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).