# Elementary Geometry: Plane

American Book Company, 1903 - 358 уелЯдет
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### Ресйечьменб

 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
 Two Circles 199 Concurrent Chords 206 Maxima and Minima 222 Locus Problems 235 Ratio AND PROPORTION 242 Scale of Relation 251 Properties of a Proportion 264 Ratios of Lines POLYGONS 271

 Polygons 89 Symmetry 104 EQUIVALENCE OF POLYGONS 125 Equivalences involving Rectangles 137 Equivalences in a Triangle 147 Construction of Equivalent Polygons 154 Locus Problems 164 Fundamental Properties 169 Angles in Segments 186 Tangents 192
 Compounding of Ratios 279 Similar Triangles 285 Similar Polygons 295 Surface Ratios 305 Ratios in the Circle 315 Locus Problems 322 Associated Numerical Ratios 328 Measurenumber 334 Measurement of Triangles 341 РнехмбфйкЬ дйкбйюмбфб

### ДзмпцйлЮ брпурЬумбфб

УелЯдб 150 - 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.
УелЯдб 149 - 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.
УелЯдб 7 - LET it be granted that a straight line may be drawn from any one point to any other point.
УелЯдб 40 - When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other.
УелЯдб 138 - If a straight line be divided into any two parts, the square on the whole line is...
УелЯдб 197 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
УелЯдб 82 - 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.
УелЯдб 265 - 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.
УелЯдб 309 - 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'.
УелЯдб 289 - ... 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.