n. The act of projecting, throwing, or shooting forward: as, the projection of a shadow upon a bright surface; hence, the act or process of throwing, as it were, something that is subjective into the objective world; the act of giving objective or seeming reality to what is subjective: as, the projection of a sensation of color into space as the quality of an object (a colored thing).n. That image or figure which results from the act of projecting an idea or a sensation.n. That which projects; a part projecting or jutting out, as of a building extending beyond the surface of the wall; a prominence.n. The act of projecting, or scheming or planning: as, he undertook the projection of a new enterprise.n. In geometry, the act or result of constructing rays or right lines through every point of a figure, according to certain rules.n. The act or result of constructing rays through every point of a figure, all passing through one point, and cutting these rays by a plane or other surface, so as to form a section on that surface which corresponds point for point with the original figure.n. In chartography, the act or result of constructing a figure upon a plane or other surface, which corresponds point by point with a sphere, spheroid, or other figure; a map-projection (which see, below).n. The mental operation in consequence of which objects of the imagination or retinal impressions appear to be seen external to us.n. In alchemy, the act of throwing anything into a crucible or other vessel, especially the throwing of a portion of philosopher's stone upon a metal in fusion with the result of transmuting it; hence, the act or result of transmutation of metals; humorously, the crisis of any process, especially of a culinary process.n. Same as gromonic map-projection.n. Same as zenithal map-projection. — Clarke's map-projection, a perspective map-projection in which the distance of the eye from the center of the sphere is 1.368 times the radius. This projection was invented by the English geodesist Colonel A. R. Clarke. — Collignon's map-projection.n. The quadrilateral map-projection.n. The central equivalent projection. — Conform map-projection. Same as orthomorphic map-projection. — Conical map-projection.n. Properly, a map-projection the development of a tangent or secant cone upon which the sphere is conceived to have been projected by lines of projection perpendicular to its axis.n. Any projection which may naturally be regarded as the development of a projection upon a cone. — Cylindrical map-projection.n. A parallelogrammatic or square map-projection.n. A map-projection showing the earth in repeated stripes, as Mercator's.n. A perspective or central projection in which the center is at infinity. — Delisle's map-projection, the secant conical projection proposed by Mercator, and applied by J. N. Delisle to the great map of Russia. — Discontinuous map-projection, a map-projection which follows one law in one part, and another in another part. Also called broken map-projection, irregular map-projection. — English map-projection. Same as globular map-projection . — Equidistant map-projection, a zenithal map-projection in which the radius of each almucantar is equal to its angular distance from the zenith. This map-projection, invented by the French mathematician Postel in the sixteenth century, is frequently employed for star-maps, etc. — Equivalent map-projection, a map-projection which represents all equal surfaces on the spheroid by equal areas on the map. Also called equal-surface map-projection. — Equivalent stereographic map-projection, an equivalent map-projection in which the parallels are represented by parallel straight lines at distances from the equator proportional to the tangents of half the latitudes. This projection was proposed in 1862 by M. de Prépetit Foucaut. — Flamsteed's map-projection. Same as sinusoidal map-projection. — Foucaut's map-projection, the equivalent stereographic map-projection. — Fournier's map-projection.n. A meridional map-projection in which the meridians are equidistant ellipses, while the parallels are circular arcs equally dividing the central and extreme meridians.n. A map-projection in which the meridians are as in , but the parallels are straight lines as in the meridional orthogonal projection. These map-projections were proposed in 1646 by the French geographer Fournier. — Gauss's map-projection. Same as Lagrange's map-projection. — Glareanus's map-projection, a discontinuous map-projection differing from that of Apianus only in setting the parallels at the same distances as in the meridional orthographic map-projection. It was invented by the Swiss mathematician Loriti or Glareanus, and published in 1527.n. Globular map-projection. Any projection of a hemisphere with curvilinear meridians and parallels.n. A meridional hemispherical map-projection in which the equator is a straight line, the semimeridians are circular arcs dividing the equator into equal parts, and the