Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Wilson, Hinkle & Company, 1873 - Geometry - 276 pages

Contents

 LOGICAL TERMS 9 CHAPTER II 17 AXIOMS OF DIRECTION AND DISTANCE 23 PROBLEMS 28 PERPENDICULAR AND OBLIQUE LINES 38 CHAPTER IV 52 TANGENTS 58 ANGLES AT THE CENTER 64
 EQUIVALENT SURFACES 135 CHAPTER VII 143 DIVISION OF THE SUBJECT 26 156 CHAPTER VIII 163 QUADRATURE OF THE CIRCLE 172 CHAPTER IX 177 DIEDRAL ANGLES 185 TRIEDRALS 195

 INTERCEPTED ARCS 72 POSITIONS OF TWO CIRCUMFERENCES 78 CHAPTER V 85 EQUALITY OF TRIANGLES 93 QUADRILATERALS 119 CLASSIFICATION OF SURFACES 24 128
 POLYEDRALS 209 PYRAMIDS 222 MEASURE OF VOLUME 232 SIMILAR POLYEDRONS 239 CHAPTER XI 245

Popular passages

Page 98 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 52 - 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 182 - ... the plane at equal distances from the foot of the perpendicular, are equal...
Page 141 - 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 124 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 238 - Corollary. — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Page 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed by ;r. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Page 214 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.
Page 233 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 57 - Problem. — To draw a line through a given point parallel to a given line. Let a perpendicular fall from the point on the line.