The**number**, the**symbol**and the **idea**

## REDUCED NUMBERS

All numbers can be reduced to

the first 9 single-digit numbers.

Ex : 127 = 1 + 2 + 7 = 10

et 10 = 1 + 0 = 1

The number 127’s reduction

is the number 1.

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## FIGURATE NUMBERS

Numbers can be represented

in space as a function of

the numberof units they contains.

Ex : number 3 contains 3 units.

It can be drawn from three points

or a triangle.

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## IDEA-NUMBERS

Pythagoras, who coined the term "cosmos", defined the Three Worlds as:

• World of Archetypes (which later became the Theory of Ideas with Plato);

• Microcosm, or small world, Man;

• Macrocosm, the large world, the Universe.

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### The ancient numerology of Pythagoras

The number, the symbole and the idea

**Geonumerology** is an interdisciplinary approach which aims to restore **the ancient numerology of Pythagoras **to its former glory. It is therefore at the heart of the teaching of this philosopher's teaching that Geonumerology finds its source.

**Arithmetic** and **geometry** were, along with astrology and music, the four sciences that were taught at the time within the framework of the Quadrivium.

Pythagoras is certainly the first great philosopher of the Western tradition. It was he who invented the word **philosophy**. Everyone knows Pythagoras for his multiplication tables or his theorem. But what is less known is that his mathematics actually leads to a metaphysics, being convinced that**numbers are the principle and the key to the entire universe**.

His main idea is to have considered the universe as an ordered whole, a "**Cosmos**", where the numbers serve as a support for a **vibratory reality**. We can therefore legitimately consider Pythagoras as the father of current physics.

As Man, or **microcosm**, is the image of the universe, the **macrocosm**, the laws that apply to one also apply to the other.

The initiatory process which characterizes his teaching is related to the **realisation of the Self** in psychology as well as to the quest for the philosopher's stone of the **alchemists**. These three paths invite us to direct our gaze inward, in a process of introspection to the discovery of our soul.

## The 9 numbers numerology

The reduced number

10 = 1 + 0 = 1

11 = 1 + 1 = 2

12 = 1 + 2 = 3

13 = 1 + 3 = 4

14 = 1 + 4 = 5

15 = 1 + 5 =6

16 = 1 + 6 =7

17 = 1 + 7 =8

18 = 1 + 8=9

...

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**The principle of reduction**

The **theosophical reduction **(from the Greek: *theos*, divine or Gods and *sophia*, wisdom) corresponds to the current **9-numbers of numerology**. It consists in reducing all numbers to the first 9.

**The principle of correspondence**

« The theosophical reduction was an operation familiar to Pythagoreans who neglected numbers greater than 10, so they reduced numbers greater than 10 to the first nine numbers, taking into account only their root or pythmen, i.e., substituting the remainder of their division by nine, or the number nine even when the number was a multiple of nine. »

Arthuro Reghini ~ Sacred Numbers in the Pythagorean Masonic Tradition

In the time of Pythagoras (6th century B.C.), the **letters** of the Greek alphabet were used to designate **numbers**: Alpha for One, Beta for Two, Gamma for Three, Delta for 4, and so on.

Numerology derives from this principle and applies a **numerical value **to each letter of your name which making it possible to calculate the number for any name or word by adding together the values of its letters.

**The Matrix Layout**

This is the layout adopted in geonumerology and derived directly from the tables created by Pythagoras.

The interest of such an arrangement is to allow a **cartesian approach**(abscissa and ordinate) of the first 9 numbers, where each one has a place assigned to it in relation to the whole.

**Representative numbers**

The numbers 1, 5 and 9 keep their place in the matrix whatever the arrangement, in rows or columns. They are representative numbers.

## Figurate numbers

From number to shapes

The Tetractys from Pythagoras

**Pythagorean geometry**

**Figurate numbers** allow us to create a bridge between arithmetic and geometry. They derive from the use of **small pebbles** represent the units that make up numbers with symmetrical **geometric shapes**.