parallels are circular arcs dividing the extreme and central meridians into equal parts. This projection, invented in 1660 by the Italian Nicolosi, has been extensively employed ever since.n. La Hire's map-projection. — Gnomonic map-projection.n. A perspective map-projection from the center of the sphere. All great circles are represented by straight lines.n. Hence, by extension — Any map-projection representing all great circles by straight lines. Such a projection can contain but one half of the sphere on an infinite plane. This system is probably ancient. — Harding's map-projection. Same as Lagrange's map-projection. — Herschel's map-projection. Same as Lagrange's map-projection. — Homalographic (or homolographic) map-projection, an equivalent map-projection in which the meridians are ellipses meeting at the poles, and the parallels and equator are parallel straight lines: invented by the German mathematician Mollweide in 1805. It has been considerably used. — Intermediary map-projection, a zenithal map-projection in which, z being the zenith distance of an almucantar, r its radius on the map, and n a constantn. r = n tan z/n.n. This projection was invented by A. Germain. — Irregular map-projection. Same as discontinuous map-projection. — Isocylindric map-projection. an equivalent map-projection the development of a cylinder upon which the sphere has been orthogonally projected. It was invented by the German mathematical philosopher J. H. Lambert. — Isomeric map-projection, the zenithal equivalent map-projection, invented by J. H. Lambert, and the best of the equivalent projections. — Isospherical map-projection. Same as isomeric map-projection. — Jaeger's map-projection, a discontinuous projection in the shape of an eight-pointed star. It was proposed by Jaeger in 1865, and was modified by Petermann. — James's map-projection, a perspective map-projection in which the center of projection is distant from that of the sphere by 1.5 times the radius. It was invented by the English geodesist Sir Henry James. — Lagrange's map-projection, an orthomorphic map-projection in which the sphere is shown a finite number of times on a finite number of sheets, but in which all the north poles (or zeniths) coincide, as well as all the south poles (or nadirs). The projection was invented by J. H. Lambert, and has been called by many names. It has been used in a government map of Russia. — La Hire's map-projection, a perspective projection having the center of projection at a distance from the center of the sphere equal to 1.707 times the radius. This projection, proposed by the French geodesist La Hire in 1701, has been frequently used. — Littrow's map-projection, an orthomorphic projection in which the meridians are hyperbolas and the parallels ellipses, all these conies being confocal. This projection has two north and two south poles, all four coincident at infinity, and shows the sphere twice on two sheets, which are merely perversions of each other. It has many remarkable properties. It was invented by the Bohemian astronomer Littrow in 1833. — Lorgna's map-projection. Same as isomeric map-projection. — Map-projection by balance of errors, that zenithal projection which makes the “misrepresentation” a minimum, as determined by least squares. If r is the radius of an almucantar on the chart, z its zenith distance, and Z that of the limit of the chart, which cannot exceed 126° 24′ 53″, thenn. r = cot ½z log sec ½z + tan ½z cot½Z log sec ½Z.n. Map-projection by development, a projection upon a developable surface which is then developed into a plane. — Mercator's map-projection, an orthomorphic map-projection in which the whole sphere is shown in equal repeating stripes. The point at infinity represents the whole sphere, and the zenith and nadir do not elsewhere appear. As ordinarily used, the poles are taken as these points, when the meridians appear as equidistant parallel lines, and the parallels as parallel lines cutting them at distances from the equator proportional to log tan ½ latitude. This has the advantage that the points of the compass preserve the same directions all over the map. This projection, invented by the Flemish cosmographer Mercator in 1550, is the most useful of all. — Meridional map-projection, a map-projection which seems to be projected upon the plane of a meridian, showing the poles at the extremities of a central meridian. — Modified Flamsteed's map-projection. Same as Bonne's map-projection. — Mollweide's map-projection. Same as homolographic map-projection. — Murdoch's map-projection, one of three conical map-projections in which the part of the cone of which the map is a reduced development is equal to the spherical zone represented. These were invented by Patrick Murdoch in 1758. — Orthographic map-projection, a perspective map-projection from an infinitely distant center. — Orthomorphic map-projection, a map-projection which preserves all angles — that is, the shapes of all infinitesimal portions