Elements of Geometry and Trigonometry |
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Page 25
... side EF : then B A D CE F will the triangles be equal in all their parts . For , let ABC be applied to DEF in such a manner that the angle B shall coincide with the angle E , the side BC taking the direction EF , and the side BA BOOK I. 25.
... side EF : then B A D CE F will the triangles be equal in all their parts . For , let ABC be applied to DEF in such a manner that the angle B shall coincide with the angle E , the side BC taking the direction EF , and the side BA BOOK I. 25.
Page 26
... BC is equal to EF , the vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side ... side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side ...
... BC is equal to EF , the vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the side ... side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side ...
Page 27
... side , their sum will be less than that of the two remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will the sum of BO and 00 ...
... side , their sum will be less than that of the two remaining sides of the triangle . Let be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then will the sum of BO and 00 ...
Page 28
... sides and the included angle of the one equal to two sides and the included angle of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC ...
... sides and the included angle of the one equal to two sides and the included angle of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC ...
Page 29
... BC > AB + EF . Taking away the common part AB , there remains ( A. 5 ) , BC > EF 2o . When G is on BC . In this case ... side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will the angle BAC be greater ...
... BC > AB + EF . Taking away the common part AB , there remains ( A. 5 ) , BC > EF 2o . When G is on BC . In this case ... side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will the angle BAC be greater ...
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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
AB² ABCD AC² 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...