A Shorter Geometry

Front Cover
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Contents

Surface
1
Direction
11
SECOND STAGE
22
Area by counting squaressquared paper
23
Parallel Straight Lines
29
More exact measurement by estimation
40
Congruent Triangles
49
Miscellaneous Exercises
60
MISCELLANEOUS EXERCISES
195
AREA OF CIRCLE
202
MISCELLANEOUS EXERCISES
211
Ratio and proportion
219
CONSTRUCTION To find the fourth proportional to three
225
CONSTRUCTION On a given straight line to construct
232
AREAS OF SIMILAR FIGURES
237
ii If AB CD two chords of a circle
243

Book I
75
CONTINUOUS CHANGE OF A FIGURE
86
LOCI
96
The locus of a point which is equidistant
102
AREA OF PARALLELOGRAM
117
To construct a triangle equivalent to
124
THE THEOREM OF PYTHAGORAS
128
Projections
136
MISCELLANEOUS EXERCISES
145
PRELIMINARY
149
CONSTRUCTION To circumscribe a circle about a given
155
CONSTRUCTION To inscribe a regular hexagon in a circle
160
THE TANGENT
166
ANGLES AT A POINT
171
CONSTRUCTION To inscribe a circle in a given triangle
172
ANGLE PROPERTIES
179
equal
183
93
188
If a pair of opposite angles of a quadri
189
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
CHAP
1
IV
16
79
19
94
22
VI
25
The Cylinder
33
XI
48
XII
60
Coordinates in Space
72
85
85
Perspective
89
ANSWERS
105
A theorem and its converse
109

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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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