Thursday, December 11, 2008

Intersting Stuff about 9

The number nine was consecrated to the Spheres and the Muses. It is the sign of every circumference; because a circle of 360 degrees is equal to 9, that is to say, 3+6+0=9. Nevertheless, the ancients regarded this number with a sort of terror: they considered it a bad presage; as the symbol of versatility, of change, and the emblem of the frailty of human affairs. Wherefore they avoided all numbers where nine appears, and chiefly 81, the product of 9 multiplied by itself, and the addition whereof, 8+1, again presents the number 9.

As the figure of the number 6 was the symbol of the terrestrial globe, animated by a divine spirit, the figure of the number 9 symbolized the earth, under the influence of the Evil Principle; and thence the terror it inspired. Nevertheless, according to the Kabalists, the figure 9 symbolizes the generative egg, or the image of a little globular being, from whose lower side seems to flow its spirit of life.

The E_n_nead, signifying an aggregate of 9 things or persons, is the first square of unequal numbers.


Every one is aware of the singular properties of the number 9, which, multiplied by itself or any other number whatever, gives a result whose final sum is always 9, or always divisible by 9.


Nine, multiplied by each of the ordinary numbers, produces an arithmetical progression, each member whereof, composed of two figures, presents a remarkable fact; for example:

1...2...3...4...5...6...7...8...9..10

9..18..27..36..45..54..63..72..81..90


The first line of figures gives the regular series, from 1 to 10. The second reproduces this line doubly; first ascending, from the first figure of 18, and then returning from the second figure of 81.

It follows, from the curious fact, that the half of the numbers which compose this progression represents, in inverse order, the figures of the second half:

9...18..27..36..45 = 135 = 9.._and_ 1 + 3 + 5 = 45 = 9

90..81..72..63..54 = 360 = 9.

-- -- -- -- -- --- --

99 99 99 99 99 495 = 18 = 9.



So 9² = 81 ...81² = 6561 = 19 = 9 ...9x2 = 18 ...18² = 324 = 9.


9x3=27 ...27² = 729 = 18 = 9. 9x4 = 36 ...36² = 1296 = 18 = 9.


_And so with every multiple of_ 9--_say_ 45, 54, 63, 72, etc.


Thus 9x8 = 72 ...72² = 5184 = 18 = 9.


And further:


18 27 36 72

18 27 36 72

--- --- --- ---

144 = 9 189 = 18 = 9 216 = 9 144 = 9

18 = 9 54 = 9 = 108 = 9 504 = 9


324 = 9...18 = 9 729 = 18= 9 1296 = 18 = 9 5184 = 18 = 9

108

108

----

864 = 18

108 = 9

-----

11664 = 18 = 9.


_And so the cubes:_


27²=729x729=18=9 18²=324=9 9²=81 81²=6561=18=9

729 324 6561

---- ---- ----

6561=18=9 1296=18=9 6561=18=9

1458 =18=9 648 =18=9 39366 =27=9

5103 =9 972 =18=9 32805 =18=9

39366 =27=9

------ ------ ------

531441=18=9 104976=27=9 43,046,721=27=9.


All this making 9s extremely fascinating.

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