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 vii
... Parallelogram , The Area of a Triangle ,. Formula for the Sine and Cosine of Half an Angle , Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , Area of a Regular Polygon ,. To find the Circumference of a Circle ...
... Parallelogram , The Area of a Triangle ,. Formula for the Sine and Cosine of Half an Angle , Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , Area of a Regular Polygon ,. To find the Circumference of a Circle ...
Page 17
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A ...
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A ...
Page 43
... HMB is equal to its alternate angle MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
... HMB is equal to its alternate angle MBC ( P. XX . , C. 2 ) : hence , GHK is equal to ABC ; which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
Page 47
... parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then AB is equal to DC , and AD to BC . For , draw the diagonal BD . Then , because AB and DC are parallel , the angle DBA is equal to its ...
... parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then AB is equal to DC , and AD to BC . For , draw the diagonal BD . Then , because AB and DC are parallel , the angle DBA is equal to its ...
Page 48
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then is it a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , have the sides D of the one equal to the sides of the other , each ...
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then is it a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , have the sides D of the one equal to the sides of the other , each ...
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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