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### Contents

 FIRST STAGE 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
 Construction To find the fourth proportional to three 225 Proportional compasses 236 ii If AB CD two chords of a circle 243 ii The external bisector of an angle of 249 If a straight line stands on another straight 257 AnGles of a trianGle a polyGon 265 Inequalities 273 Index and List of Definitions 297

 Table of facts or theorems 75 Continuous change of a figure 86 Construction To draw a straight line parallel to a given 95 The locus of a point which is equidistant 102 Area by counting squaressquared paper 114 Area of trianGle 120 The theorem of PythaGoras 128 Projections 136 A a + bkak + bk 142 PAgE 149 Construction To circumscribe a circle about a given 155 In equal circles or in the same circle 163 Construction To draw the tangent to a circle at a given 169 AnGles at a point 171 Angle properties 179 Miscellaneous exercises 195 Area of circle 202 Miscellaneous exercises 211 Ratio and proportion 219
 CHAP PAGE I Planes and Lines 1 1 Parallel positions of Planes and Lines 7 7 Perpendicular positions of Lines and Planes 11 11 Oblique positions of Planes and Lines 16 16 Skew Straight Lines 20 Loci 25 25 The Prism 27 27 The Cylinder 33 33 The Pyramid 37 37 The Cone 44 44 The Sphere 48 48 The Solid Angle 60 60 The Regular Solids the Principle of Duality Eulert Theorem 65 65 Coordinates in Space 72 72 Plan and Elevation 75 75 Perspective 3 c 89 89 Miscellaneous Exercises 93 93 Answers 105 105 Index 107 107

### 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.