A Shorter Geometry

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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

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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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