Elements of Geometry and Trigonometry |
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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 Circumference of ...
... 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 Circumference of ...
Page 17
... PARALLELOGRAM is a quadrilateral which has its opposite sides parallel , two and two . There are and rhomboids . two varieties of parallelograms : rectangles 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 and rhomboids . two varieties of parallelograms : rectangles 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A ...
Page 43
... interior angle HMB ; are parallel , the angle HMB MBC ( P. XX . , C. 2 ) : hence , which was to be proved . Cor . The opposite angles of a parallelogram are equal . PROPOSITION XXV . THEOREM . In any triangle , the BOOK I. 43.
... interior angle HMB ; are parallel , the angle HMB MBC ( P. XX . , C. 2 ) : hence , 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 . 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 . 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 . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the ...
... parallelogram . In the quadrilateral ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...