The Solution of Equations

abscissas ALEXANDER MACFARLANE algebraic equation algebraic solution applied approximate value Compute the roots Crelle's Journal cubic equation curve decimal places derivative equation determined equa equal roots equation f(x equation whose roots equation x³ expressed feet four roots given equation given quintic hence hyperbola imaginary cube roots imaginary fifth roots infinite equation infinite number intersections J₁ Maclaurin's formula MANSFIELD MERRIMAN mathematical negative roots Newton's rule nth degree nth root number of real numerical values obtained Prob quadratic equation quartic equation real root lies reduced regula falsi required to find root OX roots of unity s₁ S₂ second term series is convergent solvable squares Sturm's theorem substituting symmetric functions table of sines three real roots three roots three values tion TRANSCENDENTAL EQUATIONS trigonometric solution trinomial equation unknown quantity values of f(x whence x₁ Y₁