Mackey A G - Encylopedia of Freemasonry - The Grand Masonic ...

FORTY-SEVENTH
FORTY-SEVENTH 271
uge of forty days and nights, and the same
number of days in which the waters remained
upon the face of the earth ; the Lenten season
of forty days' fast observed by Christians with
reference to the fast of Jepus in the Wilderness,
and by the Hebrews to the earlier desert fast
for a similar period ; of the forty years spent in
the Desert by Moses and Elijah and the Israelites,
which succeeded the concealment of
Moses the same number of years in the land of
Midian . Moses was forty days and nights on
the Mount. The days for embalming the dead
were fort The forty years of the reign of
Saul, of David, and of Solomon ; the forty
days of grace allotted to Nineveh for repentance
; the forty days' fast before Christmas
in the Greek Church ; as well as its being the
number of days of mourning in Assyria,
Phenicia, and Egypt, to commemorate the
death and burial of their Sun God ; and as well
the period in the festivals of the resurrection
of Adonis and Osiris; the period of forty days
thus being a bond by which the whole world
ancient and modern, Pagan, Jewish, and
Christian, is united in religious sympathy .
Hence, it was determined as the period of
mourning by the Supreme Council of the
A . A. Scottish Rite of the Northern Jurisdiction
U . S.
Forty-Seventh Problem . The forty-seventh
problem of Euclid's first book, which has
been adopted as a symbol in the Master's
Degree, is thus enunciated : "In any rightangled
triangle, the square which is described
upon the side subtending the right
angle is equal to the squares described upon
the sides which contain the right angle ."
Thus, in a triangle whose perpendicular is 3
feet, the square of which is 9, and whose base
is 4 feet, the square of which is 16, the hypothenuse,
or subtending side, will be 5 feet,
the square of which will be 25, which is the
sum of 9 and 16 . This interesting problem, on
account of its great utility in making calculations
and drawing plans for buildings, is sometimes
called the "Carpenter's Theorem ."
For the demonstration of this problem the
world is indebted to Pythagoras, who, it is
said, was so elated after making the discovery,
that he made an offering of a hecatomb, or a
sacrifice of a hundred oxen, to the gods . The
devotion to learning which this religious act
indicated in the mind of the ancient philosopher
has induced Masons to adopt the problem
as a memento, instructing them to be
lovers of the arts and sciences .
The triangle, whose base is 4 parts, whose
perpendicular is 3, and whose hypothenuse is
5, and which would exactly serve for a demonstration
of this problem, was, according to
Plutarch, a symbol frequently employed by
the Egyptian priests, and hence it is called by
M . Jomard, in his Exposition du Systeme
Met ' des Anciens Egyptiens, the Egyptian
trianglg e . It was, with the Egyp tians, the
symbol of universal nature, the base representing
Osiris, or the male principle ; the perpendicular
Isis, or the female principle ; and
the hypothenuse, Hors, their son, or the
produce of the two principles . They added
that 3 was the first perfect odd number, that
4 was the square of 2, the first even number,
and that 5 was the result of 3 and 2 .
But the Egy~t~ians made a still more important
use of this triangle . It was the standard
of all their measures of extent, and was
applied by them to the building of the pyramids.
The researches of M . Jomard, on the
Egyptian system of measures, published in
the magnificent work of the French savants on
Egypt, has placed us completely in possession
of the uses made by the Egyptians of this fortyseventh
problem of Euclid, and of the triangle
which formed the diagram by which it was
demonstrated .
If we inscribe within a circle a triangle,
whose perpendicular shall be 300 parts, whose
base shall be 400 parts, and whose hypothenuse
shall be 500 parts, which, of course, bear
the same proportion to each other as 3, 4, and
5 ; then if we let a perpendicular fall from the
angle of the perpendicular and base to the
hypothenuse, and extend it through the hypothenuse
to the circumference of the circle,
this chord or line will be equal to 480 parts, and
the two segments of the hypothenuse, on each
side of it, will be found equal, respectively, to
180 and 320. From the point where this cord
intersects the hypothenuse let another line fall
perpendicularly to the shortest side of the triangle,
and this line will be equal to 144 parts,
while the shorter segment, formed by its junction
with the perpendicular side of the triangle,
will be equal to 108 parts . Hence, we may derive
the following measures from the diagram :
500, 4801 400, 320, 180, 144, and 108, and all
these without the slightest fraction . Supposing,
then, the 500 to be cubits, we have
the measure of the base of the great pyramid
of Memphis . In the 400 cubits of the
base of the triangle we have the exact
length of the Egyptian stadium . The 320
gives us the exact number of Egyptian
cubits contained in the Hebrew and Babylonian
stadium . The stadium of Ptolemy is
represented by the 480 cubits, or length of
the line falling from the right angle to the
circumference of the circle, through the hypothenuse.
The number 180, which expresses
the smaller segment of the hypothenuse being
doubled, will give 360 cubits, which will be
the stadium of Cleomedes . By doubling the
144, the result will be 288 cubits, or the length
of the stadium of Archimedes ; and by doubling
. the 108, we produce 216 cubits, or the
precise value of the lesser Egyptian stadium .
In this manner, we obtain from this triangle
all the measures of length that were in use
among the Egyptians ; and since this triangle,
whose sides are equal to 3, 4, and 5, was the
very one that most naturally would be used in
demonstrating the forty-seventh problem of
Euclid ; and since by these three sides the
Egyptians symbolized Osiris, Isis, and Horus,
or the two producers and the product, the
very principle, expressed in symbolic language,
which constitutes the terms of the problem
as enunciated by Pythagoras, that the