GONIOMETRY, a method of measuring angles, so called by M. de Lagny, who published several papers on this method in the Memoirs of the Academy of Sciences in the years 1724, 1725, 1729. M. de Lagny's method of goniometry consists in measuring the angles with a pair of compasses, and that without any scale whatsoever, except an undivided semicircle. Thus, having any angle drawn upon paper to be measured, produce one of the sides of the angle backwards behind the angular point; then with a pair of fine compasses describe a pretty large semicircle from the angular point as a centre, cutting the sides of the proposed angle, which will intercept a part of the semicircle. Take this intercepted part exactly between the points of the compasses, and turn them successively over upon the arc of the semicircle, to find how often it is contained in it; and as after this there is commonly some remainder, take such remainder in the compasses, and in like manner find how often it is contained in the last of the integral parts of the first arc; and if there be again some remainder, find in like manner how often this last is contained in the former; and so on continually, till the remainder become too small to be taken and applied as a measure. By this means may be obtained a series of quotients, or fractional parts, one of another, which being properly reduced into one fraction, give the ratio of the first arc to the semicircle, or of the proposed angle to two right angles, or a hundred and eighty degrees, and consequently that angle itself in degrees and minutes.