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AMNER'S EIGHT YEARS'
Euclid, Algebra, & Mensuration,
WORKED OUT IN FULL, AS MODELS FOR
PUPIL-TEACHERS AND CANDIDATES,
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.
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