secantadj.n.
/ˈsiːkənt/ A. adj. Geometry.
Of a line or surface in relation to another line or surface; Cutting, intersecting.
ΘΚΠ
the world > relative properties > number > geometry > line > [adjective] > relating to intersection
secant1594
intercept1716
1594 T. Blundeville Exercises ii. f. 55 v They call the line Secant the Hipothenuse.
1864 Webster's Amer. Dict. Eng. Lang. Secant plane, a plane cutting a surface or solid.
1866 R. A. Proctor 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. (Elliptical for secant line.)
a. Trigonometry. One of the three fundamental trigonometrical functions (cf. tangent n. 1a, sine n.2 2a): originally. 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 modern 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. Abbreviated sec. See secans n.
ΘΚΠ
the world > relative properties > number > geometry > [noun] > branches of > trigonometry > functions of
right sine1581
sine1593
secant1594
tangent1594
secans1599
cosine1635
cotangent1635
cosecant1706
sec.-
1594 T. Blundeville Exercises ii. f. 102 The Table of Secants.
1681 S. Colvil Mock Poem (1751) 23 In which scheme if ye draw some lines, Ye may have secants, tangents, signs.
1753 Philos. Trans. 1751–2 (Royal Soc.) 47 443 We have..to find..the secant of the spherical hypothenuse.
1811 C. Hutton Course Math. III. 55 The secant of an arc.
1868 J. N. Lockyer Elem. Lessons Astron. §516. 243 The secant of A (written sec. A).
b. Geometry. A line that cuts another; esp. a straight line that cuts a curve in two or more parts.
ΘΚΠ
the world > relative properties > number > geometry > line > [noun] > which divides or intersects
midlinea1398
secant1684
section1820
bisectrix1854
ground-line1857
secancy1857
transversal1881
1684 Elem. Geom. 24 From the Center D, draw the Secant DC.
1728 E. Chambers Cycl. Secant, in Geometry, a Line that cuts another, or divides it into Two Parts.
1798 C. Hutton Course Math. I. 304 The Angle formed, Without a Circle, by two Secants, is Measured by Half the Difference of the Intercepted Arcs.
1881 J. Casey 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.
1887 J. H. Smith Geometr. Conic Sect. 18 Hence a secant to the parabola cuts the curve in two points only.
This entry has not yet been fully updated (first published 1911; most recently modified version published online March 2022).
<
adj.n.1594