III. or red blue blue To prove the opposite sides of the quadrilateral are equal. 6. Discourage mere memorizing. Many students form during the first weeks of study the habit of relying too much upon their memories, a habit which often proves disastrous to their future geometrical work. 7. Figures should be drawn as accurately as possible and as general as possible, i.e. a figure relating to a triangle in general should not be a right or an isosceles triangle, etc. 8. Give frequent written examinations containing some simple original work. red GEOMETRY INTRODUCTION 1. A physical body, such as a block of wood or iron, occupies a definite portion of space. The boundary which separates a body from space is called the surface of the body. If the material composing such a body could be removed without altering the surface, there would remain a portion of space called a geo metrical solid or a solid. A B D E 2. A solid is a limited portion of space. It has three dimensions, length, breadth, and thickness. 3. Surfaces are the boundaries of solids, as ABED or ADHC (Fig. 1). They have two dimensions, length and breadth. 4. Lines are the boundaries of surfaces, as AB, AD (Fig. 1), etc., and have but one dimension, length. 5. Points are the boundaries or extremities of lines, and are without dimension, having position only. Surfaces may be conceived as existing independent of the solids whose boundaries they form. In like manner, lines and points may exist independently in space. FIG. 2. 6. Solids, surfaces, lines, and points are called geometrical magnitudes. |