Tangent
in geometry, a straight line which meets or touches a circle or curve in one point, and which, being produced, will not cut it. In Euclid (III. 16, Cor.) it is proved that any line drawn at at its extremity is a tangent to the circle. right angles to the diameter of a circle In trigonometry, the tangent of an arc or angle is a straight line, touching the circle of which the arc is a part at one extremity of the arc, and meeting the diameter passing through the other extremity; or it is that portion of a tanarc, and limited by a secant drawn gent drawn at the first extremity of an arc, and limited by a secant drawn through the second extremity. The tan- gent is always drawn through the initial extremity of the arc, and is reckoned positive upward, and consequently, negative downward. The tangent of an arc or angle is also the tangent of its supplement. The arc and its tangent have always a certain relation to each other, and when the one is given in parts of the radius, the other can always be computed by means of an infinite series.
Tables of tangents for every arc from 0° to 99°, as well as of sines, cosines, etc., are computed and formed into tables for trigonometrical curves are tangent to each other at a common point, when they have a common gent plane to a curved surface is the limit of all secant planes to the surface through the point. The point is called the point of contact. Two surfaces are tangent to each other when they have, at least, one point in common; through which, if any number of planes be passed, the sections cut out by each plane will be tangent to each other at the point.
Another definition is this: Two surfaces This point is called the point of contact. purposes.
Two TANGENT are tangent to each other when they have a common tangent plane at a common point. This point is the point of contact.
Artificial tangents, tangents expressed by logarithms. Methods of tangents, the name given to the calculus in its early period. When the equation of a curve TANKS TANJORE (native, Tanjúr, or Tanjávúr), a town of India, capital of a district in the Madras province. 180 miles S. S. W. of Madras city, in the midst of an extensive plain, on one of the branches of the lower Kaveri. The principal edifices of Tanjore are the palace of the old rajahs, a dismantled fort and the is given, and it is required to determine Great Pagoda. This last has a perpenthe tangent at any point, this is called dicular part 2 stories in height, 82 feet the direct method of tangents, and when square, and above that 13 stories, formthe subtangent to a curve at any point ing an elongated pyramid about 100 feet is given, and it is required to determine high. The basement section is simple the equation of the curve, this is termed in outlines, but adorned by niches and the inverse method of tangents. These pilasters; the pyramidal portion is someterms are synonymous with the differ- what elaborately sculptured; and the ential and integral calculus. Natural whole is crowned by a dome (said to tangents, tangents expressed by natural consist of a single stone), which brings numbers. To go (or fly) off at a tangent, the total height to 190 feet. The temple to break off suddenly from one course stands in one of two great courtyards of action, line of thought, or the like, and go on to something else.
TANGHIN (Tanghinia venenifera), a tree of Madagascar, natural order Apocyпacex, bearing a fruit the kernel of which, about the size of an almond, is the 14th century. Silks, jewelry, carhighly poisonous. Trial by tanghin was formerly used in Madagascar as a test of the guilt or innocence of a suspected criminal. The person undergoing the ordeal was required to swallow a small portion of the kernel. If his stomach rejected it he was deemed innocent, but if he died, as happened in most cases, and in the same court stand several small shrines, one of which is so beautifully carved as to rival in interest the great temple. The date of the latter is not certainly known, but is with much probability referred to the beginning of pets, copper vessels, and artistic models in clay, etc., are manufactured. Pop. about 60,500.