# A Shorter Geometry

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### Contents

 Surface 1 Direction 11 SECOND STAGE 22 Parallel Straight Lines 29 Angles of a Polygon 37 Congruent Triangles 49 Miscellaneous Exercises 60 Drawing to Scale 66
 Ratio and proportion 219 SIMILAR FIGURES 226 CONSTRUCTION On a given straight line to construct 232 BC 233 RECTANGLE PROPERTIES 240 CONSTRUCTION To describe a square equivalent to a given 246 Playfairs Axiom 261 ANGLES OF A TRIANGLE A POLYGON 265

 TABLE OF FACTS OR THEOREMS 75 Book I 84 Area by counting squaressquared paper 90 COR If equal perpendiculars are erected on the same 94 AREA OF PARALLELOGRAM 117 CONSTRUCTION To construct a triangle equivalent to 124 THE THEOREM OF PYTHAGORAS 128 Projections 136 MISCELLANEOUS EXERCISES 145 PAGE 149 CONSTRUCTION To circumscribe a circle about a given 155 THE TANGENT 166 CONSTRUCTION To inscribe a circle in a given triangle 172 4 173 ANGLE PROPERTIES 179 11 186 If a straight line touch a circle and from 193 Common tangents to two circles 199 FURTHER EXAMPLES OF LOCI 205 MISCELLANEOUS EXERCISES 211
 INEQUALITIES 273 23 286 INDEX AND LIST OF DEFINITIONS 297 29 298 I 1 40 13 79 19 98 23 VII 27 124 28 The Cylinder 33 184 44 224 50 233 51 246 57 257 58 266 60 Coordinates in Space 72 Perspective 89

### Popular passages

Page xiii - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.
Page xxi - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Page xi - The locus of a point which is equidistant from two intersecting straight lines consists of the pair of straight lines which bisect the angles between the two given lines.