The Five Platonic Shapes

³⁵ Above mentioned causes of future events, which I have explained so far – although those causes, in fact, include great deal of speculation – all are much closer to the nature of the topic than those which I will mention later.

The way of their effect lays in certain outflow of light, which is heading to sublunar bodies.

Its flow, although it lacks substance and time, does have a limitation.

It expands in direct course and it changes intensity of its influence depending on the distance from the start, then according to changing intensity of shining surface of the planets, and also by the contact with non-transparent obstacles on its way.

This flow of light is continuous.

• Its influence corresponds with the importance of the star.

This applies not only to one and only star, but also to the comparison of various stars.

The Sun and Moon have the biggest visible diameters.

• This is why these powers are also most evident in them.

In other planets with smaller diameter, those powers are hardly visible.

Still, such variations of the qualities are disregarded by most astrologers, who usually divine in a way which will be described later.

³⁶ Now, another cause follows, and it concerns all planets equally.

It is known much longer than the former one, and much more admired.

There is nothing material in it, but it has mental form, not of simple, but of psychic power, of intellect and of geometrical knowledge.

The effect is not caused only by the straight lines of rays from single stars, but by any rays of any two stars which meet on Earth, be it in geometrical or in harmonious way.

The ray always occurs as descending; nothing can hinder it, not even if the whole Earth is in its way as a shadow-casting element between us and the stars, and it gives effect either from hidden stars below the Earth, or from visible stars above.

Finally, its effect is almost instantaneous during the change from geometrical to harmonic angle, and it occurs immediately or with just a slight delay, no matter if the light of the stars is changing.

The validity of this is confirmed by reliable and rich experience.

The harmonic angle in Kepler´s interpretation means an angle, which can be described by the ratio of integers related to the circumference, that is, any of the aspects. By geometrical angle, Kepler means any arbitrary angle.

³⁷ God, Creator of the world, whose material universe is of bodily, quantitative form, does not have to help further on, because every single place, every space, which is filled by material body, changes according to given proportions, which have origin in fixed forms of the order of creation – I demonstrated this in my Mysterium Cosmographicum.

Movements of the bodies are the life of the universe. They may either harmonize pleasantly, or operate together very harshly, having the proportions determined by given planar forms – regular polygons.

The movement of the body resonates with the shape of the planar form.

Inasmuch as no more than five fixed orders (platonic bodies) are possible in geometry, so also the number of harmonic originators from regular planar patterns derived from those five cannot be more than eight, which I will, please God, demonstrate at some other time, in a work entitled Harmonia Mundi.

Five platonic bodies are:

1. Tetrahedron
2. Cube or regular hexahedron
3. Octahedron
4. Dodecahedron
5. Icosahedron

³⁸ There are 8 kinds of exactly given relationships.

The effect of heaven on Earth is executed through stellar rays, which meet on Earth and form angles.

Therefore, the 8 harmonic relationships will depend on size of those angles.

The classical authors did not consider more than 5 aspects, which are commonly known as conjunction, opposition, square, trine and sextile.

Yet, my idea is to add three: quintile (72 grades), biquintile (144 grades) and sesquiquartile (90+45 = 135 grades, i.e. trioctile).

Those have subsequently been confirmed by manifold experience*.

The classical aspects hereby mentioned correspond with: a point, a line segment, a triangle, a square and a hexagon.

Kepler here adds to those aspects the angles found in pentagon and in octagon .

³⁹ The reason why the effect of two planets so effectively increases under the actual bend of an aspect I can imagine only as a vital capability, which on one side dwells in the capacity of the geometrical pattern, and which forms the aspects, and on the other side in the capability of the body, in which all this operates, in which that influence fulfills.

It is not enough when 2 rays unite in some angle.

Variable angle is formed by 2 rays also the day before and after the aspect, but the effect occurs in the moment when the angle has a ratio exactly corresponding to given aspect.

If the angle does not form an aspect, there is no effect.

The same thing occurs during the movement of the body.

