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

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            <s xml:id="echoid-s1110" xml:space="preserve">
              <pb o="60" file="0072" n="72"/>
            K D, eſſe quantitates proportionaliter analogas om-
              <lb/>
            niquaque: </s>
            <s xml:id="echoid-s1111" xml:space="preserve">quod etiam intelligẽdum eſtſi ſemihyper-
              <lb/>
            bola cum omnibus duplicetur. </s>
            <s xml:id="echoid-s1112" xml:space="preserve">Annulus ergo præ-
              <lb/>
            dictus etiam duplicatus ad partes K B, erit corpus
              <lb/>
            ſibi ſimilare, ad modum quo cylindrus K D, ſic du-
              <lb/>
            plicatus eſt corpus ſibi ſimilare. </s>
            <s xml:id="echoid-s1113" xml:space="preserve">Hoc eſt, quod ſicut
              <lb/>
            cylindrus ſectus planis baſibus parallelis, ſemper ſe-
              <lb/>
            catur in proportione partium axis, ſic etiam in tali
              <lb/>
            proportione ſecabitur talis annulus. </s>
            <s xml:id="echoid-s1114" xml:space="preserve">Sicuti ergo
              <lb/>
            centrum grauitatis cylindri, cuiuslibetque eius par-
              <lb/>
            tis contentæ inter plana baſibus parallela eſt in me-
              <lb/>
            dio axis; </s>
            <s xml:id="echoid-s1115" xml:space="preserve">ſic etiam centrum grauitatis talis annuli, & </s>
            <s xml:id="echoid-s1116" xml:space="preserve">
              <lb/>
            cuiuslibet eiuſdem ſegmenti reſecti plano C L, pa-
              <lb/>
            rallelo, erit vel in medio E F, vel in medio partis
              <lb/>
            E F, correſpondentis parti annuli, vel quæ ſit al-
              <lb/>
            titudo partis annuli. </s>
            <s xml:id="echoid-s1117" xml:space="preserve">Quæ omnia vtique nobis vi-
              <lb/>
            dentur admitabilia, & </s>
            <s xml:id="echoid-s1118" xml:space="preserve">neicimus an fortè corpus huic
              <lb/>
            ſimile in tota geometria adinueniatur, præter vni-
              <lb/>
            cum, quod antequam ad vlteriora progrediamur,
              <lb/>
            intelligimus in propoſitione ſequenti explicare.</s>
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        <div xml:id="echoid-div64" type="section" level="1" n="44">
          <head xml:id="echoid-head55" xml:space="preserve">PROPOSITIO XX.</head>
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            <s xml:id="echoid-s1120" xml:space="preserve">Exceſſus fruſti crnici propoſit. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">ſupra conoides hyper-
              <lb/>
            bolicum, eſt æqualis cylindro ſuper minore baſi frusti,
              <lb/>
            & </s>
            <s xml:id="echoid-s1123" xml:space="preserve">circa diametrum cum ipſo: </s>
            <s xml:id="echoid-s1124" xml:space="preserve">& </s>
            <s xml:id="echoid-s1125" xml:space="preserve">hoc tam ſecundum to-
              <lb/>
            tum, quam ſecundum partes proportionales.</s>
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