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.

[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