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Question
Find the third proportion to the following :
(x - y) and m (x - y)
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Solution
Let z be lhe third proportion
(x - y) : m (x - y) : : m (x - y) : z
⇒ (x -y) x z - m(x - y) x m (x - y)
⇒ (x - y) z = m2 (x - y)2
⇒ z = m2 (x - y)
The third proportion is m2 (x - y) .
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