Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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 straight lines , one in each face , and both perpendicular to the edge at ...
... 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 straight lines , one in each face , and both perpendicular to the edge at ...
Page 158
... edges of the angle , and the portions of the planes lying between the edges are called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , BSC , CSD , DSA . and whose faces are ASB ...
... edges of the angle , and the portions of the planes lying between the edges are called faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , BSC , CSD , DSA . and whose faces are ASB ...
Page 174
... edges of a triedral angle , is greater than the third . Let SA , SA , SB , and SC , 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 ...
... edges of a triedral angle , is greater than the third . Let SA , SA , SB , and SC , 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 ...
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 BSC ...
... 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 BSC ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude 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 difference 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 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 slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
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.