Should be an absurd philosophising to claim that a man moves by moving the objects by simply looking on them, without necessity to use his body to execute a move.

⁴⁰ That capability which gives power to the aspects does not reside in stars themselves.

Those aspects affect the Earth.

• Those effects do not come from the actual activity of the stars, but from the certain position of 2 stars with regard to the Earth.

For the vital power which gives motion to the bodies does not reside in objects, but it is there where the kind of the object is represented (it is represented in the ideas of the objects) thus this power, which gives growth, movement and life to the planets, gives it also to the huge Earth globe itself.

Any vital capability is a picture of geometricizing God in His creation.

• This picture is provoked to action through those heavenly geometries or harmonies of aspects.

⁴¹ The perfect activities of the Earth are:

• the generation of metals
• preservation of terrestrial heat
• exudation of vapours through progeneration of streams
• rains and other atmospheric conditions

These prove that it comes from some kind of vital power.

It shows that the image of Earth is not simple, as it occurs for instance in stones.

• Instead, it is an image which gives life.

⁴² The Earth has its own motion.

It does not have a human soul nor the characteristics of animals or plants.

But it does have a vital power of its kind.

Thus, according to the ancients, some kind of vital power dwells:

1. In man
2. In animals
3. In plants
4. In the Earth.

⁴³ Should be absurd and unjustifiable to attribute to the vital power the ability to understand geometry, and at the same time to consider it to be a kind of unanimated object.

An example is a tree.

The tree does not have common sense. Yet it can – upon command of the Creator – progenerate an exact pattern of leaves for the benefit of the fruit and for its own growth as well.

Every single seed retains beauty which comes from numbers.

A plenty of plants are quinary (with leaves in five-fold pattern), not for material need to transform an apple from the tree – it would not be possible to keep the quinary during such a transformation – but for the creative connection, which has a beauty innate to a quinary pattern.

The description given above is rather enigmatic, because the power remains inside and it spreads the quinary it posesses.

I will give another example. A simple man does not meditate upon a geometric proportion, which a sound has to another sound; yet the outer harmony of stringed instruments enters his mind through his ears and gives him joy.

However, this is not accomplished neither by the the regulation of mingling sounds, nor by gentle ear-soothing (for some sounds are often hurtful, and nevertheless their harmony causes delight), nor by any other cause hitherto detected, but it is accomplished, as I will show in Harmonia Mundi, by the fact that geometry creates a form of harmony.

Thus, encouraged by those examples, let´s dare to ascend even to the point where we believe that the Earth has life-giving mobile power, and that there is a kind of geometrical emotion in that power, because this power is some kind of mobile capability, which is stimulated upon high level when nourished by harmonious aspects.

In this way then, as the ear is stimulated by harmony to sharp listening and hearing, the Earth is stimulated by geometrical connection of accelerating rays (as we say, of the warm and wet power) in such a way, that the Earth itself gives effect upon accelerating of plants´ functions and it exudes a great abundance of vapour.

⁴⁴ However, although the influences of aspects slightly differ from various characteristics or nature of planets, as explained above, the Earth is influenced by geometrical mingling of contraries of influences of Saturn and Mars on one side, and the corresponding contraries of influences of Jupiter and Venus on the other side.

This occurs almost in the same way as we observe in the bowels, where an abundance of laxatives causes movement of liquids, while an argument causes the same occurence in the bile.

As the geometrical characteristics of rays lacks capability of colour as well as of other qualities, the basic diversity of influence of aspects comes from disposition of bodies. Such a disposition is important especially for Earth, which is different in different times and at different places.

During springtime, when there is an abundance of humidity in the middle of the northern part of Earth because of its proximity to the Sun, as mentioned above, then even the slightest aspect of any planet forces this power of Earth to grow up and to exude certain quantity of vapour to produce rains.

At some other time or place, even the strongest aspect may stimulate the Earth indeed, but the effect may be weak due to the lack of proper earthly disposition.