STEREOGRAPHY, (from Tepee's., solid, and ypask.), to describe,) that branch of solid geometry which demonstrates the properties, and shows the construction, of all solids which are regularly defined. It explains the methods for construct ing the surfitces in plains, so as to form the entire body, or to cover the surface of a given solid ; or, when a solid is bounded by plain surfaces, the inclination of the planes is determined by the rules of stereography. The sections of solids are also a branch of stereography - but this we shall refer to the article STEREOTOMY, with which it is more inti mately connected.
Mr. Hamilton has denominated the principles of perspec tive by the name of stereography ; but in this sense the term is too limited, as perspective is only a branch of the doctrine of solids, and extends only to the sections of pyramids and cones, and the representations of solids.
The eleventh and twelfth books of Euclid, which treat of the properties of solids, may be looked upon as the elements of this branch of geometry ; and to them we shall refer our readers for the first elements to be acquired.
It is somewhat singular, that though the first principles of solids have long been demonstrated, no practical application to mechanical constructions has been made of them. The knowledge of solids is of the greatest importance in the con structive parts of architecture, as in masonry, bricklaying, carpentry, &c.
To be proficient in the art of construction, this branch of geometry is indispensable, and contains the very essence and foundation of the whole in abstract.
Definition solid is that which has length, breadth, and thickness.
Definition `2.—The exterior surface of a solid is called its super/lc/es.
Definition 3.—A straight line is perpendicular, or at right angles to a plane, when it makes right angles with every straight line it in that plane.
Definition is perpendicular to a plane, when the straight lines drawn in one of the planes, perpendicularly to the common section of the two planes, are perpendicular to the other plane.
Definition inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point in which the first line meets the plane, to the ftoint in which a perpendicular to the plane drawn from any point of the first line above the plane meets the same plane.
Definition inclination of a plane to a plane is the acute angle contained by two straight lines, drawn from any, the same point of their common section at right angles to it, one upon one plane, and the other upon the other plane.
Definition 7.—Two planes arc said to have the like incli nation to each other, which two other planes have, when the said angles of inclination are equal to one another.
Definition 8.—Parallel planes are such as do not meet each other, though produced.
Definition 9.—A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point.
Definition solid figures are such as have all their solid angles equal each to each, and contained by the same number of similar planes.
Definition 11.—A prism is a solid, of which the ends are similar and equal plane figures, and the sides parallelo grams.
Definition n.—W-hen the ends of the prism are perpen dicular to the it is called a right prism ; but if' other wise, it is termed Oblique.
Definition 13.—A prism, whose sides and ends are equal squares, is called a cube.
Definition 11—When the ends are parallelograms, the prism is called a parallelopiped ; and when the planes of the parallelopiped are at right angles to each other, the prism is called a rectangular prism.
Definition 15.—When the ends of the prism are circles, it is called a cylindrr ; but if the ends are ellipses, and alike situated, it is call• a cylindroid.
Definition 16.—The straight line extended between the centres of the two bases is called the axis.