The point within a circle embordered by two perpendicular parallel lines, with the Holy Bible resting on the circle, is one of the most recognizable symbols in Freemasonry. It is also one which always raises a question. How can two lines be both perpendicular and parallel?
Anyone that has ever sat through a basic geometry class knows perpendicular and parallel lines are opposite. They are each defined mathematically as follows:
Perpendicular lines: ‘Perpendicular lines are lines that intersect and form right angles.’ [1]
Parallel lines: ‘Two lines are parallel if they are in the same plane but never intersect.’ [2]
If perpendicular and parallel lines are geometrically opposite, why does our ritual refer to these two lines as both perpendicular and parallel? Clearly this is a contradiction! There are two possible explanations for this inconsistency.
First, it is possible that the word perpendicular refers to the two tangents perpendicular to the diameter of the circle.
A tangent is a line that touches the edge of a circle once. The diameter would pass through the point. In other words, both lines, and both tangents, form two 90-degree angles with the diameter of the circle.
Second, a more antiquated definition of the word perpendicular meant ‘straight up and down’, ‘vertical’, or ‘nearly vertical’.
For example, the perpendicular face of the mountain, or the perpendicular mast of a ship. The word derives from Latin: Per (through) and pendere (to hang) forms perpendiculum (plumb line).
Our ritual makes much more sense if we apply this antiquated definition of the word, ‘two hanging parallel lines’, or ‘two vertical parallel lines’.
Additionally, the word ‘pendant’ derives from the French verb pendre ‘to hang’, which also derives from the Latin pendere. After all, a pendant hangs around a person’s neck.
Many Masons do not understand that the use of the word perpendicular in our ritual is either referring to the two tangents perpendicular to the circle’s diameter or that the ritual is using an antiquated definition of the word.
The latter is more likely. This lack of understanding has even caused some grand jurisdictions to remove the word ‘perpendicular’ from the ritual altogether!
Our Masonic teachings direct us to subdue our passions and improve ourselves through Masonry. What better way to improve ourselves than by studying our ritual? However, sometimes when we examine the ritual through a modern lens, we unintentionally leave the lens cap on.
Footnotes
References
[1] Geometry Common Core (Pearson Education, Inc., Boston, Massachusetts, 2012), page 942.
[2] Downing, Douglas, Ph.D. Dictionary of Mathematics Terms (Barron’s Educational Series, Inc.; New York, 1987), page 140.
Article by: Matthew A. Leilech
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