ANGLE (from Lat. angelus, a corner) means, in geometry, the opening or inclination of two lines that cut or meet one another. If the lines are straight, the A. is rectilinear. The magnitude of an A. depends, not upon the length of the lines or legs, but upon the degree of their opening. If the legs are supposed closed, like a pair of compasses, and then gradually opened till they come into one straight line, they form a series of gradu ally increasing angles ; when half-way between shut and straight, they contain a right A. Any A. less than a right A. is called acute, and one greater is called obtuse. Angles are measured by degrees, of which a right A. contains 90. The A. made by two curved lines (curvilinear) is the same as the A. made by the tangents to the two curves at the point of intersection. Angles made by planes with one another can also be reduced to rectilinear angles. When three or more planes meet at the same point, the angular space included between them is called a solid A.
The FACIAL ANGLE, on which Camper founded a scheme for estimating the degrees of intellect and sagacity bestowed by nature on the several members of the animal king dom, was measured by him in the following way: One straight line was drawn from the ear to the base of the nose, and another from the prominent center of the forehead to the most advancing part of the upper jawbone, the head being viewed in profile. " In the angle produced by these two lines," says the physiologist, "may be said to consist not only the distinction between the skulls of the several species of animals, but also those which are found to exist between different nations; and it might be concluded that nature has availed herself at the same time of this angle to mark out the diversities of the animal kingdom, and to establish a sort of scale from the inferior tribes up to the most beautiful forms which are found in the human species. Thus it will be found that
the heads of birds display the smallest angle, and that it always becomes of greater extent in proportion as the animal approaches most nearly to the human figure. Thus there is one species of the ape tribe in which the head has a facial angle of 42°; in another animal of the same family, which is one of those simia approaching most closely to the human figure, the facial angle contains exactly 50°. Next to this is the head of the African neg-ro, which, as well as that of the Kalmue. forms an angle of 70°, while the angle discovered in the heads of Europeans contains 80°. On this difference of 10' in the facial angle the superior beauty of the,European depends; while that high character of sublime beauty which is so striking in sonic works'of ancient stafbary—a.s in the head of the Apollo and in the Medusa—is given by an angle which amounts to 100°."