# Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.

Sargent, Wilson & Hinkle, 1868 - Geometry - 420 pages
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### Contents

 LOGICAL TERMS 9 CHAPTER II 17 AXIOMS OF DIRECTION AND OF DISTANCE 23 BROKEN LINES 31 PERPENDICULAR AND OBLIQUE LINES 38 V 52 TANGENTS 58 ANGLES AT THE CENTER 64
 ISOPERIMETRY 159 RECTIFICATION OF THE CIRCUMFERENCE 172 LINES AND PLANES IN SPACE 185 CHAPTER X 213 MEASURE OF VOLUME 232 SIMILAR POLYEDRONS 239 I 245 SPHERES 250

 POSITIONS OF Two CIRCUMFERENCES 78 CHAPTER V 85 EQUALITY OF TRIANGLES 93 SIMILAR TRIANGLES 101 CHAPTER VI 119 MEASURE OF AREA 128 EQUIVALENT SURFACES 135 135 CHAPTER VII 143 REGULAR POLYGONS 151
 SPHERICAL AREAS 261 SPHERICAL VOLUMES 271 PART FOURTH TRIGONOMETRY 277 CONSTRUCTION AND USE OF TABLES 296 Right ANGLED TRIANGLES 302 CHAPTER XIII 314 Right ANGLED SPHERICAL TRIANGLES 324 IV 334

### Popular passages

Page 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Page 72 - Problem. — To draw a line through a given point parallel to a given line.
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 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
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 -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Page 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Page 260 - 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 137 - 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 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.