| 释义 |
secant, a. and n.|ˈsiːkənt|
[a. L. secant-em, pres. pple. of secāre to cut. Cf. F. sécant adj., sécante n., Sp., Pg., It. secante.]
A. adj. Geom. Of a line or surface in relation to another line or surface; Cutting, intersecting.
1593Blundevil Exerc. ii. (1597) 57 b, They call the line Secant the Hipothenuse. 1864Webster, Secant plane, a plane cutting a surface or solid. 1866Proctor Handbk. Stars 16 By increasing the true length in the proportion of the whole length of the secant line..to that part of it which lies between the point of projection and the division-point in P.A.
B. n. (Ellipt. for secant line.)
a. Trig. One of the three fundamental trigonometrical functions (cf. tangent, sine): orig. The length of a straight line drawn from the centre of a circular arc through one end of the arc, and terminated by the tangent or line touching the arc at the other end; in mod. use, the ratio of this line to the radius, or (equivalently, as a function of an angle), the ratio of the hypotenuse of a right-angled triangle to that of one side, the given angle (or, if obtuse, its supplement) being that contained between them. Abbrev. sec. See secans.
1593Blundevil Exerc. ii. (1597) 104 The Table of Secants. 1681S. Colvil Whigs Supplic. (1751) 23 In which scheme if ye draw some lines, Ye may have secants, tangents, signs. 1752Phil. Trans. XLVII. 443 We have..to find..the secant of the spherical hypothenuse. 1811Hutton Course Math. III. 55 The secant of an arc. 1868Lockyer Elem. Astron. §516. 243 The secant of A (written sec. A).
b. Geom. A line that cuts another; esp. a straight line that cuts a curve in two or more parts.
1684Elem. Geom. 24 From the Center D, draw the Secant DC. 1728Chambers Cycl. s.v., The Line AM..is a Secant of the Circle AED. 1798Hutton Course Math. I. 304 The Angle formed, Without a Circle, by two Secants, is Measured by Half the Difference of the Intercepted Arcs. 1881Casey Sequel to Euclid 92 If from any point two tangents be drawn to a circle, the points of contact and the points of intersection of any secant from the same point form a harmonic system of points. 1887J. H. Smith Geometr. Conic Sect. 18 Hence a secant to the parabola cuts the curve in two points only. |