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.

[Illustration:  tetragrammaton inscribed with an equilateral triangle and placed within a circle of rays]

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.