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 45
... polygon has sides . Let ABCDE be any polygon ; then the sum of its in- terior angles A , B , C , D , and E , is equal to two right angles taken as many times , less two , as the polygon has sides . From the vertex of any angle A , draw ...
... polygon has sides . Let ABCDE be any polygon ; then the sum of its in- terior angles A , B , C , D , and E , is equal to two right angles taken as many times , less two , as the polygon has sides . From the vertex of any angle A , draw ...
Page 46
... polygon , any interior angle is equal to twice as many right angles as the figure has 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 ...
... polygon , any interior angle is equal to twice as many right angles as the figure has 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 ...
Page 47
... polygon has sides . the interior angles is equal to two right angles taken as many times , less two , as the polygon has sides : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four ...
... polygon has sides . the interior angles is equal to two right angles taken as many times , less two , as the polygon has sides : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four ...
Page 50
... polygon is 12 right angles ; what is the polygon ? 8. What is the sum of the interior angles of a hepta- gon equal to ? 9. The sum of five angles of a given equiangular poly- gon is 8 right angles ; what is the polygon ? 10. What part ...
... polygon is 12 right angles ; what is the polygon ? 8. What is the sum of the interior angles of a hepta- gon equal to ? 9. The sum of five angles of a given equiangular poly- gon is 8 right angles ; what is the polygon ? 10. What part ...
Page 62
... Polygon is circumscribed about a circle , when each of its sides is tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A ...
... Polygon is circumscribed about a circle , when each of its sides is tangent to the circumference . 14. A Circle is inscribed in a polygon , when its circumference touches each of the sides of the polygon . ооо о POSTULATE . A ...
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Common terms and phrases
AB² ABCD AC² 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