APPROXIMATE

In Zoology, when the teeth are so arranged in the jaws, that one pa es on the side of the id there is no intervening vacancy. APPROXIMATION.ing near to. In Mathematics,(Lat. proximus',quantities nearest,are next said to.)to be approximate which are nearly but not absolutely equal In a general sense, the term approximate may be applied ■ result of natural philosophy or experimental science. For example, the magnitude of the earth, the distance of the sun, the ma es of the plants, in fact, all the elements of astronomy, are only known nearly, or by approximation. In these cases, however, the want of absolute knowledge arises from the imperfections of our senses, or the errors of our instruments. In the language of Analysis, approximation is used to denote those methods of calculation by which we obtain near values of quantities which cannot be found accurately, either on account of the nature of their composition, or the imperfections of our methods of calculation. The problem of finding the length of the circumference of a circle, by means of inscribed polygons, affords an instance of approximation to the values of geometrical quantities.Itis a principle in Geometry, that any arc of a circle, however small, is greater than its chord. Now, suppose a regular polygon of 100 sides to be inscribed in a circle, and that we know the exact length of one of the sides; it is evident that the sum of all these lengths will give an approximation to the length of the circttmferenee, though it would fall short of it by a very sensible quantity. Hut suppose that, instead of a polygon of 100 sides, one of 1000 sUes were inscribed in the circle, the a| lengths of the sides would now approach much mot J3 the length of the circumference. By continuing to multiply the number of sides, we may obtain an approximation to any68degree of nearne we please; but whatever iie number of the sides of the polygon may be, their sum [s. 82]