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 iii
... figure , that figure being taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the ...
... figure , that figure being taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the ...
Page v
... Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII ...
... Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII ...
Page 15
... FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by straight lines . The bounding lines are called sides of the polygon . The broken line , made up of all the sides of ...
... FIGURE is a portion of a plane bounded by lines , either straight or curved . 18. A POLYGON is a plane figure bounded by straight lines . The bounding lines are called sides of the polygon . The broken line , made up of all the sides of ...
Page 46
... 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 to four right angles . Let the sides of the polygon ABCDE be prolonged , in ...
... 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 to four right angles . Let the sides of the polygon ABCDE be prolonged , in ...
Page 48
... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a quadrilateral are equal and parallel , the figure is a parallelogram . In the quadrilateral ABCD , let AB be equal and parallel ...
... figure is a parallelogram ( D. 28 ) ; which was to be proved . PROPOSITION XXX . THEOREM . If two sides of a quadrilateral are equal and parallel , the figure is a parallelogram . In the quadrilateral ABCD , let AB be equal and parallel ...
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Common terms and phrases
AB² AC² 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