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@ yahoogroups.com

Cass,

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 time....got 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
party].

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 !

Frater 'M' ['M' as in Matrix and Magick]

PS. Share it with Lenny !

As far as the transcendentals go:

Cass Silva <silva_cass@yahoo.com> 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
are:
A1. "Things which are equal to the same thing are also equal to one
another.
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
another."
A5. "The whole is greater than the part."
P1. (It is possible) "to draw a straight line from any point to any
other
point."
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
distance."
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
two
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:
http://www.mathgym.com.au/history/pythagoras/pythgeom.htm#15

"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
universe."

As for the relationship between Pi and Phi... They are part of the
Golden
numbers, polygons, etc., known to all the ancient theosophists and
occultists
leading from Pythagorus, Plato, Hermes, Porphyry, Plotinus, etc.
For background
on this see:
http://goldennumber.net/pi-phi-fibonacci.htm
Also, look up "golden ratio" in www.google.com, and also try "sacred
geometry."

"e ¡Ö 2.7182818284.... is a transcendental number commonly
encountered when
working with exponential models (growth, decay, and logistic models,
and
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
these
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
the
universal forms and their interrelationships as they fractally
*involve* spherically
(like bubbles within bubbles, etc.), and ultimately *evolve* as
holographically
encoded vibratory patterns on their surfaces -- after emanating from
the
"spinergy" (abstract motion or angular momentum) of the Absolute
zero-or
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,

Lenny

Michael Angelicus <astralogos999@yahoo.com> 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
outcome
[ 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 =
2401

However these are the results: 81 + 256 + 625 +
1296 = 2258

So the sequence fails at the 4th power.

Frater 'M'

```