Question

Find the third proportion to the following :

(x - y) and m (x - y)  

Answer 1

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) .