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Euclids Geometry

Nov 29, 2005 10:36 PM
by Kathy

Dear Lenny,
I hope you didn't mind, but I posted what you explained to Gopi to a 
friend of mine on another forum for him to be able to explain it to 
me, as you know how backward I am when it comes to geometry etc. He 
has posed a question to you, feel free to answer it or not, at your 
own discretion. IlluminAlch@

Ask Lenny ... How Could It Be Euclid's Geometry ?.. if Pythagoras
preceeded him by hundred's of years and taught these principles. 
It would then have to have been Pythagoras principles.. which 
Euclid appropriated into his geometry, would it not?
The reverse is the case with the Pythagorean theorem. It wasn't 
Pythagoras who invented it, but it was his school which got it out 
to the public ... gave it air it to fly. So he gets 
credit for it as a result.
The Pythagoreans were the intellectual force behind the likes of 
Euclid and others.
They didn't just give us the 'gon' and 'hedron' show . They told 
us all was Number and Vibration...the Music of the Spheres...which 
is something we are continually learning about.
As far as the connection of......... e, to i, to Pi, to 1 [unity] 
and to 0 [integer and void].
Leonhard Euler gives us what some consider apodictic prove for 
intelligent design
in the universe in the formula:
.................... e ^ i x Pi + 1 =     
0 ................
English: e taken to the power of i [ square root of - l] times Pi 
plus 1 = Zero
How's that for combining the transcendentals with Unity and the Void?
This is one of the greatest identity theories in all of math, 
absolute genius and
absolute beauty. So you see there are myriad connections between 
all of the
transcendentals, but wait where is 'Phi' ?.
This is where the notorious Frater Angelicus comes in.
The 'determinant' of any Fibonacci series [re Golden Ratio 'phi'] 
beyond a 2 x 2 matrix [you have to give the series a chance to 
develop itself to create a preceeding 2 number ratio] into infinity 
equals Zero [ = 0]. 
So the connection of 'Phi' to one of Euler's materpieces comes 
through the Void,
through Zero [0]..a Matrix which is non-encryptable.
So here's Angelicus's adaptation upon Euler's masterpiece [so as to 
include 'Phi' because we don't want to leave 'anyone' out at the 
e ^ i (Pi) + 1 = det [n x n] (n> 2 Phi Element Matrix) = 0
[I'm sure some of the professional mathematicians can clean this up 
a bit.]
You heard it first from Yours Truly the Good Frater,  
another 'IlluminAlch' first !
your friend,
Frater 'M' ['M' as in Matrix and Magick]
PS. Share it with Lenny !
As far as the transcendentals go:

Cass Silva <> wrote:
Hello Mike
This is from my brainiac friend on another forum.  
The only propositions I know of linked to Pythagorus, are the ten 
axioms and 
propositions of mathematics that he taught, based on Euclid's 
geometry: These 
A1. "Things which are equal to the same thing are also equal to one 
A2. "If equals be added to equals, the wholes are equal."
A3. "If equals be subtracted from equals, the remainders are equal."
A4. "Things which coincide with one another are equal to one 
A5. "The whole is greater than the part."
P1. (It is possible) "to draw a straight line from any point to any 
P2. (It is possible) "to produce a finite straight line continuously 
in a 
straight line."
P3. (It is possible) "to describe a circle with any centre and 
P4. (It is true) "that all right angles are equal to one another."
P5. (It is true) "that, if a straight line falling on two straight 
lines make 
the interior angles on the same side less than two right angles, the 
straight lines, if produced indefinitely, meet on that side on which 
are the 
angles less than the two right angles."

For more on Pythagorean mathematics, see:

"It is well known that the Pythagoreans were much occupied with the 
construction of regular polygons and solids, which in their 
cosmology played an 
essential part as the fundamental forms of the elements of the 

As for the relationship between Pi and Phi... They are part of the 
numbers, polygons, etc., known to all the ancient theosophists and 
leading from Pythagorus, Plato, Hermes, Porphyry, Plotinus, etc.   
For background 
on this see:
Also, look up "golden ratio" in, and also try "sacred 

"e  2.7182818284.... is a transcendental number commonly 
encountered when 
working with exponential models (growth, decay, and logistic models, 
continuously compounded interest, for example) and exponential 
functions. e is also 
the base of the natural logarithm."

"i" is The symbol used to represent the imaginary number (The square 
root of 
minus I)

As far as I know, their is no single relationship that brings all 
numbers or symbols together, other than perhaps the relationships of 
the golden 
numbers to the sacred geometry's or to the Fibonacci series.   

However, all of these real numbers are related to the ABC theory -- 
which is 
based on the funda-mental geometry and mathematics that describes 
universal forms and their interrelationships as they fractally 
*involve* spherically 
(like bubbles within bubbles, etc.), and ultimately *evolve* as 
encoded vibratory patterns on their surfaces -- after emanating from 
"spinergy" (abstract motion or angular momentum) of the Absolute 
laya-point ("singularity") of primal space. This is also fully 
consistent with the 
metaphysics of Cosmogenesis descibed by HPB in the Secret Doctrine 
based on the 
formulas given in the Book of Dzyan.

Hope this helps,

Best wishes,


Michael Angelicus <> wrote:
Well known is the Pythagorean theorem in its most basic form of:
3 squared + 4 squared = 5 squared. [ 9 + 16 = 25.]
But Plato knew that these same numbers when 'Cubed' also formed a
special relationship which is not generally known.
3 cubed + 4 cubed + 5 cubed = 6 cubed [27 + 64 + 125 = 216]
216 is not the same as 666, but still uses three Sixes to derive its 
[ 6 x 6 x 6 = 216].
For those of you curious enough to see if there were a series here, I
took it up another dimesnsion.
3 [to power of 4] + 4 [to the power of 4] + 5 [to the power of 4] + 
6 [to the power of 4] = 7 [to the power of 4]
So this should be the expected outcome: 81 + 256 + 625 + 1296 = 
However these are the results: 81 + 256 + 625 + 
1296 = 2258
So the sequence fails at the 4th power.
Frater 'M'

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