Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page v
... Circle , Exercises , BOOK VI . Planes , and Polyedral Angles , Exercises , Polyedrons ,. Exercises , 61 84 95 97 29 188 140 142 ........ 163 165 187 BOOK VII . 189 221 1 BOOK VIII . PAGE Cylinder , Cone , and Sphere.
... Circle , Exercises , BOOK VI . Planes , and Polyedral Angles , Exercises , Polyedrons ,. Exercises , 61 84 95 97 29 188 140 142 ........ 163 165 187 BOOK VII . 189 221 1 BOOK VIII . PAGE Cylinder , Cone , and Sphere.
Page vi
... Cylinder , Cone , and Sphere , Exercises , 223 248 BOOK IX . Spherical Geometry ,. Exercises , 250 277 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for Characteristics , General Principles , ..... Table of ...
... Cylinder , Cone , and Sphere , Exercises , 223 248 BOOK IX . Spherical Geometry ,. Exercises , 250 277 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for Characteristics , General Principles , ..... Table of ...
Page 222
... two regular polyedrons of the same kind are similar . 18. Show that the surfaces of any two similar polye- drons are to each other as the squares of any two homologous edges BOOK VIII . THE CYLINDER , THE CONE , AND 222 GEOMETRY .
... two regular polyedrons of the same kind are similar . 18. Show that the surfaces of any two similar polye- drons are to each other as the squares of any two homologous edges BOOK VIII . THE CYLINDER , THE CONE , AND 222 GEOMETRY .
Page 223
... CYLINDER , THE CONE , AND THE SPHERE . DEFINITIONS . A E 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side AB , as an axis ...
... CYLINDER , THE CONE , AND THE SPHERE . DEFINITIONS . A E 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side AB , as an axis ...
Page 224
... cylinder , when its bases are inscribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circum- scribing ...
... cylinder , when its bases are inscribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circum- scribing ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence