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 , .. 106 The Area of a Triangle , 106 Formula for the Sine of Half an Angle , ... 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 To find the ...
... Parallelogram , .. 106 The Area of a Triangle , 106 Formula for the Sine of Half an Angle , ... 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 To find the ...
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 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 a parallelogram whose angles are all right angles . A ...
Page 43
... HMB MBC ( P. XX . , C. 2 ) : hence , is equal to its alternate angle 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 MBC ( P. XX . , C. 2 ) : hence , is equal to its alternate angle 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 will AB be equal to DC , and AD to BC . D For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to ...
... parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to ...
Page 48
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have : D the sides of the one equal to the sides of ...
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Then , the A Draw the diagonal DB . triangles ADB and CBD , will have : D the sides of the one equal to the sides of ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence