Page 39 - August 2018

Two Perpendicular Parallel Lines

Matthew A. Leilich, P M, Gothic-Fraternal Lodge #270, Hamilton Square, NJ

The point within a circle em-bordered Our ritual makes much more sense if
by two perpendicular, parallel lines, we apply this antiquated defi nition of the
with the Holy Bible resting on the circle, word, “two parallel hanging lines,” or “two
is one of the most recognizable symbols vertical parallel lines.” Additionally, the word
in Freemasonry. It is also one which pendant derives from the French verb pendre
always raises a question. How can two “to hang,” which also derives from the Latin
lines be both perpendicular and parallel? pendere. After all, a pendant hangs around a
person’s neck.
Anyone that has ever sat through a basic
geometry class knows perpendicular and Many masons do not understand that
parallel lines are opposite. They are each the use of the word perpendicular in our
defi ned mathematically as follows: ritual is either referring to the two tangents
perpendicular to the circle’s diameter or that
Perpendicular lines: the ritual is using an antiquated defi nition of the word. The latter
“Perpendicular lines are lines that intersect and is more likely. This lack of understanding has even caused some
form right angles.”(1) grand jurisdictions to remove the word “perpendicular” from the
Parallel lines: “Two lines are parallel if they are in ritual altogether!
the same plane but never intersect.”(2)
Our Masonic teachings direct us to subdue our passions and
If perpendicular and parallel lines are geometrically improve ourselves through masonry. What better way to improve
opposite why does our ritual refer to these two lines ourselves than by studying our ritual? However, sometimes when
as both perpendicular and parallel? Clearly, this is a we examine the ritual through a modern lens, we unintentionally
contradiction! There are two possible explanations leave the lens cap on.
for this inconsistency.

First, it is possible that the word perpendicular refers
to the two tangents perpendicular to the diameter of (1) Geometry Common Core (Pearson Education, Inc., Boston,
the circle. A tangent is a line that touches the edge of Massachusetts, 2012), page 942.
a circle once. The diameter would pass through the (2) Downing, Douglas, Ph.D. Dictionary of Mathematics Terms
point. In other words, both lines, or both tangents, (Barron’s Educational Series, Inc.; New York, 1987), page 140.
form two 90-degree angles with the diameter of the
circle.

Second, a more antiquated defi nition 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) +
pendere (to hang) forms perpendiculum (plumb line).

Volume 94 Number 6 Montana Freemason Page 39