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 50
... angle is an angle of an equi- angular decagon ? 11. How many sides has a polygon in which the sum of the interior angles is equal to the sum of the exterior angles ? 12. Construct a square , having given one of its 50 GEOMETRY . Exercises,
... angle is an angle of an equi- angular decagon ? 11. How many sides has a polygon in which the sum of the interior angles is equal to the sum of the exterior angles ? 12. Construct a square , having given one of its 50 GEOMETRY . Exercises,
Page 51
... Construct a square , having given one of its diag- onals . NOTE 1. - The complement of an angle is the difference between that angle and a right angle ; thus , EOB is the complement of AOE . NOTE 2. - The supplement of an angle is the ...
... Construct a square , having given one of its diag- onals . NOTE 1. - The complement of an angle is the difference between that angle and a right angle ; thus , EOB is the complement of AOE . NOTE 2. - The supplement of an angle is the ...
Page 85
... construct an angle equal to a given angle . Let A be the given point , AB the given line , and IKL the given angle . From the vertex K as a cen- ter , with any radius Kl , describe the arc IL , terminating in the K sides of the angle ...
... construct an angle equal to a given angle . Let A be the given point , AB the given line , and IKL the given angle . From the vertex K as a cen- ter , with any radius Kl , describe the arc IL , terminating in the K sides of the angle ...
Page 87
... construct the third angle . Let A and B be given angles of a triangle . Draw a line DF , and at some point of it , as E , construct the angle FEH equal to A , and HEC equal to B. Then , CED is equal to the required angle . D BLA For ...
... construct the third angle . Let A and B be given angles of a triangle . Draw a line DF , and at some point of it , as E , construct the angle FEH equal to A , and HEC equal to B. Then , CED is equal to the required angle . D BLA For ...
Page 88
... construct the triangle . Let B and C denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side and on DE , lay off DG ...
... construct the triangle . Let B and C denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side and on DE , lay off DG ...
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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