what is the earliest known reference to the square as a symbol and what are some of the historical symbolic meanings?

In medieval operative practice, the square was depicted in the "Mason window" of ancient cathedrals to symbolize the Mason Craft itself 1. Among early catechisms, a 1725 manuscript records the square alongside God as necessary to make a lodge, naming the Bible, Compasses, and Square as the lodge's furniture 1. Non-Masonic references to the tool as a moral emblem extend much further back into antiquity; the Chinese text The Great Learning (dating between 300 and 400 BC) defines fair dealing and reciprocal morality as the "principle of acting on the Square" 12.

Across Masonic tradition, the square serves as a symbol of morality, uprightness, and fair dealing 12. Just as operative stonecutters apply a try-square to test whether a stone is cut to a true ninety-degree angle and fit for the wall, the Speculative Mason treats it as a try-square of conscience to align his conduct with virtue 2.

Craft usage also assigns the tool several distinct symbolic roles:

As the immovable jewel of the Worshipful Master, situated in the East to signify that all light and instruction issuing from the Master must be square 2.

Joined with the compasses, as a badge of the fraternity and a emblem of duty to the Craft and to oneself 1.

In the traditional expression to "part upon the square," where the instrument is pictured in a vertical plane—one leg resting on the level floor of the lodge and the other standing upright—to signify that brethren leave without hypocrisy or resentment 1.

Within geometry, as a fundamental component of the Forty-Seventh Proposition of Euclid 1.