of the sphere. When one such map-projection has been obtained, say the polar stereographic, which is the simplest, all others may be derived from this by a transformation of the plane. Let r and θ be the polar coördinates of any point on the polar stereographic projection, let i denote the imaginary whose square is — 1, and let F denote any function having a differential coefficient. If, then, F (r cos θ; + r sin θ.i) be put into the form x + yi, x and y will be the rectangular coördinates of the corresponding point on another orthomorphic projection. Also called conform map-projection. — Parallelogrammatic map-projection, a map-projection in which the parallels are represented by equidistant straight lines, and the meridians by equidistant straight lines perpendicular to the parallels. This is an ancient projection. Also called rectangular map-projection. — Parent's map-projection, one of two perspective map-projections. In Parent's first map-projection the center of projection is distant from the center of the sphere 1.595 times the radius. In his second this distance is 1.732. — Perspective map-projection, a true projection of the sphere by straight lines from a center of projection intersecting the plane of the map. — Petermann's map-projection, a discontinuous map-projection showing the sphere in the form of an eight-pointed star. It is used to decorate the title-page of Stieler's atlas. — Polar map-projection, a map-projection showing one of the poles in the center. — Polyconic map-projection, a map-projection in which the surface of the earth is cut into an infinite number of zones parallel to the equator; a central meridian is then developed into a straight line, and then each zone is developed separately. This projection, invented by Hassler, superintendent of the United States Coast Survey, is used in all government maps of the United States. — Quadrilateral map-projection, a broken equivalent projection in which one meridian has the form of a square, of which another meridian and the equator are the diagonals. It was invented by Collignon. — Quincuncial map-projection, an orthomorphic projection of the earth into repeating squares, invented by C. S. Peirce in 1876. — Rectangular map-projection. Same as parallelogrammatic map-projection. — Ruysch's map-projection, a conical projection in which the cone cuts the equator and has its vertex at one pole, and the sphere is projected upon the cone by lines perpendicular to the axis. It was invented by Ruysch in 1508. — Sanson's map-projection. Same as sinusoidal map-projection. — Schmidt's map-projection, a meridional map-projection in which the meridians are represented by ellipses cut at equal distances by the parallels. It was proposed by the physicist G. G. Schmidt in 1801. — Sinusoidal map-projection, an equivalent map projection in which the parallels are equidistant straight lines to which the central meridian is perpendicular. This projection (so called from the form of the meridians) was first used by the French chartographer Sanson in 1650. — Square map-projection, the projection of a map which the successive meridians and parallels cut up into squares. — Stenoterous map-projection, an equivalent projection which represents the whole earth on the sector of a circle, the pole being at the center and the parallels concentric circles. It was invented by J. H. Lambert. — Stereographic map-projection, the simplest of all projections, representing the whole sphere once on one infinite plane, the parts at infinity being considered as a point. All circles on the sphere are represented circles, and the angles are preserved. The stereographic projection of the sphere is a perspective projection, a point on the surface being the center of projection; but the stereographic map-projection of the spheroid is not a perspective projection. The stereographic projection was known to the ancients, and has always been employed for special purposes. — Textor's map-projection, a modification of the isocylindrical map, by J. C. von Textor, 1808. — Transverse map-projection, a meridional map-projection. — Trapeziform map-projection, a map-projection in which the space between two meridians and two parallels is represented by a trapezoid, the sides of which are divided proportionally to determine other straight lines representing meridians and parallels. — Werner's map-projection, that equivalent map-projection which has the parallels concentric and equidistant arcs of circles, with the north pole at the center. The whole sphere has a heart shape. This was invented by Johann Werner, 1514. — Zenithal map-projection, a map-projection which is symmetrical about a central point, the almucantars being represented by concentric circles.n. The foot of the perpendicular from a point to a straight line is the projection of the point upon the line.n. The localization of pressure sensation at the extremity of a pencil, cane, etc., held in the hand, rather than in the hand itself.
