The following entries appear on pp. 784-785 and p. 800 of the 1912 edition of “An Encyclopaedia of Freemasonry and Its Kindred Sciences” by Albert G. Mackey.

Three

Everywhere among the ancients the number three was deemed the most sacred of numbers. A reverence for its mystical virtues is to be found even among the Chinese, who say that numbers begin at one and are made perfect at three, and hence they denote the multiplicity of any object by repeating the character which stands for it three times. In the philosophy of Plato, it was the image of the Supreme Being, because it includes in itself the properties of the two first numbers, and because, as Aristotle says, it contains within itself a beginning, a middle, and an end. The Pythagoreans called it perfect harmony.

So sacred was this number deemed by the ancients, that we find it designating some of the attributes of almost all the gods. The thunderbolt of Jove was three-forked; the scepter of Neptune was a trident; Cerberus, the dog of Pluto, was three-headed; there were three Fates and three Furies; the sun had three names, Apollo, Sol, and Liber; and the moon these three, Diana, Luna, and Hecate. In all incantations, three was a favorite number, for, as Virgil says, “numero Deus impari gaudet,” that is God delights in an odd number. A triple cord was used, each cord of three different colors, white, red, and black; and a small image of the Subject of charm visas carried thrice around the altar, as we see in Virgil’s eighth Eclogue (line 73): Terna tibi hæc primum, triplici dirersa colore, licia circumdo, terque hæc altaria circum effigiem duco. I.e., First I surround thee with these three pieces of list, and I carry thy image three times round the altars.

The Druids paid no less respect to this sacred number. Throughout their whole system, a reference is constantly made to its influence; and so far did their veneration for it extend, that even their sacred poetry was composed in triads.

In all the Mysteries, from Egypt to Scandinavia, we find a sacred regard for the number three, as in the father, mother and child deities, Osiris, Isis, and Horus. In the Rites of Mithras, the Empyrean was said to be supported by three intelligences, Ormuzd, Mithra, and Mithras. In the Rites of Hindustan, there was the trinity of Brahma, Vishnu, and Siva. It was, in short, a general character of the Mysteries to have three principal officers and three grades of initiation.

In Freemasonry, the ternary is the most sacred of all the mystical numbers. Beginning with the old axiom of the Roman Artificers, that tres faciunt collegium, or it requires three to make a college, they have established the rule that no less than three shall congregate to form a Lodge. Then in all the Rites, whatever may be the number of superimposed grades, there lie at the basis the three Symbolic Degrees. There are in all the Degrees three principal officers, three supports, three greater and three lesser lights, three movable and three improvable jewels, three principal tenets, three working-tools of a Fellow Craft, three principal orders of architectures three chief human senses, three Ancient Grand Masters. In fact, everywhere in the system the number three is presented as a prominent Symbol. So much is this the case, that all the other mystical members depend upon it, for each is a multiple of three, its square or its cube, or derived from them. Thus, 9, 27, 81, are formed by the multiplication of three, as 3 × 3 = 9, and 3² × 3 = 27, and 3² × 3² = 81.

But in nothing is the Masonic signification of the ternary made more interesting than its collection with the sacred delta, the symbol of Deity.

Triangle

There is no symbol more important in its significance, more various in its application, or more generally diffused throughout the whole system of Freemasonry, than the triangle. An examination of it, therefore, cannot fail to be interesting to the Masonic student.

The equilateral triangle appears to have been adopted by nearly all the nations of antiquity as a symbol of the Deity, in some of his forms or emanations, and hence, probably, the prevailing influence of this symbol was carried into the Jewish system, where the yod within the triangle was made to represent the Tetragrammaton, or sacred name of God.

The equilateral triangle, says Brother D. W. Nash (Freemasons Magazine iv, page 294), “viewed in the light of the doctrines of those who gave it currency as a divine symbol, represents the Great First Cause, the Creator and Container of all things, as one and indivisible, manifesting Himself in an infinity of forms and attributes in this visible universe.”

Among the Egyptians, the darkness through which the candidate for initiation was made to pass was symbolized by the trowel, an important Masonic implement, which, in their system of hieroglyphics, has the form of a triangle. The equilateral triangle they considered as the most perfect of figures, and a representative of the great principle of animated existence, each of its sides referring to one of the three departments of creation, the animal, vegetable, and mineral.

The equilateral triangle is to be found scattered throughout the Masonic system. It forms in the Royal Arch the figure within which the jewels of the officers are suspended. It is in the Ineffable Degrees the sacred Delta, everywhere presenting itself as the symbol of the Grand Architect of the Universe. In Ancient Craft Masonry, it is constantly exhibited as the element of important ceremonies. The seats of the principal officers are arranged in a triangular form, the three Lesser Lights have the same situation, and the Square and Compasses form, by their union on the greater light, two triangles meeting at their bases. In short, the equilateral triangle may be considered as one of the most constant forms of Masonic symbolism.

The right-angled triangle is another form of this figure which is deserving of attention. Among the Egyptians, it was the symbol of universal nature; the base representing Osiris, or the male principle; the perpendicular, Isis, or the female principle; and the hypotenuse, Horus, their son, or the product of the male and female principle.

This symbol was received by Pythagoras from the Egyptians during his long sojourn in that country, and with it he also learned the peculiar property it possessed, namely, that the sum of the squares of the two shorter sides is equal to the square of the longest side—symbolically expressed by the formula, that the product of Osiris and Isis is Horus. This figure has been adopted in the Third Degree of Freemasonry, and will be there recognized as the Forty-seventh Problem of Euclid.

The full text of the 1912 edition of Mackey’s “An Encyclopaedia of Freemasonry and Its Kindred Sciences” may be found at:

Mackey’s Encyclopaedia of Freemasonry: Volume I

Mackey’s Encyclopaedia of Freemasonry: Volume II