# The Elements of Geometry

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

### Contents

 Contranominal Converse Inverse 1 2 23 ARTICLE 24 CHAPTER IV 30 ARTICLE 48 ARTICLE 62 Equivalence how proved 82 Problems 88
 ARTICLE 169 BOOK VI 183 507 188 GEOMETRY OF THREE DIMENSIONS 213 The Universe of Discourse 251 Corresponding arcs angles 254 656 258 Equivalent triangles on same 284

 BOOK II 95 ARTICLE 100 BOOK III 115 357 126 Angles subtended by arcs 137 Common chord 144 Regular Polygons and Circles 154
 748 290 To compute perimeters 310 316 316 angles 320 THE MEASUREMENT OF VOLUMES 337 DIRECTION 343 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.