PLAN IS PlI ER E,(from Latin. planes, and Greek, clOatpa,) a projection of the sphere, and the several circles thereof, on a plane; as upon paper, or the like. In this sense, maps of the heavens and the earth, in which are exhibited the meridians, and other circles of the sphere, are called plani spheres. See PROJECTION.
In all planispheres, the eye is supposed to be a point, viewing all the circles of the sphere, and referring them to a plane on which the sphere is, as it were, flattened. This plane is called the plane of the projection.
A perspective plane is only a plane of projection placed between the eye and the object, so as to contain all the points which the several rays, drawn from the object to the eye, impress thereon. But in planispheres or astrolabes, the plane of the projection is placed beyond the object, which is the sphere. The plane of the projection is always one of the circles of the sphere.
Among the infinite number of planispheres which the diGrent planes of projection, and the different positions of the eye, would furnish, there are two or three that have been preferred to the rest. Such are that of Ptolemy, where the
plane of projection is parallel to the equator ; that of Gemma Frisius, where the plane of projection is the colure, or solstitial meridian, and the eve the pole of the meridian ; that of John de IZoyas, a Spaniard, whose plane of projection is a meridian, and the eye placed in the axis of that meridian, at an infinite distance. This last is called the anolemma. The common defect of all these projections is, that they distort and alter the figure of the constellations, so that it is not easy to compare them with the heavens ; and that the degrees in some places are so small, that they afford no room for operation.
All these faults M. de la Hire provided against in a new projection, or planisphere ; where it is proposed the eye shall be so placed, as that the divisions of the circles projected shall be sensibly equal in every part of the instrument, The plane of his projection is that of a meridian.