| 释义 |
▪ I. tangent, a. and n.|ˈtændʒənt|
[ad. L. tangens, tangent-em, pr. pple. of tang-ĕre to touch; used by Th. Fincke, 1583, as n. in sense = L. līnea tangens tangent or touching line. In F. tangent, -e adj., tangente n. (Geom.), Ger. tangente n.]
A. adj.
1. a. Geom. Of a line or surface in relation to another (curved) line or surface: Touching, i.e. meeting at a point and (ordinarily) not intersecting; in contact. Also as quasi-adv.
A surface may also be tangent to another surface along a line (e.g. a plane in contact with a cylinder). In quot. 1869, Taking place along a tangent. Cf. B. 1 b.
1594Blundevil Exerc. ii. (1597) 48 b, Our moderne Geometricians haue of late inuented two other right lines belonging to a Circle, called lines Tangent, and lines Secant. 1644Digby Nat. Bodies xiii. §8. 114 The reflexion must follow the nature of tangent surfaces. 1713Berkeley Guard. No. 126 ⁋2 Hence..the earth,..without flying off in a tangent line, constantly rolls about the sun. 1866Proctor Handbk. Stars 33 The cone, instead of being a tangent-cone, is supposed to be a secant-cone, intersecting the sphere. 1869Tyndall in Fortn. Rev. 1 Feb. 245 All the vibrations tangent to the little circle..are reflected perfectly polarized. 1876Catal. Sci. App. S. Kens. Mus. §102 Model exhibiting the simultaneous transformation..of the tangent paraboloid of the conoïd into the tangent plane of the cylinder. 1936A. W. Clapham Romanesque Archit. viii. 167 The subsidiary towers..at Mainz and Laach..are set axially and tangent at the ends of the transept. 1977Sci. Amer. Aug. 37/1 The radiation is emitted tangent to these trajectories.
†b. Cryst. Applied to a plane replacing an edge or solid angle of a crystal (which is more properly a secant plane). Obs.
1823H. J. Brooke Introd. Crystallogr. 109 Edges replaced by tangent planes. 1851Richardson Geol. v. 88 Crystals often present the appearance of having lost their edges and solid angles, which are then said to be replaced by tangent planes.
c. transf. Said of the wheel of a bicycle or tricycle having the spokes tangent to the hub.
1886Bicycling News 6 Aug. 664/1 Laced tangent wheels, hollow rims, Hancock's tyres.
2. fig. ‘Flying off at a tangent’ (see B. 1 c); divergent, erratic.
1787Burns Let. to Moore 23 Apr., If once this tangent flight of mine were over, and I were returned to my wonted leisurely motion in my old circle. 1799E. Du Bois Piece Family Biog. I. 152 The voluble loquacity and tangent style of reasoning of their new companion.
3. In general sense.
a. Touching, contiguous.
1846Ellis Elgin Marb. I. 107 Beaten together till the tangent surfaces were fitted to each other.
b. Of or pertaining to touch; tangent sense, sense of touch. nonce-use.
1802E. Darwin Orig. Soc. iii. 424 Say, did these fine volitions first commence From clear ideas of the tangent sense?
B. n.
1. Math. (ellipt. for tangent line.) [= Fr., Ger. tangente.]
a. Trig. One of the three fundamental trigonometrical functions (cf. secant, sine), originally considered as functions of a circular arc, now usually of an angle (viz. that subtended by such arc at its centre): orig. The length of a straight line perpendicular to the radius touching one end of the arc and terminated by the secant drawn from the centre through the other end; in mod. use, the ratio of this line to the radius, or (equivalently, as a function of the angle) the ratio of the side of a right-angled triangle opposite the given angle (if acute) to that of the side opposite the other acute angle (the tangent of an obtuse angle being numerically equal to that of its supplement, but of opposite sign). Abbrev. tan.
Tables of tangents and cotangents were constructed and used by the Arab mathematicians of the 9th and 10th c. (see Nallino Al Battani, Opus astronomicum, Milan 1903, i. 182); but began to be constructed in Christendom late in the 15th c. The names tangens and secans, introduced by Thos. Fincke (Finkius) in 1583, had no connexion with the names used by the Arabs.
