APPROACH

, the curve of equable approach. It was first proposed by Leibnitz, namely, to find a curve, down which a body descending by the force of gravity, shall make equal approaches to the horizon in equal portions of time. It has been found by Bernoulli and others, that the curve is the second cubical parabola, placed with its vertex uppermost, and which the descending body must enter with a certain determinate velocity.—Varignon rendered the question general for any law of gravity, by which a body may approach towards a given point by equal spaces in equal times. And Maupertuis also resolved the problem in the cafe of a body descending in a medium which resists as the square of the velocity. See Hist. de l' Acad. des Sciences for 1699 and 1730.

Method of Approaches, a name given by Dr. Wallis, in his Algebra, to a method of resolving certain problems relating to square numbers, &c. This is done by first assigning certain limits to the quantities required, and then approaching nearer and nearer till a coincidence is obtained.—In this sense, the method of Trial-and-error, or double rule of False Position, may be considered as a method of approaches.