WOOLWICH MATHEMATICAL PAPERS

ST. JOHN'S COLLEGE, CAMBRIDGE; INSTRUCTOR OF MATHEMATICS AT THE
ROYAL MILITARY ACADEMY, WOOLWICH

London

MACMILLAN AND CO., LIMITED

NEW YORK: THE MACMILLAN COMPANY

1901

All rights reserved

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)b+a2 = (a+b)2, and give the construction by which the proposition is proved.