All this, of course, is nothing more nor less than the phallus and cteis, or lingam and yoni, under a different form.

The symbol of the right-angled triangle was afterwards adopted by Pythagoras when he visited the banks of the Nile; and the discovery which he is said to have made in relation to the properties of this figure, but which he really learned from the Egyptian priests, is commemorated in Masonry by the introduction of the forty-seventh problem of Euclid's First Book among the symbols of the third degree. Here the same mystical application is supplied as in the Egyptian figure, namely, that the union of the male and female, or active and passive principles of nature, has produced the world. For the geometrical proposition being that the squares of the perpendicular and base are equal to the square of the hypothenuse, they may be said to produce it in the same way as Osiris and Isis are equal to, or produce, the world.

Thus the perpendicular—Osiris, or the active, male principle—being represented by a line whose measurement is 3; and the base—Isis, or the passive, female principle—by a line whose measurement is 4; then their union, or the addition of the squares of these numbers, will produce a square whose root will be the hypothenuse, or a line whose measurement must be 5. For the square of 3 is 9, and the square of 4 is 16, and the square of 5 is 25; but 9 added to 16 is equal to 25; and thus, out of the addition, or coming together, of the squares of the perpendicular and base, arises the square of the hypothenuse, just as, out of the coming together, in the Egyptian system, of the active and passive principles, arises, or is generated, the world.

In the mediaeval history of the Christian church, the great ignorance of the people, and their inclination to a sort of materialism, led them to abandon the symbolic representations of the Deity, and to depict the Father with the form and lineaments of an aged man, many of which irreverent paintings, as far back as the twelfth century, are to be found in the religious books and edifices of Europe.[137] But, after the period of the renaissance, a better spirit and a purer taste began to pervade the artists of the church, and thenceforth the Supreme Being was represented only by his name—the tetragrammaton—inscribed within an equilateral triangle, and placed within a circle of rays. Didron, in his invaluable work on Christian Iconography, gives one of these symbols, which was carved on wood in the seventeenth century, of which I annex a copy.

But even in the earliest ages, when the Deity was painted or sculptured as a personage, the nimbus, or glory, which surrounded the head of the Father, was often made to assume a triangular form. Didron says on this subject, "A nimbus, of a triangular form, is thus seen to be the exclusive attribute of the Deity, and most frequently restricted to the Father Eternal. The other persons of the trinity sometimes wear the triangle, but only in representations of the trinity, and because the Father is with them. Still, even then, beside the Father, who has a triangle, the Son and the Holy Ghost are often drawn with a circular nimbus only." [138]

The triangle has, in all ages and in all religions, been deemed a symbol of Deity.

The Egyptians, the Greeks, and the other nations of antiquity, considered this figure, with its three sides, as a symbol of the creative energy displayed in the active and passive, or male and female, principles, and their product, the world; the Christians referred it to their dogma of the trinity as a manifestation of the Supreme God; and the Jews and the primitive masons to the three periods of existence included in the signification of the tetragrammaton—the past, the present, and the future.

In the higher degrees of Masonry, the triangle is the most important of all symbols, and most generally assumes the name of the Delta, in allusion to the fourth letter of the Greek alphabet, which is of the same form and bears that appellation.

The Delta, or mystical triangle, is generally surrounded by a circle of rays, called a "glory." When this glory is distinct from the figure, and surrounds it in the form of a circle (as in the example just given from Didron), it is then an emblem of God's eternal glory. When, as is most usual in the masonic symbol, the rays emanate from the centre of the triangle, and, as it were, enshroud it in their brilliancy, it is symbolic of the Divine Light. The perverted ideas of the pagans referred these rays of light to their Sun-god and their Sabian worship.