[n. of action f. L. approximā-re: see APPROXIMATE and -TION.]
1. The action of bringing or coming near in place, time, or any conception to which ideas of space apply; approach; the state of being near, proximity. lit. and fig.
1646. Sir T. Browne, Pseud. Ep., 283. Unto that position it had been in a middle point, and that of ascent, or approximation.
1664. Power, Exp. Philos., III. 188. The World’s decay and approximation to its period.
1794. Sullivan, View Nat., II. 417. The approximation of the comet … near to our earth.
1849. Miss Muloch, Ogilvies, xxxvi. (1875), 273. Striving … to bring the young man in closer approximation to her chair.
1870. H. Macmillan, Bible Teach., xvi. 395. It is in diatoms and confervæ … that the vegetable kingdom makes an approximation to the animal.
† b. spec. in Med. Communication of a disease by contact; c. in Hort. = APPROACH sb. 11. Obs.
1678. Phillips, Approximation … in Natural Magick … see Transplantation.
1753. Chambers, Cycl. Supp., Approximation … transplanting a disease into some other subject, whether animate or vegetable, by bringing it in immediate contact with the patient.
1765. Tucker, Lt. Nat., II. 111. That method the gardeners call grafting by approximation.
2. The action of approaching in feeling or personal relations; advance towards union in sentiment or interests.
1834. Southey, Sir T. More (1831), I. 233. An approximation of feeling among those whom opinions have divided.
1850. Merivale, Rom. Emp. (1865), II. xii. 38. The renewed approximation of Pompeius to the party from which he had been so long estranged.
3. A coming or getting near to identity in quantity, quality or degree; an approach to a correct estimate or conception of anything. concr. The result of such a process.
1660. H. More, Myst. Godl., V. xvi. 199. The nearer approximation of the Root of 666 to 26 then to 25.
1672. Jacomb, Comm. Rom., viii. (1868), 56. The excellency of persons … to be measured by their … approximation to that which is most excellent.
1748. Hartley, Observ. Man, I. iii. § 2 ¶ 87. The true Root, or such an Approximation as is practically equivalent.
1854. Sir G. Nicholls, Eng. Poor Law, I. 13. An approximation to the principle of a Poor Law.
1868. Gladstone, Juv. Mundi, v. (1870), 143. I take them as very rough approximations to the truth.
1868. Peard, Water-farm., vi. 73. How an approximation to the cost of construction may be obtained.
4. Math. A process of solving problems, wherein a continual approach is made to the exact quantity.
1695. Wallis, in Phil. Trans., XIX. 2. Mr. Newton’s Method of Approximation for the Extracting of Roots.
1838–9. Hallam, Hist. Lit., II. II. viii. § 5. He devised a method of solving equations by approximation.
