Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 62
Page 25
... BC to the side EF : then B CE 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.
... BC to the side EF : then B CE 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.
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 . A 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 ...
... side , their sum will be less than that of the two remaining sides of the triangle . A 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 ...
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 . 2c . When G is on BC . In this ... side AB is equal to the side DE , the side AC to DF , and BU greater than EF , then will the angle BAC be greater than ...
... BC > AB + EF . Taking away the common part AB , there remains ( A. 5 ) , BC > EF . 2c . When G is on BC . In this ... side AB is equal to the side DE , the side AC to DF , and BU greater than EF , then will the angle BAC be greater than ...
Other editions - View all
Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence