Tangarat

Same as Tanagra. Bri on, 1760. tangence (tan'jens), n. [F. tangence; as tangen(t) + -ce.] Same as tangency. tangency (tan'jen-si), n.; pl. tangencies (-siz). [As tangence (see -cy).] The state of being tangent; a contact or touching. Also called taction.-Problem of tangencies, among the old ge ometers, a branch of the geometrical analysis, the general object of which was to describe a circle pa ing through given points, and touching straight lines or circles given in position, the number of data being always limited to three. tangent (tan'jent), a. and n. [= F. tangent = Sp. Pg. It. tangente, E. tact, tactile, contact, contingent, etc.] I. a. Touching; in geom., touching at a single point: as, a tangent line; curves tangent to each other. -Stationary tangent plane of a surface. See stationary. Tangent plane, a plane which touches a curved surface, as a sphere, cylinder, etc. II. n. 1. In geom .: ( a ) A straight line through two consecutive points (which see, under con secutive ) of a curve or surface. If we take the line through any two points of the locus, and then, while one of these points remains fixed, consider the other as brought by a continuous and not infinitely protracted motion along the locus into coincidence with the former, the line in its final position will be a tangent at that point. The idea of time which appears in this definition is only so far e ential that some parameter must be used in order to define a tangent at a singular point, and this parameter must be such as to present no discontinuity or point-singularity at that point. A tangent at an ordinary point of a curve or surface may be defined, without the use of any parameter, simply as a line through two points infinitely close together; although, if the doctrine of limits is used to explain away the idea of infinity, a parameter will be used for that purpose. A curve has only one tangent at an ordinary point, or a mere line-singularity, or a cusp, but IMG:content-2833.jpg:[blocks in formation] Tangent-The equation of the curve is y2=(1-x)2x3. a , ordinary tangent; b , nodal tangent; c , cuspidal tangent; d , inflectional tangent. has two or more tangents at a node. A surface has a single infinity of tangents lying in one plane at an ordinary point; and two of these (real or imaginary), called the inflectional tangents, pa through three or more consecutive points of the surface. On the nodal curve of a surface the tangents lie in two or more tangent planes; at a conical point they are generators of a quadric cone. The tangents of a curve in space form two sets which are all generators of one developable. There are points upon some curves and surfaces at which, according to the doctrine of limits, there are no tangents. Such is the point in the second figure where the two multiple tangents intersect; for, as a second point on the curve moves toward this, the line through the two points will oscillate faster and faster, without tending toward any limit. In the same sense, a curve may have no tangent Multiple Tangents. at any may be dulating line with small un dulations on the large ones, and still smaller on these, and so on ad infinitum, the lengths and amplitudes of the undula tions being duly proportioned. But an intelligence situated on such a curve might see that the tangent had a definite direction, for there is no logical absurdity in this. It is antagonistic to the principle of duality which rules modern geometry define the tangent of a plane curve as the line through two consecutive points on the curve. On the contrary, the definition of a plane curve is a locus de scribed by the parametric motion of a line with a point upon it, the point slipping along the line and the line turning about the point; and such a generating line is a tangent. In like manner, a surface is the locus formed by a plane with a point upon it, the position of the point in the surface and the aspect of the surface about the point varying, the one and the other, according to the variations of the same pair of independent parameters. Such a plane is a tangent plane, and a tangent may equally be conceived as through two consecutive points, or as the line of intersection of two consecutive tangent planes. The tangent plane of a spacious curve is a line lying in a plane and having a point upon it, the plane turning continuously about the line, the point 6179 strings, and produce tones. Its action was not like that of the pianoforte-hammer, since it remained in contact with the string, and fixed the pitch of the tone by the place where it struck. If pre ed too hard, it raised the pitch by increasing the string's tension. Accordingly the tone of the clavichord was nece arily weak. - Artificial tangents. See artificial. - Chief tangent, a tangent to a surface which is also a tangent of the intersection of the surface by the tangent plane at the same point of tangency. - Conjugate, cotriple, double, imaginary, inflectional tangent. See the adjectives. - Ideal tangent, a real line touching a real curve at two imaginary points. Inverse method of tangents, the method of finding the curve belonging to a given tangent. -- Method of tangents. (a) A method of obtaining the quadrature of a curve by means of an evaluation of the tangent to it, due to Roberval. (b) Any method of drawing a tangent to a curve. - Multiple tangent. See multiple.-Natural tangents, tangents expre ed by natural numbers. -Principal tangent, a tangent bisecting the angle between the chief tangents at the point of tangency.-Principal tangent conic. See conic. Stationary tangent of a curve. See stationary. - Tangent balance, a balance in which no weights are used, but the position of the beam, as indicated by a pointer moving over a graduated scale, shows the weight: chiefly used for weighing letters. Also called bent-lever balance. - Tangent Tangent Balance. galvanometer. See galvanometer. Tangent sailing. Same as middle - latitude sailing. See latitude. Tangent scale, in ordnance, a notched piece of metal fitted to slide cir cum fere non the of a piece of ar Tangent Scale. tillery, the notches being at stated distances from the axis of the gun. In sighting, the scale is turned till one of its notches corresponding to the desired elevation or range is brought into intersection with the plane of the trajectory. - Tangent screw, a screw attached to or forming part of a clamp, and serving to move pieces clamped together relatively to one another with a slow motion. - To fly or go off at a tangent, to pa suddenly from one line of action or train of thought to another diverging widely from the first. From Dodson and Fogg's it [his mind] flew off at a tan gent to the very center of the history of the queer client. Dickens , Pickwick Papers, xxii. tangent (tan'jent), v. t. [ The velocity is as the square of the time, and the curve is therefore a parabola tangent ing the time with its ver tex at the start of motion. Nystrom, Elem. of Mechanics, p. 158.