a. [ad. L. convergent-em, pr. pple. of convergĕre to CONVERGE: so in mod.F.]
1. Inclining toward each other, or toward a common point of meeting; tending to meet in a point or focus; = CONVERGING ppl. a. 1.
1727–51. Chambers, Cycl., Converging, or Convergent lines in geometry are those which continually approximate, or whose distance becomes continually less and less.
1794. Martyn, Rousseau’s Bot., xvi. 198. The filaments and anthers are convergent or bend towards each other.
1835. Browning, Paracelsus, V. 145. Some point where all those scattered rays should meet Convergent in the faculties of man.
1869. Tyndall, Notes on Light, § 79. Light moves in straight lines, which receive the name of rays. Such rays may be either divergent, parallel, or convergent.
b. of things immaterial, operations, etc.
Convergent breeding: ‘similarity in external characters concealing fundamental differences of structure in different animals’ (Syd. Soc. Lex., 1882).
c. Composed of or formed by converging lines.
(Convergent squint: strabismus in which the axes of the eyes converge.)
1831. Brewster, Optics, iv. § 39. 34. The convergent point of converging rays.
1862. Sat. Rev., 8 Feb., 140. If General M’Clellan … meditates a convergent attack on all parts of the South.
1870. T. Holmes, Surg. (ed. 2), III. 248. Strabismus may be either convergent or divergent.
2. Math. CONVERGING 2, as in convergent scries. Convergent fractions: see B.
1816. R. Jameson, Char. Min. (1817), 208. A crystal is said to be convergent, when … the series converges rapidly as 15, 9, 3.
1858. Todhunter, Algebra, xl. § 554. An infinite series is said to be convergent when the sum of the first n terms cannot numerically exceed some finite quantity, however great n may be.
1867. Wolstenholme, Math. Problems, 53. heading, Convergent Fractions.
1885. Watson & Burbury, Math. Th. Electr. & Magn., I. 32. Hence the series P1 + P2 + … is a convergent series.
3. Convergent-nerved (Bot.), (of leaves) having convergent nerves, ribs, or veins.
1882. in Syd. Soc. Lex.
B. sb. = convergent or converging fraction.
1858. Todhunter, Alg., xliv. (1875), 369. The fractions formed by taking one, two, three … of the quotients of the continued fraction a + 1/b + 1/c + &c. are called converging fractions or convergents … The convergents taken in order are alternately less and greater than the continued fraction. Ibid., 371. Every convergent is nearer to the continued fraction than any of the preceding convergents.
Mod. The first four convergents of π (3.14159 …) are 3/2, 22/7, 333/106, 355/113.
