# Treatise on Plane and Solid Geometry: For Colleges, Schools and Private Students : Written for the Mathematical Course of Joseph Ray

Sargent, Wilson & Hinkle, 1864 - Geometry, Modern - 276 pages

### Contents

 PART FIRST INTRODUCTORY 9 CHAPTER II 17 AXIOMS OF DIRECTION AND DISTANCE 23 CHAPTER III 28 PERPENDICULAR AND OBLIQUE LINES 38 CHAPTER IV 52 TANGENTS 58 ANGLES AT THE CENTER 64
 REGULAR POLYGONS 151 DIVISION OF THE SUBJECT 26 156 ISOPERIMETRY 159 RECTIFICATION OF THE CIRCUMFERENCE 172 CHAPTER IX 177 DIEDRAL ANGLES 185 122 192 TRIEDRALS 195

 POSITIONS OF TWO CIRCUMFERENCES 78 CHAPTER V 85 EQUALITY OF TRIANGLES 93 SIMILAR TRIANGLES 101 CHAPTER VI 119 CLASSIFICATION OF SURFACES 24 128 EQUIVALENT SURFACES 135 CHAPTER VII 143
 POLYEDRALS 209 PYRAMIDS 222 MEASURE OF VOLUME 232 SIMILAR POLYEDRONS 239 CHAPTER XI 245 SPHERICAL AREAS 261 SPHERICAL VOLUMES 271

### Popular passages

Page 94 - 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 48 - 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 137 - 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 259 - The area of the surface of a sphere is equal to the area of the...
Page 254 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180� and less than 540�. (gr). If A'B'C' is the polar triangle of ABC...
Page 133 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Page 223 - ... the two planes are equal polygons. Each side of one of the sections is parallel to the corresponding side of the other section, since they are the intersections of two parallel planes by a third. Hence, that portion of each side of the prism which is between the secant planes, is a parallelogram. Since the sections have their sides respectively equal and parallel, their angles are respectively equal. Therefore, the polygons are equal. 674. Corollary — The section of a prism made by a plane...
Page 233 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 187 - Theorem. — The intersections of two parallel planes by a third plane are parallel lines. Let AB and CD be the intersections of the two parallel planes M and N, with the plane P.
Page 247 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.