« ΠροηγούμενηΣυνέχεια »
ST. JOHN'S COLLEGE, CambridDGE; INSTRUCTOR OF MATHEMATICS AT THE
MACMILLAN AND CO., LIMITED
NEW YORK: THE MACMILLAN COMPANY
All rights reserved
MATHEMATICAL EXAMINATION PAPERS
FOR ADMISSION INTO
Royal Military Academy, Woolwich,
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.