works on this interesting and useful branch of study. While on the Continent much has been written on the subject, few publications have appeared in England (and those chiefly translations) calculated to serve as text books for the general student. The consequence is that, while in the schools of other countries it is almost universally taught, in our own it is comparatively little known. In the following pages, the object of the Writer has been to furnish as much practical information on the subject of Geometrical Drawing generally, as the limits of the work would allow; and he is not aware of the existence of any one English work in which the same amount of a similar character of information is to be found as is here given. It is intended to publish a sequel, embracing Orthographic and Isometric Projection, Perspective, and the Projection of Shadows, as applied to the delineation of solids, the whole forming a general application of the principles inculcated in the present volume. The following are some of the works which have been consulted :-The Woolwich Papers on Geometrical Drawing; Monge's Géométrie Descriptive, etc.; Sonnet's Géométrie Théorique et Pratique, etc.; Johnson's Translation of the Book of Industrial Design, by M. Armengaud, Ainé, and MM. Armengaud, Jeune, and Amouroux, etc. London, November, 1860. 99 Criterion for determining the parallelism of two lines Criterion for determining whether two lines, whose plans cross, The method of expressing the inclination of a plane by means PRACTICAL GEOMETRY. DEFINITIONS. (1) A solid is a body which has length, breadth, and thickness. The elements of a solid are points, lines, and surfaces. (2) A point has position but no magnitude, e.g., the position of the intersection of two lines. (3) A line has length only. Lines are straight or curved, as A and B. (4) Surfaces are flat or plane, and curved. (5) Parallel lines are lines situated in the same plane and equally distant from each other throughout, e.g., the opposite edges of a book. (6) A horizontal line is level, as A. It takes its name from the horizon, to which it is parallel. (7) A vertical line is a line perpendicular to the horizon, as C If a weight be suspended by a thread in a still atmosphere, the thread will represent a vertical line. B (8) Oblique or inclined lines are straight lines which are neither horizontal nor vertical, as D (9) A plane rectilineal angle is the inclination of two straight lines to one another, meeting or cutting each other in a point, as B A C (10) "When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it." The angles A B C, A B D, are right angles. Obs. 1. Because DB is in the same straight line with в c, the A E angles A B C, A B D are called ad jacent angles, while the angles D B C A B D, A B E are called contiguous angles, B E not being in the same straight line with D B. Obs. 2. A perpendicular line need not be a vertical line. The angles A B C, A B D are right angles, and A B is per pendicular to DC, as in the preceding figure. B A C (11) An acute angle is less than a right angle, as E B C in last figure but one. (12) An obtuse angle is greater than a right angle, as E B D, Obs. An angle is named by a letter at the apex as B. def. 9. |