USED IN THE MATHEMATICAL SCIENCES. Abbreviation, in Arithmetic, &c. the reducing of Fractions to lower terms. Aberration, in Astronomy, an apparent motion of the celestial bodies. Absciss, or Abscissa, is a part or segment cut off from a line, terminated at some certain point, by an ordinate to a curve. Absolute Number, in Algebra, that term or number of an equation, that is completely known. Abundant Number, in Arithmetic, a number the sum of whose aliquot parts is greater than the number itself. Accelerated Motion, that which receives fresh accessions of velocity, either uniform or variable. Adjacent angle, in Geometry, an angle which is immediately contiguous to another, so that they have one common side, Affected or Adfected Equation, in Algebra, one which contains two, or more several powers of the unknown quantity. Affirmative or Positive quantity; one, which is to be added, or taken effectively. Algebra, a method of performing the calculations of all kinds of quantities by means of general signs or characters. Aliquot part, such a part of a number as will exactly divide it without a remainder. Allernation or Permutation of quantities, the varying or changing the order or position of them. Analysis, the method of resolving problems by reducing them to equations. Angle in geometry, the mutual inclination of two lines, or two planes. Approximation, a continual approach, nearer and nearer to a root or any quantity sought. Apses or Apsides, are the two points in the orbits of planets, when they are at their greatest and least distance from the sun or the earth, and the line which joins them is called the sign of Apsides. Asymptote, properly a right line which approaches nearer and nearer to some curve, or it may be considered as a tangent to the curve, when conceived to be infinitely produced. Axiom, a self-evident truth, or a proposition immediately asserted to, when the terms of it are properly understood. Aris, in Geometry, the straight line in a plain figure, about which it revolves, to generate a solid. Binomial, a quantity consisting of two terms or members connected by the sign+or —. Biquadratic Equation, one in which the unknown quantity rises to the 4th power. Bisection, the division of a quantity into two equal parts. Catenary, a curve line into which a chain or cord forms itself, by hanging freely from two points of suspension. Catoptrics, that part of Optics which explains the laws and properties of light reflected from Specula. Centre of Gravity, that point about which all the parts of a body in any situation exactly balance each other. Characteristic, of a logarithm, the same as Index or Exponent. Chord, a right line, connecting the two extrems of an arc. Circumgyration, the revolving motion of any body about a centre. Coefficients in Algebra, numbers or given quantities usually prefixed to letters or unknown quantities, by which they are multiplied. Combinations, the alterations or variations of any number of quantities, &c. in all possible ways. Commensurable quantities or magnitudes, such as have some common aliquot part, or which may be measured or divided without a remainder, by the same measure or divisor. Common, applied to an angle, line, measure, or the like, that belongs to two or more figures, &c. Compasses, a Mathematical instrument for describing circles, measuring and dividing lines, &c. Complement, in general, what is wanting or necessary to complete some certain quantity or thing. Composite number, one that is compounded of, or made up by the multiplication of, two other numbers, greater than 1. Compound quantities, in Algebra, such as are connected together by the signor — Concavity, that side of a figure or body which is hollow. Concentric, having the same centre. Conchoid or Conchiles, the name of a curve, invented by Nicomedes. Concrete numbers, are those that are applied to express, or denote any particular subject, as 3 men, 2 pounds. Concurring or Congruent figures, in Geometry, are such as, being laid upon one another, do exactly coincide. Condensation, the compressing or reducing a body into less bulk, or space, whereby it becomes more dense. Cone, a kind of round pyramid, or a solid body having a circle for its base, and its sides formed by right lines drawn from the circumference of the base to a point at top, being its vertex. Conic Sections, the figures made by cutting a cone by a plane. Conoid, a figure resembling a cone, except that the slant sides from the base to the vertex are not straight lines, as in the cone, but curved. Consequent, the latter of the two terms of a ratio. Constant quantities, such as remain invariably the same, while others increase or decrease. Construction, in Geometry, the art or manner of drawing or describing figures, the lines of a problem, &c. Contact, Angle of, the opening between a curve line and a tangent to it, particularly the circle and its tangent. Continued