An often seen and seldom explained tool in Freemasonry, the quadrant (or protractor) is, in our jurisdiction, used in two very specific ways.  The first, and most common configuration is its combination with the compass (in the place of the square) to represent the office of Past Master.  The second is when it is combined with the symbol of our fraternity, the square and compass, to form the jewel of the Grand Master.  In other jurisdictions, this symbol represents the office of Past Master.  Regardless of the office it represents, the tool itself appears to have the same meaning. 

The quadrant was apparently proposed by mathematician, astronomer, natural philosopher, geographer, and astrologer, Ptolemy (c. 100 AD – c. 170 AD), as a replacement for the astrolabe. In his mathematical and astronomical treatise, Almagest, Ptolemy describes a “plinth” which could measure the altitude of the noon sun by projecting the shadow of a peg on a graduated arc of 90 degrees. Although his device was much larger and included several moving parts, it was the precursor for the tool we know today.

In speculative Freemasonry, the quadrant shows the angle at which the compasses are opened.  This measure is always 60˚, as this is the angle of an equilateral triangle, which is itself a symbol of balance.  The quadrant measures due boundaries (the circle drawn by the compass) and it serves as a reminder for the man that it was or is their responsibility to ensure that the Masons under his jurisdiction make proper use of their own compasses.  As suggested by Ptolemy, when paired with the compass, the quadrant can be used as a sextant (a navigating tool used in measuring altitude).  Imbued with this meaning, it symbolizes that the holder has navigated the course of his Lodge (as Master or Grand Master) and is qualified to assist or advise his successors, should the need arise.