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 15
... sides of the polygon . The broken line , made up of all the sides of the ... number of their sides or angles . A Polygon of three sides is called a ... side of the one is equal to the first side BOOK I. 15.
... sides of the polygon . The broken line , made up of all the sides of the ... number of their sides or angles . A Polygon of three sides is called a ... side of the one is equal to the first side BOOK I. 15.
Page 46
... sides , less four right angles , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same ...
... sides , less four right angles , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same ...
Page 99
... number of lincar units in its base by the number of linear units in its altitude . Scholium 2. The product of two ... sides . PROPOSITION V. THEOREM . The area of a parallelogram is equal to the product of its base and altitude . Let ...
... number of lincar units in its base by the number of linear units in its altitude . Scholium 2. The product of two ... sides . PROPOSITION V. THEOREM . The area of a parallelogram is equal to the product of its base and altitude . Let ...
Page 111
... number of parallels be drawn cutting two lines , they will divide the lines proportionally . For , let be the point ... sides of a triangle proportionally , it will be parallel to the third side . Let ABC be a triangle , and let D.E ...
... number of parallels be drawn cutting two lines , they will divide the lines proportionally . For , let be the point ... sides of a triangle proportionally , it will be parallel to the third side . Let ABC be a triangle , and let D.E ...
Page 124
... number of triangles , similar , each to each , and similarly placed . I et ABCDE and FGHIK be two similar polygons ... sides about these angles proportional ; they are , therefore , similar ( P. XX . ) . Since these triangles are similar , we ...
... number of triangles , similar , each to each , and similarly placed . I et ABCDE and FGHIK be two similar polygons ... sides about these angles proportional ; they are , therefore , similar ( P. XX . ) . Since these triangles are similar , we ...
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Common terms and phrases
ABē ACē 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