Proportion, that in which the consequent of the first ratio is the same with the antecedent of the second, &c. Converging lines, such as continually approximate until they meet. Coverging series, a series of terms that always decrease the further they proceed, or which tend to a certain magnitude or limit. Convex, round or curved and protuberant on the surface. Coordinates, the general term used, when the abscissa and ordinates of a curve are considered corresponding, whether they are at right angles with each other or not. Corollary, a consequence drawn from some proposition or principles already advanced or demonstrated, without the aid of any other proposition. Cubature of a solid, the measuring of the space contained in it, or finding the solid content of it. Cube, a regular solid body, enclosed by six equal sides or faces, which are squares. Curve, a line whose several parts proceed bowing, or tend different ways. Curvilinear Angle, figure, superficies, &c. such as are formed or bounded by curves. Cycloid, a curve, conceived to be described by a point in the circumference of a wheel, moving forward in a straight line. Cylinder, a solid having two equal circular ends, and every plane section parallel to the ends, a circle equal to them also. Cylindroid, a solid resembling a cylinder, but differing from it, in having ellipses for its ends or bases. Decagon, a plane geometrical figure of ten sides, and ten angles. Declination, the distance of the sun, star, &c. from the Equinoctial, either northward or southward. Diagonal, a right line drawn across a figure, from one angle to another. Diagram, a scheme for the explanation or demonstration of any figure or of its properties. Differential, an indefinitely small quantity, part, or difference, called also an Infinitesimal. Differential method, a method of finding quantities by means of their successive differences. Dimension, the extension of a body considered as measurable, also used with regard to the power of quantities in equations. Diophantine problems, certain questions relating to square and cubic numbers, and to right angled triangles. Dioptrics, that part of Optics, which explains the effects of light as refracted by passing through different mediums. Directrix, a particular right line, perpendicular to the axis of a Conic Section. Dirigent, a term expressing the line of motion, along which a dis cribent line, or surface is carried in the genesis of any plane or solid figure. Disc, the body or face of the sun or moon, such as it appears to us. Divergent or Diverging lines, those whose distance is continually increasing. Dodecagon, a regular polygon of twelve equal sides and angles. Duodecimals, a kind of multiplication in Arithmetic by which artifi cers square their dimensions. Duplicate ratio, the square of a ratio, or the ratio of the squares of two quantities. Dynamics, the science of moving powers. Elimination, in Algebra, that operation by which any number n of equations, containing n unknown quantities, are reduced to one equation involving only one unknown quantity. Ellipse or Ellipsis, one of the Conic Sections, popularly called an an oval. Elliptoid, an infinite or indefinite Ellipse. Epicycloid, a curve generated by the revolution of a point of the periphery of a circle, which rolls along or upon the circumference of another circle. Equation, in Algebra, an expression of equality between two different quantities. Equimultiples, the products of quantities equally multiplied. Excentric, a term applied to such figures, circles, &c. as have not the same centre. Excess, in Trigonometry, the excess of the sum of the three angles of any spherical triangle, above two right angles. Exponent, the number of quantity expressing the degree or elevation of the power. Expression, any Algebraical quantity, simple or compound. Extermination, the taking away of certain unknown quantities from depending equations, so as to have only one equation and one unknown quantity. Factors, a name given to two numbers that are multiplied together. Fluent, the variable quantity, in the doctrine of Fluxions, which is considered as increasing or decreasing. Fluxion, the rate or proportion at which a flowing or varying quantity eacreases its magnitude or quantity. Focus, a certain point in the Ellipse, Hyperbola, and Parabola, where the rays reflected from all parts of these curves concur, or meet. Function, an Algebraical expression any how compounded of a certain letter or quantity with other quantities or numbers, said to be a function of that letter or quantity. Generating line or figure, that which by any kind of supposed motion, may generate or produce some other figure, plane, or solid. Half-Tangents, the tangents of the half arcs. Heptagon, a figure of seven sides and angles. Hexagon, a figure of six sides and angles. Homologous, in Geometry, applied to the corresponding sides of similar figures |