <s xml:id="echoid-s1654" xml:space="preserve">Inſuper patet, quod cum in ſchol. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1656" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">18.
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            <s xml:id="echoid-s1658" xml:space="preserve">probatum ſit, conum, trilineum quadraticum, exceſ-
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            ſum cylindri circumſcripti hemiſphærio, & </s>
            <s xml:id="echoid-s1659" xml:space="preserve">hemiſ-
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            phæroidi, & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">exceſſum tubi cylindrici ſuper annulum
              <lb/>
            latum ex hyperbola circa ſecundam diametrum, eſſe
              <lb/>
            quantitates proportion aliter analogas, patet in-
              <lb/>
            quam, his pro ſexta addi differentiam conoideorum
              <lb/>
            prædictam.</s>
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        <div xml:id="echoid-div89" type="section" level="1" n="61">
          <head xml:id="echoid-head72" xml:space="preserve">SCHOLIVM II.</head>
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            <s xml:id="echoid-s1662" xml:space="preserve">In propoſit. </s>
            <s xml:id="echoid-s1663" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1664" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">de Infinit. </s>
            <s xml:id="echoid-s1667" xml:space="preserve">Parab. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">cuius
              <lb/>
            ſchema hic apponimus, probauimus, quod ſi </s>
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