In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.
Running through these volumes in order, we have in the second the memoir, Summatio quarundam serierum singularium, the memoirs on the theory of biquadratic residues, in which the notion of complex numbers of the form a--bi was first introduced into the theory of numbers; and included in the Nachlass are some valuable tables.
He was professor of mathematics in the university of Deseret and wrote several books on this subject, these including Cubic and Biquadratic Equations (1866).
BIQUADRATIC (from the Lat.
In mathematics, the biquadratic power or root of a quantity is its fourth power or root (see ALGEBRA); a biquadratic equation is an equation in which the highest power of the unknown is the fourth (see EQUATION: Bgquadratic).