Suppose we are given triangle ABC, and let D lies in (AB) be such that |angleDCA| = |angleABC|.
Prove that d(A, C) is the mean proportional between d(A, B) and d(A, D).
the symbol ~ is a notation for similar, i.e. when he wrote $\displaystyle \Delta ABC \sim \Delta ACD$, then he meant that the two triangles are similar..