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The operation of reducing to a lower degree; -- said of equations.

em which admits of a limited number of solutions. -- Determinate quantities, Determinate equations (Math.), those that are finite in the number of values or solutions, that is, in which the conditions of the problem or equation determine the number.

ial, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.

ate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x2 + y2 an exact square.

on is the great safeguard of all other liberties. Macaulay. Discussion of a problem or an equation (Math.), the operation of assigning different reasonable values to the arbitrary quantities and interpreting the result. Math. Dict.

The result of eliminating n variables between n homogeneous equations of any degree; -- called also resultant.

To cause to disappear from an equation; as, to eliminate an unknown quantity.

Act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.

n inequality of the moon's motion is its orbit to the attraction of the sun, by which the equation of the center is diminished at the syzygies, and increased at the quadratures by about 1º 20'.

The process of finding the roots of an equation. [Obs.]

To state in enlarged form; to develop; as, to expand an equation. See Expansion, 5.

l function. Exponential curve, a curve whose nature is defined by means of an exponential equation. -- Exponential equation, an equation which contains an exponential quantity, or in which the unknown quantity enters as an exponent. -- Exponential quantity (Math.), a quantity whose exponent is unknown or variable, as…

Family of curves or surfaces (Geom.), a group of curves or surfaces derived from a single equation. -- In a family way, like one belonging to the family. "Why don't we ask him and his ladies to come over in a family way, and dine with some other plain country gentlefolks" Thackeray. -- In the family way, pregnant. [C…

mon asymptote. The curve has a double point, and a leaf-shaped loop; whence the name. Its equation is x3 + y3 = axy.

f x. Algebraic function, a quantity whose connection with the variable is expressed by an equation that involves only the algebraic operations of addition, subtraction, multiplication, division, raising to a given power, and extracting a given root; -- opposed to transcendental function. -- Arbitrary function. See und…

d; as, a gruphic writer. Graphic algebra, a branch of algebra in which, the properties of equations are treated by the use of curves and straight lines. -- Graphic arts, a name given to those fine arts which pertain to the representation on a fiat surface of natural objects; as distinguished from music, etc., and also…

se it is impossible to have the idea of body without that of solidity. Fleming. Identical equation (Alg.), an equation which is true for all values of the algebraic symbols which enter into it.

An identical equation.

Wanting any of the usual floral organs; -- said of a flower. Incomplete equation (Alg.), an equation some of whose terms are wanting; or one in which the coefficient of some one or more of the powers of the unknown quantity is equal to 0.

te some artifice of analysis. Their values are subsequently determined. -- Indeterminate equation (Math.), an equation in which the unknown quantities admit of an infinite number of values, or sets of values. A group of equations is indeterminate when it contains more unknown quantities than there are equations. -- I…