Squaring the circle
“Squaring the circle” is an ancient geometrical/mathematical challenge to construct a square with the exact same area as a given circle using only a finite number of steps with a straightedge and a compass. It was first proposed by the ancient Greek mathematicians. It was proven mathematically impossible in 1882.
However, “Squaring the circle” remains a philosophical riddle.
The compasses create a circle, which has neither beginning or end and is therefore infinite, representing the spiritual.
The set square creates a square, which starts and finishes at the sides and is therefore finite, representing the physical.
So by Squaring the circle, you are making the spiritual physical or bringing Heaven down to Earth, which is exactly what the medieval stonemasons were trying to do whilst constructing the cathedrals.
The square and compasses and the ‘Squaring the circle’ geometrical problem, also featured heavily in 17th century Alchemical works, not just in Masonic imagery.
“Fac ex mare & fœmina circulum, inde quadrangulum, hinc triangulum, fac circulum & habebis lap. Philosophorum” (Make a circle out of the man and woman, derive from that a quadrangle [square], from that a triangle, and make a circle, and you will have the Philosopher’s Stone).