## Definitions

### from The American Heritage® Dictionary of the English Language, 4th Edition

• adj. Of or relating to the fourth degree.
• n. An algebraic equation of the fourth degree.

• adj. Of a polynomial expression, involving only the second and fourth powers of a variable, as x4 + 3x2 + 2. Sometimes extended to any expression involving the fourth power of variable (but no higher powers), as x4 − 4x3 + 3x2 − x + 1.

### from The Century Dictionary and Cyclopedia

• Containing or referring to a fourth power, or the square of a square; quartic.
• n. In mathematics, the fourth power, arising from the multiplication of a square number or quantity by itself.

• n. an equation of the fourth degree
• adj. of or relating to the fourth power
• n. an algebraic equation of the fourth degree
• n. a polynomial of the fourth degree

## Examples

• He however extended and developed it, and after his pupil Ferrari had discovered the solution of the biquadratic equation by means of the cubic, he felt justified in publishing it.

The Catholic Encyclopedia, Volume 3: Brownson-Clairvaux

• The solution of cubic and of biquadratic equations, at first only in certain particular forms, but later in all forms, was mastered by

The Age of the Reformation

• [534] Thomas Baker (c. 1625-1689) gave a geometric solution of the biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684).

A Budget of Paradoxes, Volume II (of II)

• Modern, Sixteenth-Century attention to this ancient matter, as by Cardano and his followers, introduced the modern issues of cubic and biquadratic algebraic functions in an attempted algebraic form.

LaRouche's Latest

• However, the Eighteenth-Century defenders of the incompetence of both Descartes and Newton, such as de Moivre, D'Alembert, Euler, and Lagrange, claimed to have proven their case against Leibniz, by simply accepting de Moivre's proposal that they agree to denounce what they termed, fraudulently, as "imaginary" roots of the relevant cubic and biquadratic functions.

LaRouche's Latest

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Rational Review

• The different positions of FH are determined, by the roots of a biquadratic equation.

Outlines of Natural Philosophy: Being Heads of Lectures Delivered in the University of Edinburgh

• Or if you want to find the roots of the biquadratic without taking away the fccond term 1 fuppofe it to be of this fornix and the values of x will be

A Treatise of Algebra: In Three Parts ; Containing

• After the fame manner you may find like Theorems for the roots of biquadratic equa - tions, or of equations of any dimcnfion whatever.

A Treatise of Algebra: In Three Parts ; Containing

• 'Thus any cubic equation may be conceived as generated by the multiplication of/i&r« fimple equations, or of one quadratic and one fimple equafion« A biquadratic as generated by the ilitikiplication of four Jimple equations, or of two quadratic equations \ or ladly) of one cubic and one Jimpk equation ..' '

A Treatise of Algebra: In Three Parts ; Containing