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 viii
... Cone , 121 Area of the Surface of a Sphere , 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a ...
... Cone , 121 Area of the Surface of a Sphere , 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a ...
Page 209
... polyedral angle . Furthermore , no other regular polygons can be grouped so as to form a salient polyedral angle ; therefore , Only five regular polyedrons can be formed . 14 BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
... polyedral angle . Furthermore , no other regular polygons can be grouped so as to form a salient polyedral angle ; therefore , Only five regular polyedrons can be formed . 14 BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
Page 210
... CONE , AND THE SPHERE . DEFINITIONS . 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . E P Thus , if the rectangle ABCD be turned about the side AB , as an axis , it will ...
... CONE , AND THE SPHERE . DEFINITIONS . 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . E P Thus , if the rectangle ABCD be turned about the side AB , as an axis , it will ...
Page 211
... contact . 5. A CONE is a volume which may be generated by a right - angled triangle revolving about one . of the sides adja- cent to the right angle , as an axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
... contact . 5. A CONE is a volume which may be generated by a right - angled triangle revolving about one . of the sides adja- cent to the right angle , as an axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
Page 212
... cone S - CDBE . The fixed line SA , is called the axis of the cone ; the curved surface generated by the hypothenuse SB , is called the convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ...
... cone S - CDBE . The fixed line SA , is called the axis of the cone ; the curved surface generated by the hypothenuse SB , is called the convex surface of the cone ; the circle generated by the side AB , is called the base of the cone ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence