The Forty-Seventh Problem of Euclid

The Forty-Seventh Problem of
Euclid
—One of the most important symbols of Masonry is the Forty-Seventh Problem of
Euclid. The principles illustrated by it form the foundation of numbers, geometry,
and mathematical symbolism. It represents perfectly the Tetragrammaton and the
operation of divine law. It is the problem of the right angle triangle. The three sides
represent the divine trinity, and the trine as a whole represents the unity of God. The
perpendicular line forming one side of the triangle is the Masonic Plumb,
corresponding kabalistically to the masculine letter Jod, also to Osiris of Egypt, and
to God the Father.
Now nature manifests herself in every septenary by means of three active principles,
and four passive forms. The vertical side is consequently divided into three parts
representing the three active principles. The number three expresses action, and
these three divisions correspond to the three strongest positions of the sun; on the
Ascendant, on the Mid-heaven, and on the Descendant. It also corresponds in
astrology to the three qualities and the three degrees of emanation, into which the
zodiacal signs are divided. Likewise it corresponds to the three active portions of the
human constitution; the ego, the divine soul, and the animal soul.
The horizontal side of the triangle is the Masonic Level, corresponding kabalistically
to the feminine letter He, also to Isis of Egypt, and to the Virgin Mary of later times. It
is divided into four sections to designate the four forms by which the three active
principles always manifest. All material things have four relative states—three
dimensions and position—and express the active qualities of attraction, repulsion,
and motion. The attractive power is represented by gravitation. The repulsive power
is illustrated by the cohesion which enables it by repelling other substances to keep
its own identity without yielding to their gravitational attraction and fusing with
them into a homogeneous mass. Motion is denoted by the change of relative position
of every object in the universe.
The number four expresses realization, and corresponds astrologically to the four
quadrants of the heavens, and to the four triplicities into which the zodiac is divided.
In man it corresponds to the four forms of his constitution; spiritual body, astral body,
etheric body, and physical form.
The union of 3 with 4, of a plumb with a level, gives us aMasonic Square of 7, which,
properly interpreted reveals the Lost Word of the Master. To become that word,
however, it must relinquish the square aspect, and be transformed into two interlaced
trines having as a common center the 7th point. As the triangle is presented, however,
the third factor of the figure is the meeting point of the 3 and 4, of Sun and Moon, of
active and passive, of Jod and He. This right angle is the key to the solution of
Euclid’s problem, even as it is the symbol of the solution of man’s. Astrologically it
is the meeting point of planetary energies on the earth, corresponding to the Vau of
the word, to the Overshadowing Intelligence of Egypt, to the Holy Ghost of
Christianity, to vibration in the natural world, and in human life to union.
Mathematical evolution means the multiplication of a number by itself. The
evolution of man is accomplished through the union of the 3 principles with the 4
elements. Their multiplication gives the number of the signs of the zodiac through
which the impersonal soul must successively pass, and their union produces 7, the
number of component parts of man’s constitution.
Evolve the side 3, and the side 4—that is, multiply each by itself—and the sum of
these two is equal to the evolution of the third side. This third side, the evolution of
which results from the evolution of principles and elements, has the number 5, the
symbol of man. This demonstrates, according to the Ancient Hermetic System of
Numbers, the evolution of man.
This hypotenuse is the fourth factor of the figure, the product of the union of
masculine and feminine forces. It represents, therefore, the climax of evolution on
the physical plane. The area of the figure is 6, signifying temptation. This leads to the
union of 3 and 4 to evolve man, symbolized by 5, who possesses a 7-fold constitution.
The hypotenuse corresponds to the life resulting from the union of solar and lunar
rays upon the earth. It also corresponds in man to intellect, kabalistically to the final
He of the divine word, to the Egyptian Horus, and in modern religion to the Son of
God.
The figure of the 47th problem of Euclid (see illustration at front of chapter)
therefore, by its three sides, representing man’s principles, and his forms, expresses
the cycle of life. This cycle indicates the struggle by the area, 6, which must express
through the sides, the sum of which is 12, the number of the zodiacal signs under the
influence of which all evolution expresses. By adding together the evolved
sides—each side multiplied by itself—we have the number 50, typifying the number
of steps that lead man to adeptship, that evolve man into superman. It is said that
Moses was able successfully to take 49 of these steps, but failing in the last he was
denied entrance into the promised land. He could see this land of plenty, he had the
wisdom to see this final step, but was unable to take it. This, perhaps, was not so much
the fault of Moses as that of the times in which he lived.


By CC Zain