Proportional COMPASSES are those whose joint lies between the points terminating each leg. They are either simple or compound. In the former the centre is fixed, so that one pair of these serves only for one proportion. The latter consist of two parts or sides of brass, which lie upon each other so nicely as to appear but one when they are shut. The sides open easily, and move about a centre, which is itself moveable in a hollow canal cut through the greater part of their length. To this centre, on each side, is affixed a sliding piece, of a small length, with a fine line drawn on it, serving as an index, to be set against other lines or divisions placed upon the compasses on both sides. These lines are, 1. a line of lines; 2. a line of superficies, areas, or planes; 3. a line of solids; 4. a line of circles, or rather of polygons to be inscribed in circles. These lines are all unequally divided; the three first from one to twenty, the last from six to twenty.
The use of the first is to divide a line into any number of equal parts; by the second and third are found the sides of like planes or solids in any given proportions; and by the fourth, circles are divided into any number of equal parts, or any polygons inscribed in them.