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solid geometry, as all that is absolutely necessary for him to know in connection with either will be explained to him as occasion arises. As we cannot form a conception of the magnitude of any material 17 c 18 FIRST PRINCIPLES OF object without reference to one or more of its dimensions, and as each of these involves the idea of extension in some direction, the word length, or its representative, "a line," would appear to be the first term used in geometry requiring definition, but as a line can have no existence till it is generated or drawn, our first term must be that of the generator, or " point." We therefore define A point, as having no magnitude, that it is used to denote "position" only, and is represented geometrically by a dot or mark made by any pointed instrument, such as a pen, pencil, etc. A line, as the path made by a point moving over a surface. It may be straight, crooked, or curved, according to the direction in which the point travels or moves. A straight line, as the shortest path that can be made by a point moving from one position to another, or the nearest distance between two points, as the line A between points 1 and 2. A crooked line, as the path of a point that has changed its direction after moving in a straight line for a given distance 1 to 2, as the line B from 1 to 3. A curved line, as the path of a point that continually changes its direction, as the line C from 4 to 5. If the path of a moving point changes in such a way as to enclose a certain amount of surface, then the enclosed surface is called a " figure,"