[1583Fincke Geometriæ Rotundi v. 64 De semicirculi sinibus, tangentibus, secantibus. Ibid. 73 Recta sinibus connexa est tangens peripheriæ aut eam secans.] 1594Blundevil Exerc. ii. (1597) 57 b Of which Arke the line AD is the Tangent, and the line CD is the Secant thereof. 1635[see cotangent]. 1658Phillips, Tangent,..a Mathematical Term used chiefly in Astronomy,..signifies, a right line perpendicular to the Diameter drawn by the one extream of the given Arch, and terminated by the Secant. 1690Leybourn Curs. Math. 397 Which Scales of Tangents..let be extended to 75 deg. at least. 1728Pemberton Newton's Philos. 366 The refracting powers..will be in the duplicate proportion of the tangents of the least angles, which the refracted light can make with the surfaces of the refracting bodies. 1828Hutton Course Math. II. 3 As the arc increases from o, the sines, tangents, and secants, all proceed increasing, till the arc becomes a whole quadrant.., and then the sine is the greatest it can be..; and both the tangent and secant are infinite.
b. Geom. A straight line which touches a curve (or curved surface), i.e. meets it at a point and being produced does not (ordinarily) intersect it at that point. spec. in Surveying, a tangent to a curve at a point (tangent point) where the curve starts or finishes; freq. attrib., as tangent distance, tangent length, the length of such a tangent from the tangent point to its intersection with the other tangent.
In Higher Geometry a tangent is regarded as the limiting position of a line intersecting a curve when the two (or more) points of intersection coincide, and is hence defined as a straight line passing through two (or more) consecutive points of the curve. If the curve be conceived as traced by a moving particle, the tangent at any point of it represents the direction of motion at that point; hence a body moving in a curve, when the restraining force is withdrawn, flies off at a tangent, i.e. along the tangent (cf. the fig. use in c). At a point of inflexion, where the curvature (i.e. deviation from the straight line) changes its direction, the tangent intersects as well as touches the curve.
1655T. Gibson Syntaxis Math. xiii. 142 To draw a tangent [cf. 1551 Recorde Pathway, touche line] to any point assigned in any section, or from any point without the section. 1704J. Harris Lex. Techn. I, Tangent, of a Parabola, (or other Conick Section, or Geometrical Curve) is a Right Line Drawn, cutting the Ax Produced, and touching the Section in one Point without cutting it. 1706W. Jones Syn. Palmar. Matheseos 221 A Tangent to any point of the Circumference [of a circle] is Perpendicular to the Radius drawn to that Point. 1832Nat. Philos. II. Introd. Mech. p. xvi. (Usef. Knowl. Soc.), If a stone, whirled round in a sling, gets loose at the point A.., it flies off in the direction AB: this line is called a tangent. 1850T. Baker Rudimentary Treat. Land & Engin. Surveying ii. ii. 171 Find the radii, as BO, CO′; the tangent point, as C′; and the junction point, as C, with the position of the common tangent at the junction point. 1862W. J. M. Rankine Man. Civil Engin. i. v. 111 The places where permanent marks of the course of the line are chiefly required are on the tangents of curves. 1902R. E. Middleton et al. Treat. Surveying II. v. 61 Find length of tangent for a 3° curve with central angle of 35° 42′. 1978J. G. McEntyre Land Survey Systems x. 329 An easement curve is a transition curve utilized to increase the degree of curvature gradually from the tangent point to the circular portion of a curve. 1983J. C. McCormack Surveying Fundamentals xxi. 384 The tangent distances are taped from the P.I. [sc. point of intersection] down both tangents to locate the P.C. and P.T.
c. In general use, chiefly fig. from b, esp. in phrases (off) at, in, upon a tangent, i.e. off or away with sudden divergence, from the course or direction previously followed; abruptly from one course of action, subject, thought, etc., to another.
1771Smollett Humph. Cl. (1815) 219 After having twelve times described this circle, he lately flew off at a tangent to visit some trees at his country-house in England. 1815Paris Chit-Chat (1816) II. 92 The passengers on the roof, being at the highest point of projection flew off in a tangent, and were precipitated..into a field of new-mown hay. 1825Bentham Ration. Reward 393 That manner which they have..of flying off in tangents when they are pressed. 1865Lecky Ration. (1878) I. 284 note, Flying off at a tangent from his main subject. 1875Whitney Life Lang. viii. 150 To abandon the established habits of speech and go off upon a tangent. 1879M. E. Braddon Clov. Foot x, Smoking his cigar, and letting his thoughts wander away at a tangent every now and then.
