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CODLEIANA

AMNER'S EIGHT YEARS'

SCHOLARSHIP QUESTIONS

(DEDUCTIONS, ETC.),

IN

Euclid, Algebra, & Mensuration,

WORKED OUT IN FULL, AS MODELS FOR

PUPIL-TEACHERS AND CANDIDATES,

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LONDON:
J. T. AMNER, 127 LAUSANNE ROAD,

PECKHAM, S.E.
MOFFATT & PAIGE, 21 PATERNOSTER SQUARE, E.C.

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QUEEN'S SCHOLARSHIP

EXAMINATIONS.

Scholarship Examination for 1871.

EUCLID 6. Construct a square equal to the sum of three given squares.

Let A, B, and C be the sides of the three given squares: it is required to construct a square equal in area to the three squares described upon the straight lines A, B, and C.

ABC

F

D

E

Construction. Make DE equal to A.

At D draw DF at right angles to DE (1. 11), and equal to B (1. 3).

Join FE (Post. I).

At F in the straight line FE draw FG at right angles to FE (1. 11); and make FG equal to C (1. 3).

Join GE; then

The square described upon GE is equal to the squares described on A, B, and C.

Proof.-Because the angle FDE is a right angle, the

A

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