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

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 
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 
triangleatB),a +b =5,soh=sqrt(5).
of a right triangle, then 
taking the square root
of the result. Thus, l
= 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.


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