n, and this translation must have
come into the hands of the patrons of the building craft at the very
time when the Gothic style had its origin; it was the only Latin
translation known in Europe, and was, some centuries later, the
text-book of the first printed edition of Euclid.

The Operative Masons had always formed their Right-Angled Triangles by
means of mundane measures of 3, 4, and 5 units to each side
respectively, as was done by the Harpedonaptae of Egypt 5000 years ago,
and 2500 years later by Pythagoras, and this same method continues to
be used to this day; but to those of a religious turn of mind, who had
only lately become conversant with Euclid, and looked upon Geometry
not only as the height of all learning, but, as they progressed in the
knowledge of its bearing on the Science of building, actually made it
synonymous with Tectonic Art (the old MSS. which have come down to us
from that time _invariably_ state that "at the head of all the
Sciences stands _Geometry which is Masonry_"), there must have come a
wave of wonderful enthusiasm when they first discovered that the
Geometrical way of creating a Right Angle, as given in Euclid I. ii.,
was by means of an Equilateral Triangle, by joining the Apex with the
centre of the base. This Equilateral Triangle was the earliest symbol
we know of the Divine _Logos_ in connection with that wonderful figure
the Vesica Piscis; and as the Bible declared that the Universe was
created by the Logos (the Word), so the Square which represented the
Universe was naturally created by means of the Equilateral Triangle. A
great mystery this must have appeared to those who, like the Hellenic
philosophers, postulated that everything on Earth has its counterpart
in Heaven, and who, in their religious mysticism, were always looking
for signs of the transcendental in their temporal surroundings.

But in what awe and reverence must they have held Geometry, when they
further found that the Equilateral Triangle, representing the Logos,
was itself generated, as shown in the _first_ Problem of Euclid, upon
which the whole Science of Geometry was therefore based, by the
intersection of two Circles! These two Circles were held by the
Greeks, at the beginning of our Era, to represent the Past and Future
Eternities generating the Logos; but the whole figure (Euclid I. i.)
was at the time we are now dealing with looked upon by Mediaeval
Architects as representing the Three Divine _personae_