Practical Geometry.- Application of Algebra to Geometry, and GEOMETRY. DEFINITIONS. 1. Geometry is the science which treats of position, and of the forms, measurements, mutual relations, and properties of limited portions of space. SPACE extends without limit in all directions, and contains all bodies. 2. A Point is mere position, and has no magnitude. 3. Extension is a term employed to denote that property of bodies by virtue of which they occupy definite portions of space. The dimensions of extension are length, breadth, and thickness. 4. A Line is that which has extension in length only. The extremities of a line are points. 5. A Right or Straight Line is one all of whose parts lie in the same direction. 6. A Curved Line is one whose consecutive parts, however small, do not lie in the same direction. 7. A Broken or Crooked Line is composed of several straight lines, joined one to another successively, and extending in different directions. When the word line is used, a straight line is to be understood, unless otherwise expressed. 8. A Surface or Superficies is that which has extension. in length and breadth only. 9. A Plane Surface, or a Plane, is a surface such that (9) if any two of its points be joined by a straight line, every point of this line will lie in the surface. 10. A Curved Surface is one which is neither a plane, nor composed of plane surfaces. 11. A Plane Angle, or simply an Angle, is the difference in the direction of two lines proceeding from the same point. The other angles treated of in geometry will be named and defined in their proper connections. 12. A Volume, Solid, or Body, is that which has extension in length, breadth, and thickness. These terms are used in a sense purely abstract, to denote mere space whether occupied by matter or not, being a question with which geometry is not concerned. Lines, Surfaces, Angles, and Volumes constitute the different kinds of quantity called geometrical magnitudes. 13. Parallel Lines are lines which have the same direction. be Hence parallel lines can never meet, however far they may produced; for two lines taking the same direction cannot approach or recede from each other. Two parallel lines cannot be drawn from the same point; for it parallel, they must coincide and form one line. PLANE ANGLES. To make an angle apparent, the two lines must meet in a point, as AB and AC, which meet in the point A. Angles are measured by degrees. A 14. A Degree is one of the three hundred and sixty equal parts of the space about a point in a plane. If, in the above figure, we suppose AC to coincide with AB, there will be but one line, and no angle; but if AB retain its posi tion, and AC begin to revolve about the point A, an angle will be formed, and its magnitude will be expressed by that number of the |