The symbol of the triangle has always played a large role in human history. Many of us still remember to some extent the Pythagoras theorem regarding the right-angled triangle. The relationship described in it was of a practical importance in the life of ancient cultures, for instance when delineating arable land. It also had a special esoteric significance.
How is a triangle formed? Its three vertices certainly determine it, but what are these vertices? It is understood that they are simply points in a relationship. Today, the notion of a point is not unfamiliar to us, thanks to a deeper comprehension of geometry. We also use this concept quite commonly in our everyday language, for example when talking about a point of view, a starting point, etc. But what exactly is a point?
A point is a purely abstract concept, a mental creation that defines something that has no dimensions and therefore is not bound by them. It is an idea, something that does not exist physically, and yet is used to describe various phenomena.
So it can be said that the triangle is representative of three mental ideas. Perceived in this way, it has been of great importance in approaching and understanding a diverse range of esoteric knowledge. For example:
In mystic freemasonry the triangle is the basic principle and final aim of all construction. In esoteric Gnostic Christianity, the triangle is represented by the three crosses on the hill of Golgotha. In the philosophy of the Rosycross, it is represented by the three aspects of the ego: the Divine Spirit, the Life Spirit and the Human Spirit. In the magic of astrosophy we find the fiery triangle drawn by Aries, Leo and Sagittarius. In the Gnostic planetarium, we see the triangle radiate as Uranus, Neptune and Pluto, the three mighty signs in Serpentarius and Cygnus. We know the cosmic triangle as the aspects of Father, Son, and Holy Spirit, and the super-cosmic triangle as the three aspects of the Logos.
We can identify different types of triangles such as right-angled triangles, isosceles triangles, equilateral triangles among others, and can see that the nature of each is determined by the length of its sides, i.e., by the distances between its vertices.
An equilateral triangle for instance, has all its sides the same length, so it can be said that the ideas determining its vertices are in mutual balance, in full harmony. These ideas can be identified with the three most important aspirations that manifest themselves in people’s lives, even if we are unaware of them. They are:
1. An unequivocal, rational orientation towards the deepest goal of human existence; a faith of the mind – the unknowable God the Father.
2. An understanding of the ‘life path’ that should be followed; a knowledge of the heart – God’s Son revealing the Father.
3. The ability to act boldly and consciously, enabling a practical walking of this path; the correct application of the will – the Holy Spirit.
It is the same balance that is found in the equilateral triangle that represents these three aspirations, indicating that they are active and function in us in full harmony. Only such a state enables real progress along the path leading to the goal of our being.
These concepts have been known for a long time. This is supported by the following fragment from the Parable of the Three Kings, which Marco Polo brought back from his travels to Persia.
‘… three kings of that country went to worship a prophet who was newly born in the land of the Jews. These three kings carried with them three offerings, namely gold, incense, and myrrh, to learn if that prophet was either God, an earthly king, or a physician. For to make this distinction, they said to each other, if he takes the gold then he is an earthly king, and if he takes the incense he is God, and if he takes the myrrh then he is a physician.
And it came to pass - indeed when the three kings were come to the place where the infant God was born, the youngest of the three kings went off alone to the house where he was to see the infant, and found that he was like unto himself, for Christ seemed of his own age and of his own likeness. Then he came forth much wondering at this.
Afterwards the second king followed, who was of middle age; and just as the first, it seemed to him the child was of similar likeness and age, and again he also came forth all astonished.
Then went the third king also, who was of a greater age, and it happened just the same to him as to the other two before, and he also came forth in much thought.
And when the three kings were all come together they each said to the other what they had seen and found, and they made very great wonder at this, and said that they will all go together at once. Then they went all together before the infant, and going in found him attended by the angels and of the likeness and age that he was, for he was only thirteen days old. Then they worshiped him and offered him gifts of gold, incense and myrrh. And the infant took the offerings, all three at once.’
Here the figures of the three kings can be associated with the aforementioned aspirations of mind, heart and will. Then the story tells us that we should make every effort to ensure that all three develop in us simultaneously and in harmony. Only then can we see our life path as it really is.
Spiritual schools like the one founded by Pythagoras, have always taught this path. The Golden Rosycross also finds its foundation, the purpose of its existence and activity, in this same spiritual path as reflected in the three vertices of the equilateral triangle.
 Jan van Rijckenborgh, The Call of the Brotherhood of the Rosycross, ch. 7: Fiery Triangle, Rozekruis Pers, 1988.
 It seems that the term "physician" should be understood here as a kind of "sage-healer" or even Paraclete (healer, comforter and adviser) - especially in view of translations into some other languages.
 Text based on the English translation of Marco Polo, Le Devisement du monde: The Description of the World, Chapter 31: The Three Magi Went to Worship Christ, A.C. Moule & Paul Pelliot, George Routledge & Sons Limited, London 1938.