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-s496" xml:space="preserve">
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            conoidis; </s>
            <s xml:id="echoid-s497" xml:space="preserve">intraque fruſtum conicum, & </s>
            <s xml:id="echoid-s498" xml:space="preserve">ſupra minori ba-
              <lb/>
            ſi ipſius inſcribatur cylindrus. </s>
            <s xml:id="echoid-s499" xml:space="preserve">Erit exceſſus fruſti coni-
              <lb/>
            ci ſupra cylindrum ſibi inſcriptum æqualis conoidi hy-
              <lb/>
            perbolico, tam ſeeundumtotum, quam ſecundum partes
              <lb/>
            proportionales.</s>
            <s xml:id="echoid-s500" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s501" xml:space="preserve">COnoides hyperbolicum A B C, cuius diame-
              <lb/>
            ter D B, latus tranſuerſum E B, centrum F,
              <lb/>
            aſymptoti hyperbolæ genitricis F G, F H, intelli-
              <lb/>
            gatur incluſum intra fruſtum conicum G I K H, cu-
              <lb/>
            ius oppoſita plana parallela ſint I k, G H, & </s>
            <s xml:id="echoid-s502" xml:space="preserve">in ipſo
              <lb/>
            ſit inſcriptus cylindrus I M. </s>
            <s xml:id="echoid-s503" xml:space="preserve">Dico exceſſum fruſti
              <lb/>
            G I k H, ſupra cylindrum I M, æqualem eſſe conoi-
              <lb/>
            di A B C, tam ſecundum totum, quam ſecundum
              <lb/>
            partes proportionales. </s>
            <s xml:id="echoid-s504" xml:space="preserve">Sumatur enim in diametro
              <lb/>
            arbitrariè punctum O, per quod agatur planum
              <lb/>
            N O P, G H, parallelum, ſecans omnia ſolida, vt in
              <lb/>
            ſchemate. </s>
            <s xml:id="echoid-s505" xml:space="preserve">Quoniam enim quadratum N O, eſt æ-
              <lb/>
            quale tam rectangulo N Q P, cum quadrato Q O,
              <lb/>
            quam rectangulo N R P, cum quadrato R O. </s>
            <s xml:id="echoid-s506" xml:space="preserve">Ergo
              <lb/>
            rectangulum N Q P, cum quadrato Q O, erit æ-
              <lb/>
            quale rectangulo N R P, cum quadrato R O. </s>
            <s xml:id="echoid-s507" xml:space="preserve">At
              <lb/>
            ex 2. </s>
            <s xml:id="echoid-s508" xml:space="preserve">conic. </s>
            <s xml:id="echoid-s509" xml:space="preserve">propoſit, 10. </s>
            <s xml:id="echoid-s510" xml:space="preserve">rectangulum N Q P, eſt æ-
              <lb/>
            quale quadrato I B, ſeù quadrato R O. </s>
            <s xml:id="echoid-s511" xml:space="preserve">Ergo reli-
              <lb/>
            quum rectangulum N R P, erit æquale quadrato
              <lb/>
            Q O. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Quare etiam armilla circularis N R P, erit æ-
              <lb/>
            qualis circulo Q T. </s>
            <s xml:id="echoid-s513" xml:space="preserve">Punctum autem O, ſumptum
              <lb/>
            eſt arbitrariè; </s>
            <s xml:id="echoid-s514" xml:space="preserve">ergo omnes Armillæ genitæ ex reuo-
              <lb/>
            lutione trianguli G I L, circa B D, erunt </s>
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