DESCRIPTIVE GEONETRY, the art of representing a definite body upon two planes, at right angles with each other, by lines finning perpendicularly to the planes from all the points of the concourse of every two contiguous sides of the body, and from all points of its contour ; and, vice from a given representation to ascertain the parts of the original object.
Descriptive geometry may therefore be considered synonymous with orthographiral projection, 111)011 which subject, with the exception of a treatise by Nr. P. Nieholson, (first published in 1795, and re-published with improve ments in the year 1809), nothing had appeared in the English language, until the publication of this Dictionary.
About the year 179-1, the celebrated Ninge, who has been called the inventor of descriptive geometry, published in France his Geometric Descriptive, one of the most elegant and lucid elementary works in existence. Previous to the appearance of this work, the science of perspective and many other applications of geometry to the arts, had required isolated methods of obtaining lines. angles, or areas. described under laws not readily admitting of the application of algebra, and its consequence, the construction of tables. The des. criptive geometry of Monge is a systematized form of the method by which a ground-plan and an elevation are made to give the form and dimensions of a building. The pro jections of a point upon two planes at right angles to each other being given, the position of the point itself is given. From this it is possible, knowing the projections of any solid figure upon two such planes, to lay down on either of those planes, a figure similar and equal to any plane section of the solid.
This necessary and neglected part of education, had been also much cultivated by Mr. Nicholson, and with such success. that his works have always been referred to by succeeding writers as authorities. hi addition to the treatise above mentioned, and also some iiarts of the carpentry in Rees' Cyclopedia ; the numerous valuable articles in this Dictionary attest the sound practical knowledge of the writer, and his perfect acquaintance with the subjects on which he has written. It is due to his memory, to state that he had
at that time no knowledge of any foreign work on Descripti‘e Geometry, and that the treatise by Nonge did not fall into his hands until the year 1812. While strongly recommend ing that work, however, to the study of all those who are desirous of attaining truth in delineation, lie con siders his own views, differently conceived, as undoubtedly they were, from those of Monge, to have equal claims to originality.
As we are desirous of omitting nothing that may tend to enlarge the bounds of science, we shall here insert so much of Nonge's work as we conceive to be conducive to this end, referring \[r. Nicholson's own ideas on this branch of geo metry, to the article PROJECTION, a name better understood in this country than that of Descriptive Geometry.
To facilitate the knowledge of this subject, the reader should be well acquainted with the eleventh book of The Elements of Euclid. which treats particularly of planes, and the manner in which solids are constituted.
"Figure 1.—If from all the points of an indefinite right line, however situated in space. we imagine perpendiculars to be dropped upon a given plane, L an x o, all the points of these perpendiculars will fall upon the plane in another inde finite right line, a b, for they will be all comprised in the plane described by A a, perpendicular to the plane 1. at x o, and can only meet the latter in the line of intersection com mon to both planes, which is a right line.
"The right line a b, which passes through the projections . _ of all the points of the right line A B, upon the plane L m is called the projection of the right line A 13 upon this plane.
As two points are sufficient for determining the position of a right hue ; it is only necessary, in constructing the pro jection of a right line, to construct the projections of two of its points, and the line which they describe will be the required projection.