Spinoza's Assumptions

Postulate: The following should be taken for granted.

All the matter of which this visible world is composed was in the beginning divided by God into particles as near as possible equal to one another.

These were not spherical because a number of tiny spheres joined together do not fill a continuous space.

These parts were of different shapes and medium size – of a size intermediate between all those of which the heavens and the stars are now composed.

The parts possessed in themselves the same amount of motion as is now found in the world and moved with equal speed.

Individually, they moved around their own centers, each independently of the others. These compose a fluid body such as we think the heavens to be.

Many also moved in unison around certain other points, equidistant from one another and arranged in the same way as are now the centers of the fixed stars.

Others, moved around a somewhat greater number of other points that are equal to the number of the planets, thus forming as many different vortices as there now are stars in the world. See the diagram in Art. 47 Part 3 of the Principia.

This hypothesis, regarded in itself, implies no contradiction.

It ascribes to matter nothing except divisibility and motion. These modifications already exist in reality in matter.

Matter is boundless, and one and the same in the heavens and on earth. These modifications have been in the whole of matter without any danger of contradiction.

This hypothesis is the simplest, and therefore easiest to know. This is because it supposes no inequality or dissimilarity in the particles into which matter was divided in the beginning, nor yet in their motion.

By this hypothesis, matter only has divisibility and local motion.

That everything observed in nature can be deduced from this hypothesis.

First, we shall deduce from it the fluidity of the heavens, explaining how this is the cause of light.

Then we shall proceed to the nature of the sun and the fixed stars.

After that we shall speak of comets, and lastly of the planets and their phenomena.

Definitions

1. Ecliptic - the part of a vortex that, in rotating about its axis, describes the greatest circle.
2. Poles - the parts of a vortex that are farthest away from the ecliptic or that describe the smallest circles.
3. Conatus to motion - not some thought, but that a part of matter is so situated and stirred to motion that it would in fact be going in some direction if it were not impeded by any cause.
4. Angle - whatever in any body projects beyond a spherical shape.

Axioms

1. A number of small spherical bodies joined together cannot occupy a continuous space.
2. A portion of matter divided into angular parts, if its parts are moving about their own centers, requires more space than if its parts were all at rest and all their sides were immediately contiguous to one another.
3. The smaller a part of matter is, the more easily it is divided by the same force.
4. Parts of matter that are moving in the same direction and in that motion do not withdraw from one another are not in actuality divided.