A Freemasonic term based on the square level used by ancient & modern stone masons. According to "
Encyclopedia of Freemasonry, Vol II, Albert Mackey" the meaning of the square is:
"... In Freemasonry, it is a symbol of morality. This is its general signification, and is applied in various ways: 1. It presents itself to the neophyte as one of the three great lights; 2. To the Fellow-Craft as one of his working tools; 3. To the Master Mason as the official emblem of the Master of the Lodge" (Enc. of Freemasonry Vol II, Albert Mackey pp. 708)
Thus, the term "on the square" is much the same as "squared away," or "fair and square." To talk to a person "on the square" means to talk in a blunt and
straightforward manner, as not to
beat around the bush.