Ritualistically, this is a symbol of control of conduct; a standard of right living. The symbol has an extreme antiquity. Early Egyptian monuments are carved with the Alpha and the Omega or symbol of God in the center of a circle embordered by two upright parallel perpendicular serpents, representing the power and wisdom of the Creator. The symbol apparently came into Masonry from an operative practice, known to but a few Master workmen on Cathedrals and great buildings.
Any school boy knows it now; put a dot on a circle anywhere; draw a straight line across the circle through its center; connect the dot with the points at which the line through the center cuts the circle; the result is a perfect square.
This was the Operative Master’s great secret -- knowing how to “try the square” It was by this that he tested the working tools of the Fellows of the Craft; did he do so often enough, it was impossible either for their tools or their work “to materially err”.
Excerpted from “Handbook for Candidate’s Coaches” By The Committee on Ritual and Donald G. Campbell, Past Grand Lecturer, Grand Lodge F.&A.M. of California.