Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 15
... sides of the polygon . The broken line , made up of all the sides of the polygon , is called the perimeter of the ... number of their sides or angles . A Polygon of three sides is called a triangle ; one of four sides , a quadrilateral ...
... sides of the polygon . The broken line , made up of all the sides of the polygon , is called the perimeter of the ... number of their sides or angles . A Polygon of three sides is called a triangle ; one of four sides , a quadrilateral ...
Page 46
... sides , less four , 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 order ...
... sides , less four , 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 order ...
Page 99
... number of linear 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 linear 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 A ...
... 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 A ...
Page 124
... number of triangles , similar , each to each , and similarly placed . Let 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 . Let 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
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following