CHAPTER III.
.
The Theosophic Numbers and Operations--Signification of the Numbers.
THE NUMBERS.
THE ancients had a conception of numbers which is almost lost in modern times.
The idea of the Unity in all its manifestations led to numbers being considered as the expression of absolute laws. This led to the veneration expressed for the 3 or for the 4 throughout antiquity, which is so incomprehensible to our mathematicians.
It is however evident that if the ancients had not known how to work any other problems than those we now use, nothing could have led them to the ideas we find current in the Hindu, Egyptian, and Greek Universities. 1
What then are these operations, that our savants do not know?

They are of two kinds: theosophic reduction and theosophic addition.
These operations are theosophic because they cause the essential laws of nature to penetrate throughout the world; they cannot be included in the science of phenomena, for they tower above it, soaring into the heights of pure intellectuality.
They therefore formed the basis of the secret and oral instruction confided to a few chosen men, under the name of Esoterism.

1. Theosophic Reduction.
Theosophic reduction consists in reducing all the numbers formed of two or several figures to the number of a single figure and this is done by adding together the figures which compose the number, until only one remains.

EXAMPLE:
10 = 1 + 0 = 1
11 = 1 + 1 = 2
12= 1 + 2 = 3
126 = 1 + 2 + 6 = 9
2488 = 2 + 4 + 8 + 8 = 22 = 2 + 2= 4

This operation corresponds to that which is now called the proof by 9.
2. Theosophic Addition.
Theosophic addition consists in ascertaining the theosophic value of a number, by adding together arithmetically all the. figures from the unity to itself inclusively.
Thus the figure 4, in theosophic addition, equals all p. 28 the figures from 1 to 4 inclusively added together, that is to say, 1 + 2 + 3 + 4 = 10.
The figure 7 equals--
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 = 2 + 8 = 10.
Theosophic reduction and addition are the two operations which it is indispensable to know, if we would understand the secrets of antiquity. 1
Let us now apply these rules to all the numbers, that we may discover the law which directs their progression.
Theosophic reduction shows us, first of all, that all numbers, whatever they may be, are reducible in themselves to the nine first, since they are all brought down to numbers of a single figure.
But this consideration is not sufficient, and theosophic addition will now furnish us with new light.
Through it we find that 1, 4, 7, 10 are equal to 1.
for: 1 = 1
4 = 1 + 2 + 3 + 4 = 10 = 1
7 = 1 +2 + 3 + 4 + 5 + 6 + 7 = 28 = 10= 1
10 = 1
So that all the three numbers ultimately return to the figure 1, thus--
1. 2. 3 4. 5. 6
4 =10 =1 7 = 28 = 10 = 1


Or one could write--
1. 2. 3
(1)
4. 5. 6
(1), etc.
The results of this consideration are: (1) That all the numbers in their evolution, reproduce the 4 first;
(2) That the last of these 4 first, the figure 4, represents the unity at a different octave.
The sequence of the numbers may therefore be written in this way

1. 2. 3
4. 5. 6
7. 8. 9
10. 11. 12
13. 14. 15
16. 17. 18
19 ...........

We may notice that 4, 7, 10, 13, 16, 19, etc., are only different conceptions of the unity, and this may be proved by the application of theosophic addition and reduction thus--

1 = 1
4= 1 + 2 + 3 + 4 = 10 = 1
7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 = 10 = 1
10 = 1
13 = 4 = 10 = 1
16 = 7 = 28= 10 = 1
19 = 10 = 1, etc., etc.

We see that in every three numbers the series reverts to the unity abruptly, whilst it returns to it progressively in the two intermediate numbers.
p. 30
Let us now repeat that the knowledge of the laws of numbers and the study of them, made as we have here indicated, will give the key to all occult science.
We must now sum up all the preceding statements in the following conclusion: that all numbers may be reduced, in a final analysis, to the series of the 4 first, thus arranged--

1. 2. 3
4

THE SIGNIFICATION OF NUMBERS.
But our knowledge of the numerical science of the ancients does not end here. It also attributed a meaning to each number.
Since we have reduced the series of all the numbers to the 4 first, it will suffice for us to know the meaning attributed to these 4 first.
The Unity represents the creative principle of all numbers, since the others all emanate from it; it is the active principle pre-eminent.
But the Unity alone cannot produce anything except by opposing itself to itself thus 1/1. From this proceeds duality, the principle of opposition represented by two, the passive principle pre-eminent.
From the union of the Unity and Duality proceeds the third principle, which unites the two opposites in one common neutrality, 1 + 2 = 3. Three is the neuter principle pre-eminent.
But these three principles all reduce themselves into
p. 31
the fourth, which merely represents a new acceptation of the Unity as an active principle. 1
The law of these principles is therefore as follows--
Unity
or return to unity. Opposition
antagonism. Action of opposition
upon the unity.
Active
1 Passive
2 Neuter
3
Active
4 Etc. . . . .
Active
1
Passive
2 Passive-Active
4
Neuter
3

Footnotes
26:1 See Fabre d'Olivet, La Langue Hébraïque Restituée et Saint-Yves d'Alveydre, Mission des Juifs.
28:1 See for more details Traité Elémentaire de Science Occulte, by Papus, chap. ii.
31:1 See for further enlightenment the Traité Elémentaire de Science Occulte, p. 49 and following.