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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 ! your friend, 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'

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