ST. JOHN'S COLLEGE, CAMBRIDGE; INSTRUCTOR OF MATHEMATICS AT THE ROYAL MILITARY ACADEMY, WOOLWICH London NEW YORK: THE MACMILLAN COMPANY 1901 All rights reserved mali 395.30.21 COT HARVARD LEGE JAN 29 1902 LIBRARY Farrar fund. GLASGOW: PRINTED AT THE UNIVERSITY PRESS BY ROBERT MACLEHOSE AND CO. MATHEMATICAL EXAMINATION PAPERS FOR ADMISSION INTO Royal Military Academy, Woolwich, JUNE, 1891. OBLIGATORY EXAMINATION. I. EUCLID (Books I.-IV. AND VI.). [Ordinary abbreviations may be employed; but the method of proof must be geometrical. Proofs other than Euclid's must not violate Euclid's sequence of propositions. Great importance will be attached to accuracy.] I. Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. 2. Describe a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 3. On the perpendicular AD of an equilateral triangle ABC another equilateral triangle EAD is described ; show that its perpendicular EF is one-fourth of the perimeter of the triangle ABC. 4. Enunciate that proposition in Euclid's second book which is expressed directly in algebraic symbols by the formula (2a+b)6+ao = (a + b)?, and give the construction by which the proposition is proved. |