Page 21 - The.Ancient.Secret.of.the.Flower.of.Life-Vol2

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Square Roots and 3-4-5 Triangles
There's another aspect of this 8-by-10 grid that I sometimes talk
about, but I'll touch it lightly now.
Some of you may know that the Egyptians reduced their entire
philosophy to the square root of 2, the square root of 3, the square
root of 5 and the 3-4-5 triangle. It just so happens that all those
components are in this drawing of the first level of
consciousness, and it's extremely rare that such a thing would
happen in the way it is occurring. In Figure 9-17a, if the length
of the sides of the small squares is taken as 1, then the diagonal
line A is the square root of 2; the diagonal B is the square root of
5, and line C is the square root of 3, from the equilateral triangle of
the vesica piscis.
For example,
by the square
root of 5,1 mean that
Fig. 9-17a. The square root of 2 (the if four grid squares are a
triangle at A), the square root of 5* unit (1) [Fig.9-17b],
(the triangle at B) and the square root
of 3 (the triangle at C).
then line D would be 1
and line E would be 2.
Note: The Pythagorean theorem re- The Pythagorean
lates the hypotenuse of a triangle to its
sides:
rule states that the di-
agonal (hypotenuse) of
222 22 h = a + b or h = sqrt(a +b )
where h is the hypotenuse and a and b
a right triangle is de-
rived by adding the
represent the length of the sides.
squares of the two sides *Thus when a = 2 and b = 1 (as in the
12
triangleatB),a +b =5,soh=sqrt(5).
of a right triangle, then
taking the square root
2
of the result. Thus, l
1
= 1 and 2 = 4; then
Fig. 9-17b. The square-root-of-five (V5) triangle shown anothet
1 + 4 = 5, making way, using four grid squares instead of one as equal to 1.0.
the diagonal the
square root of 5 (sqrt5 )• That's what they mean by the square root of
5. See Figure 9-17b, where four grid squares equal one unit.
A 3-4-5 triangle is perfectly inscribed in Figure 9-17c. If you
count the length of two squares as one unit for your yardstick,
then line F is exacdy 3 units (6 squares) and line E will be 4 (8
squares). Since these sides measure 3 and 4, then the diagonal
has to be 5, making a 3-4-5 triangle. In fact, there are eight of
them in this figure that are perfectly inscribed, whirling around
the center. What is so rare is that the 3-4-5 triangles are inscribed
exactly at the points where the circle crosses the square to form
the phi ratio. These are amazing synchronicities that you
wouldn't happen upon by pure coincidence. Now let's do this
Fig. 9-17c. One of the eight 3-4-5 triangles inscribed in the
drawing a little differently.
circleinthisgrid. Hereoneunitis2grid-squarelengths.
2 3 6 £? THE ANCIENT SECRET OF THE FLOWER OF LIFE
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