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 handwritten notes

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          <p>
            <s xml:id="echoid-s1136" xml:space="preserve">
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            æqualis conoidi A B C; </s>
            <s xml:id="echoid-s1137" xml:space="preserve">ſi cylindrus I M, adda-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1138" xml:space="preserve">Ergo exceſſus cum cylindro, nempe fruſtum
              <lb/>
            G I k H, erit æquale cylindro, & </s>
            <s xml:id="echoid-s1139" xml:space="preserve">conoidi ſimul.
              <lb/>
            </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Ablato ergo conoide, exceſſus fruſti ſupra conoides
              <lb/>
            remanebit æqualis cylindro.</s>
            <s xml:id="echoid-s1141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1142" xml:space="preserve">Non alio modo oſtendetur æqualitas partium,
              <lb/>
            proportionalium, v. </s>
            <s xml:id="echoid-s1143" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1144" xml:space="preserve">exceſſum fruſti G N P H,
              <lb/>
            ſupra fruſtum conoidis A Q T C, æqualem eſſe
              <lb/>
            cylindro R M. </s>
            <s xml:id="echoid-s1145" xml:space="preserve">Quia ex dictis in præcitata propo-
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s1146" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1147" xml:space="preserve">exceſſus fruſti G N P H, ſupra cylindrum
              <lb/>
            R M, eſt æqualis ſegmento A Q T C; </s>
            <s xml:id="echoid-s1148" xml:space="preserve">addito ergo,
              <lb/>
            vt prius, cylindro R M, & </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ablato ſegmento A Q T C,
              <lb/>
            intentum probabitur. </s>
            <s xml:id="echoid-s1150" xml:space="preserve">Quare patuit talia ſolida æ-
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            qualia fore tam ſecundum totum, quam ſecundum
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            partes.</s>
            <s xml:id="echoid-s1151" xml:space="preserve"/>
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          <head xml:id="echoid-head56" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s1152" xml:space="preserve">Sed etiam præſens propoſitio poſſet immediate
              <lb/>
            per indiuiſibilia oſtendi. </s>
            <s xml:id="echoid-s1153" xml:space="preserve">Sumpto enim arbitrariè
              <lb/>
            puncto O, & </s>
            <s xml:id="echoid-s1154" xml:space="preserve">acto plano N O P, G H, paralle-
              <lb/>
            lo. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Ex propoſit. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">conic. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">rectangulum N Q P,
              <lb/>
            eſt æquale quadrato I B, ſeù quadrato R O. </s>
            <s xml:id="echoid-s1160" xml:space="preserve">Et
              <lb/>
            conſequenter armilla circularis N Q P, eſt æqua-
              <lb/>
            lis circulo R O S: </s>
            <s xml:id="echoid-s1161" xml:space="preserve">& </s>
            <s xml:id="echoid-s1162" xml:space="preserve">omnes armillæ ęqualis omni-
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            b s irculis; </s>
            <s xml:id="echoid-s1163" xml:space="preserve">& </s>
            <s xml:id="echoid-s1164" xml:space="preserve">exceſſus prędictus ęqualis cylindro
              <lb/>
            I M. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">Sed hac conſtructione adhibita, demonſtratio
              <lb/>
            non reducitur ad modum Archimedeum, quia in prę-
              <lb/>
            dicto exceſſu nequeunt inſcribi tubi cylindrici.</s>
            <s xml:id="echoid-s1166" xml:space="preserve"/>
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