Pythagoras was the first to make the connection between **numbers****, geometric shapes** and spatial dimensions. Below is a visualisation of the number 10, the fourth triangular number and central symbol of the Pythagorean school, named the

**Tetractys**.

« They saw numbers as a stream, a flow of units or monads, reflecting the infinite multiplication of one and the same divine Unit. These units, represented by points or groups of points, were translated in the forms of the sensible world by geometrical figures, in two or three dimensions. »

Matila Ghyka ~ The Golden Number

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**Tetrahedron, symbol of number 4**

Given the total parallelism between **arithmetic** and **geometry**, it is thus possible to visualize the number in space using points, or pebbles (*calculi* in Latin), according to the number of units it contains:

- 1 point for the number 1;
- 2 points for the number 2, the line (1D);
- 3 points for the number 3, the triangle (2D);
- 4 points for the number 4, the tetrahedron (3D).

A figured number is an integer that is usually represented by points and which forms a regular geometric figure.

Geonumerology is therefore a mixture of **numerology** and **geometry**. Geometry will allow us to figure the number, to give it body in space, to grasp its lines of force and finally to discover the **idea** hidden behind the symbol.

**Theosophical addition & triangular numbers**

To know the **Theosophical addition **of a number, it is enough to add up arithmetically all the numbers from the unit to it.

Thus the number 4 gives in theosophical addition: 1 + 2 + 3 + 4 = 10.

This operation corresponds in all respects to the way **Triangular numbers** (1, 3, 6, 10, ...) are elaborated.

1 = 1

2 = 1 + 2 = 3

3 = 1 + 2 + 3 = 6

4 = 1 + 2 + 3 + 4 = 10

5 = 1 + 2 + 3 + 4 + 5 = 15

6 = 1 + 2 + 3 + 4 + 5 + 6 = 21

7 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

8 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

9 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

The first 9 triangular numbers

The **Number** represents the **Idea**. He is the Father. **Geometry** is the Mother of Creation, it generates the **forms**. Each Number inhabits the form that is "destined" for it. Thus the metaphysical abstraction of the Number materializes in geometry, it takes shape.

« Each number responds to a characteristic idea and hieroglyph, so that the laws of number combinations verify the combination of symbols and ideas. (...) This law is one of the best keys to open the ancient mysteries. »

Édouard Schuré ~ The Great Initiates

## The Three Worlds

Archetypes, Microcosm and Macrocosm

1 = 1

3 = 3

6 = 6

10 = 1 + 0 = 1

15 = 1 + 5 = 6

21 = 2 + 1 = 3

28 = 2 + 8 = 1

36 = 3 + 6 = 9

45 = 4 + 5 = 9

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**Secret value of numbers**

All integers are associated with one of the following 4 **secret values**: **1**, **3**, **6** or **9**.

The secret value of a number is obtained by applying the process of theosophical **addition **to it followed by **reduction**.

Let's take an example: the number 7

- The theosophical addition of the number 7 gives: 1 + 2 + 3 + 4 + 5 + 6 + 7 =
**28** - The theosophical reduction of the number 28 is : 2 + 8 = 10 = 1 + 0 =
**1** - The secret value of 7 is therefore at 1

**Worlds and reflections**

If the numbers 4 and 7 are the**refections **of the Divine World in the Human World and in the Natural World, then there must be a human reflection in the Divine and Natural Worlds as well as a natural reflection in God and Man .

**The law of analogy**

The keystone of the esoteric teaching of Pythagoras rests on the idea of the **interdependence**of all the elements of the cosmos by a link, a primordial energy, associated by some with divine love, by others with the **law of attraction**, in a word with the force that unites, or better, keeps together all parts of the universe.

**The law of one**

By applying the secret value to the first nine numbers, we see that the total of each line (see on the right), or World, gives the **Unit**.

The unit reappears every three numbers in the **Three Worlds according to a ternary law**

The unit and its **reflexions** in the two other Worlds constitute the** Divine Axis** of **Divine Attributes**(first column of the secret matrix composed only of 1) and correspond in the archetypal matrix to the numbers 1, 4 and 7.

« These three progressions represent

the Three Worlds

in which everything is enclosed. »

Pythagoras

## Field of investigation

Topics covered

**Numbers** are at the heart of the **esoteric** teaching of Pythagoras. They represent the archetypal principles on which all things are based.

The qualitative or **esoteric** study of numbers was the basis of the **philosophical** teaching of Pythagoras.

The **knowledge of oneself** led to the knowledge of the universe and the **Gods**.

The **sacred symbols** used to transmit the teaching acted on the deep **psychology** of the individual.