Pythagoras

If and r are the radii of the cation and anion respectively then by applying Pythagoras s theorem to triangle ABC we find that... 

Kingsley, P. From Pythagoras to the Turba Philosophorunr. Egypt and the Pythagoean tradition. J Warburg CourtauldInsts 57 (1994) 1-13. 

Because the first principal component is always situated in direction of the largest variation of the data, the intensity of ypc should be increased compared with the original intensities from which it was calculated, namely theoretically according to the -dimensional Pythagoras principle... 

When merging more than two signals, yAlatent is obtained either by the n-dimensional principle of Pythagoras or - better - by principal component analysis (PCA, eigenanalysis see Sect. 6.3 Danzer [1990]). 

The fundamental difference between ancient and modern science is not at all in the field of theory. Sir William Thomson was just as metaphysical as Pythagoras or Raymond Lully, and Lucretius quite as materialistic as Ernst Haeckel or Buchner. 

Inscribe the pentacle star inside a pentagon and you have the pentagram, symbol of the ancient Greek School of Mathematics founded by Pythagoras—solid evidence that the ancient Mystery Schools knew about PHI and appreciated the Divine Proportion s multitude of uses to form our physical and biological worlds. 

Pythagoras- material 1550 - 1820 2,9 Excel- lent Satisfactory Better resistance than porcelain... 

Let two objects be defined by the vectors xA (with components/variables. t4i, xA2,. ..,xAm) and xB (with components/variables xm, xB2,. ..,xBm). Most used is the Euclidean distance, [Pg.58]

Perhaps the shamanic traditions of this planet are the keepers of an understanding that uses the human body/brain/mind as its vehicle, leaving the present state of the art, which our own "scientific method" has achieved, a very poor second. This is really an old idea—the siren song of Pythagoras— that the mind is more powerful than any imaginable particle accelerator, more sensitive than... 

Dennis s rap drew on the theory of sound. If you pluck a string, it will sound in the octave in which it is struck, but it will also sound in octaves above and below its key. It has what are called harmonic overtones. If you strike the chord and then squelch it, you can still hear the harmonic overtones, a phenomenon that had fascinated Pythagoras. Dennis pointed out to us that one can use two sounds to cancel each other if the two sounds are exactly the same in relation to each other. 

The dead We believed that hyper-carbolation was to be the shamanic defeat of death, that those doorways through which the dead enter daily were to be finally thrown open to a hyper-carbolated humanity, which would then have freedom of movement to and from an eternity in which all the members of the species existed as a living reality. The presence of giants from the human past—Carl Jung, Newton and Nabokov, Bruno, Pythagoras, and Heraclitus— was an overwhelming and all-inclusive intuition that we shared and could not ignore. 

Sense he snarled. Sense You mean it does not appear to make sense to you Do you claim more intelligence than San Zorzi or Pythagoras Can you concede that smarter or better informed persons might make sense of it ... 

Pythagoras view that all reality can be expressed in numbers is one of the most important root concepts in Western science. Yet,... 

The relationships between the layers are ratios. They describe numerically the vibrations of the three essential notes in the music scale the whole note, which had a ratio of one to two the perfect fifth, which has a ratio of two to three and the perfect fourth, which has a ratio of three to four. Together with the four physical layers, these musical layers provide seven layers altogether. Like the ziggurat the Tetractys had seven layers, but here numbers have replaced the gods as emanations. To fill out the musical scale Pythagoras devised four other notes and created the Western diatonic scale with seven notes. Pythagoras believed that the seven notes captured the sound of each of the seven planets—the music of the spheres—and he used the seven vowels of the Greek alphabet to denote them. 

Luckily, however, most alchemists agreed on several basic concepts and principal stages of the Great Work. These evolved over the centuries but remained framed by a mystical, mathematical system of number symbolism derived from the school of Pythagoras. Evidence of this structure is in the following quote from an alchemical text called Rosarium Philosophorum ... 

Circa 580-490 The great Greek philosopher, mathematician, and magician, Pythagoras, studies the wisdom of Mesopotamia and Egypt and founds a mystical sect in the Greek colony in Croton, Italy, in which numbers are seen as emanations. 

We will be estimating the velocity of a molecule from kinetic theory, not the x-component of this velocity. Thus, from the Pythagoras theorem, the velocity of a molecule, v, is given by... 

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