In this paper the author constructed a square over a Jourdan curve $C$ as follows:
On $C$, from the point $P$ at $t_0$ to the point $Q$ at $t=t_0+s$, we construct the chord, and upon the chord as a side erect a square in such a way that as $s$ approaches zero the square is inside $C$. As $s$ increases we consider the two free corner points of the square, $P_c$ and $Q_c$, adjacent to $P$ and $Q$ respectively. As $s$ approaches $T$ the square will be outside $C$ and therefore both $P_c$ and $Q_c$ must cross $C$ an odd number of times as $s$ varies from zero to $T$. The points may also touch $C$ without crossing.
Unfortunately I don't understand this construction and Can anybody explain to me that what is he said exactly?