That is, if a number be divided into any two parts, the square of the number is equal to the squares of the two parts, together with twice the product of the two parts.

(11. 7.) Let the line AB contain a linear units, and the parts AC and BC, m and n linear units respectively.

A

Then a m+n;

B

squaring these equals, .. a2=(m+n)2

= m2+2mn+n2

adding n2 to these equals, ... a2+n2 = m2 + 2mn+2n2

=

= m2 + 2(m+n)n

= m2 + 2an.

=

That is, if a number be divided into any two parts, the squares of the whole number and of one of the parts are equal to twice the product of the whole number and that part, together with the square of the other part.

(11. 8.) Let the line AB contain a linear units, and the parts of it AC, BC, m and n linear units respectively.

adding n to these equals, ... a+n=m+2n; squaring these equals, .. (a+n)2 = (m+2n)2

= m2+4mn+4n2
=m2+4n(m+n)
= m2 + 4an;

transposing, .. m2 + 4an=(a+n)2.

That is, if a number be divided into any two parts, four times the product of the whole number and of one of the parts, together with the square of the other part, is equal to the square of the number made of the whole and the part first taken.

A COMPLETE SET

OF

MALE PUPIL TEACHERS'

EXAMINATION

QUESTIONS IN ALGEBRA

TO SEPTEMBER 1879 (INCLUSIVE).

WITH ANSWERS.

Compiled, Classified, and Graduated by

W. J. DICKINSON,

FORMERLY LECTURER ON GRAMMAR AND EUCLID AT THE BATTERSEA TRAINING COLLEGE'

AUTHOR OF

PRACTICAL ENGLISH GRAMMAR AND ANALYSIS, THE DIFFICULTIES OF GRAMMAR
AND ANALYSIS SIMPLIFIED,' 'HOW TO TEACH GRAMMAR AND ANALYSIS,'
AND THE DIFFICULTIES OF EUCLID SIMPLIFIED.'

LONDON: JOSEPH HUGHES,

THREE TUNS PASSAGE, PATERNOSTER SQUARE, E.C.

Miscellaneous on Addition, Subtraction, Multiplication, and Divi-

Simplification (involving a Knowledge of the Whole of the