GEOMETRY. --- DEFINITIONS. 1. If a block of wood or stone be cut in the sbape represented iu Fjg. 1, it will have six fiat faces. Each face of the block is called a surface; and if these faces are made smooth by polishing, so that, when a straight-edge is applied to any one of them, the straight edge in every part will touch the surface, the faces are called plane surfaces, or planes. 2. The edge in which any two of these surfaces meet is called a line. 3. The corner at which any three of these lines meet is called a point. » 4. For computing its volume, the block is measured in three principal directions: From left to right, A to B. From front to back, A to C. From bottom to top, A to D. These three measurements are called the dimensions of the block, and are named length, breadth (or width), thickness (height or depth).
Table of Contents
OONTEKTS; GEOMETRY; PACE; Definitions1; Straight Likes 5; Plank Angles7; Magnitude of Angles9; Angular Units10; Method of Superposition11; Symmetry13; Mathematical Terms14; Postulates15; Axioms '' 16; Symbols16; PLANE GEOMETRY; BOOK I The Straight Line; The Straight Line Vj; Parallel Lines 22; Perpendicular asd Oblique Lines 33; Triangles 40; Quadrilaterals 56; Polygons in General 66; Exercises , 72; CONTENTS; BOOK II The Circle; FAQB; Definitions 75; Ancs and Chords 77; Tangents 89; Measurement 92; Theory of Limits 94; Measure of Angies 93; Problems of Construction 106; Exercises 126; BOOK III Proportional Lines and Similar Polygons; Theory of Proportion 131; Proportional Lines 138; Similar Triangles 145; Similar Polygons 153; Numerical Properties of Figures 156; Problems of Construction 167; Problems op Computation 173; Exercises 175; BOOK IV Areas of Polygons; Areas op Polygons 180; Comparison of Polygons 188; Problems of Construction I9z; Problems op Computation 204; Exercises 205; BOOK V Regular Polygons and Circles; Regular Polygons and Circles 209; Problems of Constr