equation

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The act or process of equating or of being equated.
2. n. The state of being equal.
3. n. Mathematics A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign.
4. n. Chemistry A representation of a chemical reaction, usually written as a linear array in which the symbols and quantities of the reactants are separated from those of the products by an equal sign, an arrow, or a set of opposing arrows.
5. n. A complex of variable elements or factors: "The world was full of equations . . . there must be an answer for everything, if only you knew how to set forth the questions” ( Anne Tyler).

Century Dictionary and Cyclopedia

1. n. A making equal, or an equal division; equality.
2. n. In mathematics, a proposition asserting the equality of two quantities, and expressed by the sign = between them; or an expression of the same quantity in two terms dissimilar but of equal value: as, 3 lb. = 48 oz.; x = b + m − r. In the latter case x is equal to b added to m with r subtracted from the sum, and the quantities on the right hand of the sign of equation are said to be the value of x on the left hand. An equation is termed simple, quadratic, cubic, or biquadratic, or of the 1st, 2d, 3d, or 4th degree, according as the index of the highest power of the unknown quantity is one, two, three, or four; and generally an equation is said to be of the 5th, 6th, nth, etc., degree, according as the highest power of the unknown quantity is of any of these dimensions.
3. n. In astronomy, the correction or quantity to be added to or subtracted from the mean position of a heavenly body to obtain the true position; also, in a more general sense, the correction arising from any erroneous supposition whatever.
4. n. In chem., a collection of symbols used to indicate that two or more definite bodies, simple or compound, having been brought within the sphere of chemical action, a reaction will take place, and new bodies be produced. The symbols of the bodies which react on each other form the left-hand member of the equation, and are connected by the sign of equality with the symbols of the products of the reaction. It is called an equation because the weight of the substances reacting must exactly equal the weight of the products of reaction.
5. n. An equation for the steady motion of a liquid, namely, where p is the pressure, ρ the density, V the potential of the impressed forces, q the velocity, and C a constant for each stream-line and vortex-line, and in the case of irrotational motion a constant for all space.
6. n. with modern writers, a solution which is a particular case of the general solution;
7. n. with older writers, any solution not general. A singular solution is one which is neither general nor implied in the general solution. The complete integral of a partial differential equation is a solution containing the full number of arbitrary constants or functions.
8. n. In modern writings, the correction to be applied to the position of a planet or to the time of an eclipse, etc., owing to the finite velocity of light.
9. n. In modern astron., the excess of the true over the mean anomaly. (Gauss, Theoria Motus, I. 7.)
10. n. The equation of the argument. (Kepler, De Motibus Martis, I. iv.)
11. n. Any one of the usual equations of hydrodynamics, where the components of the velocity at fixed points of space are taken as variables: so called in contradistinction to the Lagrangian equations where the coordinates of a definite particle are taken as variables; these equations, though also discovered by Euler, having been used by Lagrauge.
12. n. A general equation of hydrodynamics, in which, instead of considering the velocity at each fixed point of space, the motion of each particle is followed out. This is called a Lagrangian equation because used by Lagrange in his “Méchanique Analitique,” though invented by Euler.
13. n. An equation of analytical geometry in which certain curves are represented by single letters. Thus, if U = 0, V = 0, W = 0, represent the equations of three circles, UV = W is the symbolic equation of a bicircular quartic
14. n. In the calculus, an equation which contains no differentials.

Wiktionary

1. n. mathematics An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
2. n. astronomy A small correction to observed values to remove the effects of systematic errors in an observation.

GNU Webster's 1913

1. n. A making equal; equal division; equality; equilibrium.
2. n. (Math.) An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them
3. n. (Astron.) A quantity to be applied in computing the mean place or other element of a celestial body; that is, any one of the several quantities to be added to, or taken from, its position as calculated on the hypothesis of a mean uniform motion, in order to find its true position as resulting from its actual and unequal motion.

WordNet 3.0

1. n. the act of regarding as equal
2. n. a state of being essentially equal or equivalent; equally balanced
3. n. a mathematical statement that two expressions are equal