2. The upright pin or wedge fixed at the back of each of the keys of a clavichord, which on the depression of the key pressed up against the string and caused it to sound, acting also as a bridge to determine the pitch of the note. [= Ger. tangent.]
[1614Prætorius Syntagma Musicum III. 68 Es hat aber ein solch Geigenwerk an statt der Tangenten [etc.]. ]
1878A. J. Hipkins in Grove Dict. Mus. I. 367 The tangents..not only produced the tones but served..to measure off the vibrating lengths required for the pitch of the notes. 1896C. W. Naylor Shaks. & Music 68 note, The German clavichord had ‘tangents’ of brass at the ends of the key levers.
3. Short for tangent scale, tangent galvanometer: see C.
1861W. H. Russell in Times 14 May, His guns were without screws, scales, or tangents. 1905Preece & Sivewright Telegraphy 404 Perhaps the most useful galvanometer for general testing purposes is the Tangent.
4. A straight section of railway track. U.S. colloq.
1895in Funk's Stand. Dict.
C. Combinations and special collocations.
(Some of these are examples of the adj. qualifying a n.)
tangent backsight = tangent scale (a); tangent balance, a balance in which the weight is shown on a graduated arc by a pointer attached to the beam; the bent-lever balance, common as a letter-balance; tangent compass = tangent galvanometer; tangent galvanometer, a galvanometer in which the tangent of the angle of deflection of the needle is proportional to the strength of the current passing through the coil; tangent scale, (a) in Gunnery, a kind of breech-sight in which the heights of the steps or notches correspond to the tangents of the angle of elevation; (b) a graduated scale indicating the tangents of angles (see quot. 1902); tangent screw, a screw working tangentially upon a toothed circle or arc so as to give it a slow motion for delicate measurements or adjustments; tangent sight = tangent scale (a).
For tangent cone, line, plane, surface, etc., see A. 1; for tangent distance, length, point, see B 1 b.
1862Catal. Internat. Exhib. II. xi. 23 The *Tangent back-sight is elevated by a rack and pinion, the latter having a micrometer wheel for finer readings than the divisions on the tangent stem allow.
1873Maxwell Electr. & Magn. (1881) II. 325 The current is..proportional to the tangent of the deviation, and the instrument is therefore called a *Tangent Galvanometer. 1876Preece & Sivewright Telegraphy 267 The insulation resistance is the only test which is taken by means of the tangent-galvanometer.
1859F. A. Griffiths Artil. Man. (1862) 51 A *Tangent scale is affixed to the breech of Guns, and Howitzers, by means of which the requisite elevation may be given. 1902Sloane Stand. Electr. Dict., Tangent scale, an arc of a circle in which the number of graduations in any arc starting from zero are proportional to the tangent of the angle subtended by such arc. The system is for use with tangent galvanometers.
1862Catal. Internat. Exhib. II. xiii. 5 Circumferenter or miner's dial, with *tangent screw adjustment. 1877Knight Dict. Mech., Tangent-screw, an endless screw tangentially attached to the index-arm of an instrument of precision, enabling a delicate motion to be given to the arm after it has been clamped to the limb, and permitting angular measurements to be made with greater exactness than could be done were the movement entirely effected by hand.
1908Treat. Serv. Ordn. Roy. Artill. 513 The *tangent sights consist of triangular nickel-plated steel bars graduated on the rear face.
▪ II. ˈtangent, v. rare.
[f. the n.]
intr. To go off or away at a tangent (see tangent n. 1 c); to fly off at an angle.
1920F. Niven Tale that is Told vii. 44 They are always tangenting away, not from what I have said, but from what they imagine I have said. 1940‘Gun Buster’ Return via Dunkirk ii. i. 85 The empty sardine tin that the Babe pitched, tangented off the side of his tin hat into the long grass. 1974K. Millett Flying (1975) ii. 201 She chuckles and then tangents off to some article..she read. |