# Elements of Geometry

Butler, Sheldon & Company, 1897 - Geometry - 398 pages
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### Contents

 PLANE GEOMETRY 19 THE CIRCLE 70 BOOK III 88 Original Theorems 119 Problems for Construction 140 AREA AND RELATIONS OF POLYGONS 143 Definitions 205 Propositions 221
 BOOK VII 269 THE CYLINDER CONE AND SPHERE 310 SPHERICAL SURFACES 339 Equal and Symmetrical Triangles 351 Measurement of Spherical Polygons 360 Original Theorems 370 MISCELLANEOUS ORIGINAL THEOREMS 382 BIOGRAPHICAL NOTES 393

### Popular passages

Page 327 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 88 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 80 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 207 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 10 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 152 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 392 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 39 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.
Page 176 - If from, a point without a circle a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the external segment.
Page 309 - Assuming that 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...