# Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students

American Book Company, 1868 - Geometry - 420 pages

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### Contents

 PART FIRST INTRODUCTORY 9 CHAPTER II 17 Axioms of Direction and of Distance 23 Broken Lines 31 Perpendicular and Oblique Lines 38 CHAPTER IV 52 Tangents 58 Angles at the Center 64
 Rectification of the Circumference 172 Diedral Angles 185 Triedrals 195 polyedrals 209 Pyramids 222 Measure of Volume 232 Similar Polyedrons 239 CHAPTER XI 245

 Positions op Two Circumferences 78 CHAPTER V 85 Equality of Triangles 93 Similar Triangles 101 CHAPTER VI 116 Trapezoids 122 Measure op Area 128 Equivalent Surfaces 135 CHAPTER VII 142 Regular Polygons 151 IsOPERlMETRY 159
 Spheres 250 Spherical Areas 261 Spherical Volumes 270 Mensuration 276 Construction and Use op Tables 296 Right angled Triangles 302 CHAPTER XIII 314 Right angled Spherical Triangles 324 CHAPTER XIV 334 Logarithmic and Trigonometric Tables 345

### Popular passages

Page 98 - If two triangles have two sides of the one equal to two sides of the...
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 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 84 - If a circle have any number of equal chords, what is the locus of their points of bisection? 21. If any point, not the center, be taken in a diameter of a circle, of all the chords which can pass through that point, that one is the least which is at right angles to the diameter. 22. If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them....
Page 117 - ABC, so that DE shall be equal to the difference of BD and CE. 22. In a given circle, to inscribe a triangle similar to a given triangle. 23. In a given circle, find the locus of the middle points of those chords which pass through a given point. 25. If a line bisects an exterior angle of a triangle, it divides the base produced into segments ^A which are proportional to the adjacent sides.
Page 307 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 237 - 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 233 - The volume of a rectangular parallelepiped is equal to the product of its three dimensions.
Page 126 - Theorem. — Two parallelograms are equal when two adjacent sides and the included angle in the one, are respectively equal to those parts in the other.