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9-tuple focus A B the inequalities absolutely convergent Analytic Coefficients analytic solutions analytic throughout Cartesian Oval compute connected region continuous function continuous real functions convergent series convergent throughout CORNELL UNIVERSITY LIBRARY derivative vanishes differential equation Equations with Analytic exist which satisfy ExISTENCE THEOREM foci invert focus at infinity follows at once four tangents fourth focus initial conditions interval A B last section nodal bicircular quartic Non-Singular Points ║ CORNELL UNIVERSITY ║ ║ CORNELL point of A B positive constant positive quantity proof just given q are analytic q are continuous quantity satisfying real analytic functions real foci real single finite real triple focus real variable region throughout ſ p(x)y satisfies equation satisfies the differential satisfies the initial series 2c series converges single finite foci single foci ſ║ solutions obtained THEORY OF LINEAR throughout an interval throughout the interval vanish throughout whole interval