# Elementary Geometry: Plane

American Book Company, 1903 - Geometry, Plane - 358 pages

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### Contents

 INTRODUCTION 1 The Construction Postulates 7 Axioms concerning Lines and Angles 16 Triangles 25 Summary of Types of Inference 45 Parallel Lines 53 Construction of Triangles 62 Quadrangles 72
 Fundamental Properties 169 Angles in Segments 186 Tangents 192 Concurrent Chords 206 Maxima and Minima 222 Locus Problems 232 RATIO AND PROPORTION 242 Scale of Relation 251

 Polygons 89 Symmetry 104 Locus Problems 112 Methods of Analysis 120 Comparison of Parallelograms 130 Equivalences involving Rectangles 137 Equivalences in a Triangle 147 Construction of Equivalent Polygons 154 Locus Problems 164
 Properties of a Proportion 264 Ratios OF LINES POLYGONS 271 Compounding of Ratios 279 Similar Triangles 285 MENSURATION 325 Irrational Numbers 332 Directed Lines 339 Measurement of the Circle Variables and Limits 346 Copyright

### Popular passages

Page 148 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 147 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Page 7 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 136 - If a straight line be divided into any two parts, the square on the whole line is...
Page 195 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Page 80 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 305 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 287 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 263 - If four magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals, viz.
Page 32 - At a given point in a given straight line, to construct an angle equal to a given angle. Let A be the given point in the straight line AB, and O the given angle.