Eldred John E. J. BROOKSMITH, B.A., LL.M., AT THE ROYAL MILITARY ACADEMY, WOOLWICH. [All Rights Reserved.] MATHEMATICAL EXAMINATION PAPERS FOR ADMISSION INTO Royal Military Academy, Woolwich, , JULY, 1880. PRELIMINARY EXAMINATION. I. GEOMETRY. 2. 1. Define a straight line, an angle, and a triangle. Distinguish between equal triangles and triangles which are equal in all respects. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal, the angle which is contained by the two sides of the one shall be equal to the angle which is contained by the two sides equal to them of the other. Shew also that the two triangles are equal in all respects. 3. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts are themselves equal and parallel. Shew also that the straight lines which join the extremities towards opposite parts, bisect each other. 4. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Shew that if a parallelogram be a rhombus, each of the parallelograms described about its diameter will also be a rhombus. 5. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by the side on which, when produced, the perpendicular falls and the straight line inter W. P. I Ι |