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

Wilson, Hinkle & Company, 1868 - 420 уелЯдет

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### Ресйечьменб

 PART FIRST INTRODUCTORY 9 DEFINITIONS 17 DIVISION OF THE SUBJECT 26 ANGLES 32 REGULAR POLYGONS 151 ISOPERIMETRY 159 RECTIFICATION OF THE CIRCUMFERENCE 172 DIEDRAL ANGLES 185
 SIMILAR POLYEDRONS 239 CHAPTER XI 245 SPHERES 250 SPHERICAL AREAS 261 SPHERICAL VOLUMES 271 MEASURE OF ANGLES 277 CONSTRUCTION AND USE OF TABLES 296 RIGHT ANGLED TRIANGLES 302

 TRIEDRALS 195 POLYEDRALS 209 PYRAMIDS 222 MEASURE OF VOLUME 232
 SPHERICAL ARCS AND ANGLES 315 Right ANGLED SPHERICAL TRIANGLES 324 LOGARITHMIC AND TRIGONOMETRIC TABLES 345

### ДзмпцйлЮ брпурЬумбфб

УелЯдб 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.
УелЯдб 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
УелЯдб 72 - Problem. — To draw a line through a given point parallel to a given line.
УелЯдб 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.
УелЯдб 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
УелЯдб 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.
УелЯдб 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
УелЯдб 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...
УелЯдб 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.
УелЯдб 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.