A Shorter Geometry

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Contents

FIRST STAGE
1
Direction
11
SECOND STAGE
22
Parallel Straight Lines
29
132
34
Angles of a Polygon
37
Congruent Triangles
49
If two angles of a triangle are equal
56
PAGE
219
CONSTRUCTION To find the fourth proportional to three
225
CONSTRUCTION On a given straight line to construct
232
AREAS OF SIMILAR FIGURES
237
PARALLEL STRAIGHT LINES
259
ANGLES OF A TRIANGLE A POLYGON
265
If two rightangled triangles have their
272
EXAMINATION PAPERS
278

Miscellaneous Exercises
60
Drawing to Scale
66
Воок
75
CONTINUOUS CHANGE OF A FIGURE
86
CONSTRUCTION To draw a straight line parallel to a given
95
SYMMETRY
106
PAGE
114
AREA OF TRIANGLE
120
Projections
136
A a+b kak +
143
PRELIMINARY
149
CONSTRUCTION To circumscribe a circle about a given
155
In equal circles or in the same circle
158
Lengths of chords
164
CONSTRUCTION To inscribe a circle in a given triangle
172
ANGLE PROPERTIES
179
E al32 a+ba
187
MISCELLANEOUS EXERCISES
195
AREA OF CIRCLE
202
MISCELLANEOUS EXERCISES
211
INDEX AND LIST OF DEFINITIONS
297
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
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 Eulers Theorem 65
65
Coordinates in Space 72
72
Plan and Elevation 75
75
Perspective 89
89
MISCELLANEOUS EXERCISES
93
ANSWERS 105
105
INDEX 107
107

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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.

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