Mathematical Papers for Admission Into the Royal Military Academy and the Royal Military College for the Years 1898-1907

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Macmillan and Company, limited, 1909 - Mathematics - 396 pages

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Page 5 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 7 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 11 - ... method for the loads shown. The heel joint, joint 1, is the first to be solved. The one-half panel load at the joint and the reaction are combined to give the effective reaction. The force polygon for the joint is drawn with the forces ^parallel to the lines of action shown in the space diagram. Since the sum of the horizontal components and the sum of the vertical components must equal zero for equilibrium, the polygon must close.
Page 3 - If two triangles have two sides of the one equal to two sides of the other...
Page 4 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 14 - A body falls from rest from a height so great that the fact that the force of gravity varies inversely as the square of the distance from the center of the earth cannot be neglected.
Page 9 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Page 3 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 12 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 9 - Prop. 13. In a system in which each pulley hangs by a separate string and the strings are parallel, there is an equilibrium when P : W :: 1 : that power of 2 whose index is the number of moveable pulleys. Prop. 14. The weight ( W') being on an inclined plane and the force (P ) acting parallel to the plane, there is an equilibrium when P : W :: the height of the plane : its length.

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