# The Elements of Geometry

J. Wiley & Sons, 1885 - Geometry - 366 pages
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### Contents

 I 1 ARTICLE 6 CHAPTER II 8 Contradictory of a class 13 Medial defined 14 Contradictories include the universe 3 24 CHAPTER V 36 A line defined 37
 436 169 Parallel lines defined 183 Straight angle defined 191 Different divisions into contradic 196 1 197 The sum of two sects defined 209 GEOMETRY OF THREE DIMENSIONS 213 dron 242

 CHAPTER VI 48 The Universe of Discourse 51 CHAPTER VIII 61 Trigon tetragon or quadrilateral 64 A plane defined 70 Equivalence 76 General Properties 88 A figure defined 93 BOOK II 95 fined 107
 725 257 angles 260 The sum of two rectangles de 289 The commutative law for rectangle 283 BOOK X 289 MENSURATION OR METRICAL GEOMETRY 303 98 304 prismatoids 342 PRINCIPLE OF DUALITY 349 EXERCISES 357 Copyright

### Popular passages

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 112 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Page 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 270 - BC with the same radius. Then a line through A touching this arc will be the required parallel. Or, use a straight edge and triangle.
Page 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Page 13 - An Acute Angle is one which is less than a right angle.
Page 104 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Page 107 - 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.