Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 40
Page 157
... edge of the angle , and the planes themselves are called faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the ...
... edge of the angle , and the planes themselves are called faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the ...
Page 158
... edges of the the portions of the planes lying called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but ...
... edges of the the portions of the planes lying called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but ...
Page 174
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle then will the sum of any two of the plane angles formed by them , as ASC and CSB , be greater than the third ASB . If the ...
... edges of a triedral angle , is greater than the third . Let SA , SB , and SC , be the edges of a triedral angle then will the sum of any two of the plane angles formed by them , as ASC and CSB , be greater than the third ASB . If the ...
Page 175
... edges of any polyedral angle , is less than four right angles . Let S be the vertex of any polyedral angle whose edges are SA , SB , SC , SD , and SE ; then will the sum of the angles about S be less than four right angles . For , pass ...
... edges of any polyedral angle , is less than four right angles . Let S be the vertex of any polyedral angle whose edges are SA , SB , SC , SD , and SE ; then will the sum of the angles about S be less than four right angles . For , pass ...
Page 176
... edges of two triedral angles are equal , each to each , the planes of the equal angles are equally inclined to each other . Let S and T be the vertices of two triedral angles , and let the angle ASC be equal to DTF , ASB to DTE , and ...
... edges of two triedral angles are equal , each to each , the planes of the equal angles are equally inclined to each other . Let S and T be the vertices of two triedral angles , and let the angle ASC be equal to DTF , ASB to DTE , and ...
Other editions - View all
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
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices 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...