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virtue of its actual condition, without any supply of energy from without. -- Intrinsic equation of a curve (Geom.), the equation which expresses the relation which the length of a curve, measured from a given point of it, to a movable point, has to the angle which the tangent to the curve at the movable point makes…

rreducible formula. Irreducible case (Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application. -- Ir`re*du"ci*ble*ness, n. -- -- Ir`re*du"ci*bly, adv.

ing. Lateral cleavage (Crystallog.), cleavage parallel to the lateral planes. -- Lateral equation (Math.), an equation of the first degree. [Obs.] -- Lateral line (Anat.), in fishes, a line of sensory organs along either side of the body, often marked by a distinct line of color. -- Lateral pressure or stress (Mech.)…

A curve of the fourth degree, invented by Pascal. Its polar equation is r = a cos + b.

throughout, except at the extremities; as, a linear leaf. Linear differential (Math.), an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients. -- Linear equation (Math.), an equation of the first degre…

act (Law), contract of which the whole evidence is given in writing. Bouvier. -- Literal equation (Math.), an equation in which known quantities are expressed either wholly or in part by means of letters; -- distinguished from a numerical equation.

A spiral whose polar equation is r2th = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.

s, the menstrual revolution of the moon; pertaining to monthly changes; as, the menstrual equation of the sun's place.

in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement.

Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation. Artificial order or system. See Artificial classification, under Artificial, and Note to def. 12 above. -- Close order (Mil.), the arrangement of the ranks with a distance of about half a pace between them; with a distance o…

One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.

The division of the terms of an equation by a known quantity that is involved in the first term. [Obs.]

y, or the specific recovery of goods or chattels; -- opposed to real action. -- Personal equation. (Astron.) See under Equation. -- Personal estate or property (Law), movables; chattels; -- opposed to real estate or property. It usually consists of things temporary and movable, including all subjects of property not…

The system of equations required for the complete expression of the relations which exist between a set of quantities. Brande & C.

its poles, particularly of a heavenly body from the north pole of the heavens. -- Polar equation of a line or surface, an equation which expresses the relation between the polar coördinates of every point of the line or surface. -- Polar forces (Physics), forces that are developed and act in pairs, with opposite ten…

Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.

That branch of algebra which treats of quadratic equations.

o the substitution of reciprocals for given quantities. See the Phrases below. Reciprocal equation (Math.), one which remains unchanged in form when the reciprocal of the unknown quantity is substituted for that quantity. -- Reciprocal figures (Geom.), two figures of the same kind (as triangles, parallelograms, prisms…

gent. When hydrogen is used the product is called also iron by hydrogen. -- To reduce an equation (Alg.), to bring the unknown quantity by itself on one side, and all the known quantities on the other side, without destroying the equation. -- To reduce an expression (Alg.), to obtain an equivalent expression of simpl…

The act or process of reducing. See Reduce, v. t., 6. and To reduce an equation, To reduce an expression, under Reduce, v. t.