Elements of Geometry and Trigonometry |
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Page 251
... spherical angles , and is denoted by 1 . The excess of the sum of the angles of a spherical tri- angle over two right angles , is called the spherical excess . If we denote the spherical excess by E , and the three angles expressed in ...
... spherical angles , and is denoted by 1 . The excess of the sum of the angles of a spherical tri- angle over two right angles , is called the spherical excess . If we denote the spherical excess by E , and the three angles expressed in ...
Page 256
... spherical pyramids , which have the triangles AOC , BOD , for bases , are together equal to the spherical wedge whose angle is BOD . PROPOSITION XVIII . THEOREM . The area of a spherical triangle is equal to its spherical excess ...
... spherical pyramids , which have the triangles AOC , BOD , for bases , are together equal to the spherical wedge whose angle is BOD . PROPOSITION XVIII . THEOREM . The area of a spherical triangle is equal to its spherical excess ...
Page 258
... spherical polygon is equal to its spherical excess multiplied by the tri - rectangular triangle . then Let ABCDE be a spherical polygon , the sum of whose angles is S , and the number of whose sides is will its area be equal to ( S - 2n ...
... spherical polygon is equal to its spherical excess multiplied by the tri - rectangular triangle . then Let ABCDE be a spherical polygon , the sum of whose angles is S , and the number of whose sides is will its area be equal to ( S - 2n ...
Page 123
... spherical excess . Find the area of a great circle of the sphere , and divide it by 2 ; the quotient will be the area of a tri - rectangular triangle . Multiply the area of the tri- rectangular triangle by the spherical excess , and the ...
... spherical excess . Find the area of a great circle of the sphere , and divide it by 2 ; the quotient will be the area of a tri - rectangular triangle . Multiply the area of the tri- rectangular triangle by the spherical excess , and the ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment semi-circumference similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...