Why are a Past Masters compasses, in his jewel, open at 60 degrees on a quadrant instead of on a square?

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Why are a Past Masters compasses, in his jewel, open at 60 degrees on a quadrant instead of on a square?

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The compasses open sixty degrees are in easy position to construct a square. The Master has worn the square while he presided; now, as Past Master, he is supposed to be in possession of the knowledge necessary to make a square, hence the position of the compasses and the quadrant. There are many geometric methods of erecting a square; the Past Master’s jewel hints at one of the simplest and most used methods as best for the Past Master to employ in instructing his successor.