PROJECTION (Lat. projectio, from projicerr, to throw forward). The act or result of con structing a figure upon a given surface, usually by means of a pencil of rays, so that it corre sponds point by point to another given figure. It thus includes perspective (q.v.). and is most simply illustrated by the shadow of an object thrown by a light on a wall, the shadow being • the projection, and the light being the vertex of the pencil nr sheaf of rays. If the centre of projection is infinitely distant the projection is called parallel projection; if also the projection rays are perpendicular to the plans of projection, we have orthogonal projeetion. The theory of projections is of great importance, both in mathe maties and in geography, being in the former • • 111 case perfectly general in its application, while in the latter only the projection of the sphere is required. Projections of the sphere are of va rious kinds, all of which are treated under MsP.
In mathematics, the theory of projections has reached a high degree of perfection, serving to generalize the ancient geometry. (see GEOM ETRY.) Its basis is the investigation and deter mination of those properties which, being true of a figure, are also true of its projection., such
properties being necessarily dependent, not on the magnitude, but on the position of the lines and angles belonging to the figure. These prop erties are generally called projective properties. For instance, the three conic sections (q.v.), the parabola, ellipse, and hyperbola, are merely va rious projections of a circle on a plane, and all positional properties of the circle are at once, by this theory, connected with similar properties of the three conic sections. The introduction of coordinates has extended the applications of the subject, and it is now employed in solving the problems of applied mathematics.
For further information, see the references given under GEOMETRY. For the use of projec tion in mechanics, consult: Poisson, Traite de meeanique (2 vols., Paris, 1811) ; Klein, Theoric des Kreisrls (2 vols., Leipzig, 1897-98) ; and Stade and Seidel, Des Wiehtiyste ass dery yeo inctrischen Zeichnen and der Projektionslehre (Leipzig, l894).