The Compass and Square
The square (tool, above) is one half of a square (figure, below) and therefore tied to the number 4. Comparing the compass and square above to the
figure below we can see that the compass also represents the equilateral triangle. The Masonic compass and square image proves to be an abbreviation
of all the symbology involved in the Rebis figure, making it a quintessential emblem of Dualism, like twin columns, the cross or the yin/yang
symbol.
Geometry (literally 'earth measure') begins with a square x  y, Cartesian coordnate grid (two crossing lines).
The image above associates the number 1 with the vertical line (like a column or the letter I). The point where a horizontal line crosses perpendicular to
that line is noted with a circle and point (symbol for the sun). A circle is generated from this point. Connecting the points where the circle meets the
lines forms a square (marked 4). An equilateral triangle (marked 3) shares the top point with the circle, line and square.
Quadratum and Triangulum
In terms of geometric design principles, the square in the circle relates to what is known as ad quadratum represented by the square (tool), while
the triangle in the circle relates to the ad triangulum represented by the compass. Geometric design entails using plane figures to determine the
regulating points and lines in a building or painting. Below we see the House of the Temple in Washington DC which, like some mayan temples, features the
ad quadratum form (with 45 degree triangles).
Vitruvius was a first century BC roman architect who wrote about principles of
design. In the 16th century Cesariano published his
translation of Vitruvius that included a copy of the following image of the plan for the Milan Cathedral which is said to reveal the fundamental
principles of the 'old geometric system of design'. Notice how the inner most circle in the plan contains the same cross, square and a triangle, as the
Rebis figure above.
As you can see above, the grid in the cathedral plan is derived from vertical pairs of (60 degree) triangles. The base of the (blue) triangle inside the
inner circle determines the floor level (earth) and the width of the opening in the front, while the height of that triangle determines where the roof line
(sky) is. We call this ad triangulum (by the triangle).
Below we inscribe a triangle within the circle of the HOT plan and see that the base of that coincides with the
floor level of the building's main entrance.
The Cross and Rhombus
Note especially that looking at the grid of twin triangles (in the cathedral plan) we can see different sized rhombus, hexagons and hexagrams. Also,
the diagonals of a rhombus form a cross. The author of the
"Canon" tells us that "the geometrical
figure forming the basis of the plan of the Milan cathedral is the rhombus or vesica... introduced into the plan as the mystical compliment of the
cross... (together) they are the emblems of the 'double soul of the Universe'. This is the mystery which the cross and the rhombus united
together signified during the Middle Ages".
The cathedral is an architectural Rebis, according to the "Canon".
The cross and rhombus are analogous to the square and compass, where the cross is masculine and the rhombus (derived from the vesica) is feminine. Below
we see the (thinly veiled phallic) cross shape of the Milan floor plan which is regulated by the quadratum while the elevation (above) is ruled by the
triangulum.
Compare to the HOT in DC.
Below is an image of 13th Century architect Hugues Libergier
(d. 1263) taken from his tomb slab, where he is seen holding an architectural model. Note the rhombus grid on the roof of that.
The Tree of Life
The Tree of Life (TOL) is analogous to Jacob's ladder (Genesis 1:28) that is set up on the earth and reaches to the heavens. The Righteous Man is said,
in Hasidism, to have his feet on the ground and his head (mind) in the heavens. The gothic cathedrals were monuments to the notions of duality and
verticality, symbolized by the upright rhombus and the TOL. Below is Albert Pike's 1871 depiction of the Tree.
Next we see one of Aleister Crowley's Tarot cards. Note that all four of Crowley's 10 cards have depictions of the TOL on them. Here we see intersecting
wands that produce a rhombus grid like above. (Note the twin pillars.)
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