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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            I M, P Q, ſeù MIL. </s>
            <s xml:id="echoid-s2063" xml:space="preserve">Pariter rectangulum L I,
              <lb/>
            M Q, cum ſit æquale rectangulo I M Q, diuiditur
              <lb/>
            in eadem rectangula. </s>
            <s xml:id="echoid-s2064" xml:space="preserve">Quare colligemus, rectan-
              <lb/>
            gulum L M Q, æquale eſſe duobus rectangulis
              <lb/>
            I M P, & </s>
            <s xml:id="echoid-s2065" xml:space="preserve">duobus rectangulis M I L. </s>
            <s xml:id="echoid-s2066" xml:space="preserve">Rectangulum
              <lb/>
            I M P, in prima figura, æquatur rectangulo EGK,
              <lb/>
            in ſecunda; </s>
            <s xml:id="echoid-s2067" xml:space="preserve">vnde duo rectangula I M P, primæ,
              <lb/>
            æquantur duobus rectangulis E G k, R S F, ſe-
              <lb/>
            cundæ: </s>
            <s xml:id="echoid-s2068" xml:space="preserve">item duo rectangula M I L, primæ, æquan-
              <lb/>
            tur duobus rectangulis L O M, N P Q, ſecundæ;
              <lb/>
            </s>
            <s xml:id="echoid-s2069" xml:space="preserve">vnde omnia quatuor rectangula primæ, æquantur
              <lb/>
            quatuor rectangulis ſecundæ. </s>
            <s xml:id="echoid-s2070" xml:space="preserve">Ergo etiam rectangu-
              <lb/>
            lum L M Q, primæ, æquabitur rectangulis E G k; </s>
            <s xml:id="echoid-s2071" xml:space="preserve">
              <lb/>
            L O M; </s>
            <s xml:id="echoid-s2072" xml:space="preserve">N P Q; </s>
            <s xml:id="echoid-s2073" xml:space="preserve">R S F, ſecundæ. </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">aimilla
              <lb/>
            circularis L M Q, ſolidi primæ figuræ, æquabitur
              <lb/>
            armillis circularibus E G k; </s>
            <s xml:id="echoid-s2076" xml:space="preserve">R S F, & </s>
            <s xml:id="echoid-s2077" xml:space="preserve">circulis
              <lb/>
            L O M, N P Q, ſecundæ. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Cumautem puncta I,
              <lb/>
            & </s>
            <s xml:id="echoid-s2079" xml:space="preserve">E, ſumpta ſint ad libitum, inuentaque ſit æqua-
              <lb/>
            litas inter plana prædicta; </s>
            <s xml:id="echoid-s2080" xml:space="preserve">rectè deducemus, necdum
              <lb/>
            omnes armillas circulares ſolidi primæ figuræ plano
              <lb/>
            A G, parallelas, ęquales eſſe omnibus armillis cir-
              <lb/>
            cularibus, & </s>
            <s xml:id="echoid-s2081" xml:space="preserve">omnibus circulis ſolidorum ſecundæ; </s>
            <s xml:id="echoid-s2082" xml:space="preserve">
              <lb/>
            ſed etiam ſolidum primæ ęquari omnibus ſolidis ſe-
              <lb/>
            cundæ.</s>
            <s xml:id="echoid-s2083" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2084" xml:space="preserve">Quod autem probatum fuit de totis, patet eo-
              <lb/>
            dem modo probari poſſe de partibus proportionali-
              <lb/>
            bus; </s>
            <s xml:id="echoid-s2085" xml:space="preserve">quia non diſſimili modo probabimus partem ſo-
              <lb/>
            lidi primæ contentam inter plana parallela L Q,
              <lb/>
            A G, ęquari parti ſolidorum ſecundæ, </s>
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