Solids Versus Fluids

61. When a fluid body is carried all at once towards some part, it necessarily carries with it the hard body which it contains.

A hard body surrounded by fluid on all sides, and resting in it means that there is an equilibrium.

No matter how large it is, it can always be impelled to one side or the other by the slightest force, whether that force comes from elsewhere or is inherent in the fluid itself.

An example is when the entire fluid is carried towards a certain place, as rivers flow towards the sea, and all the air is carried towards the west by the blowing wind.

When this happens, it is absolutely necessary for the hard body existing in such a fluid to be carried along with it.

This does not contradict the fourth rule which says that a resting body can be impelled to motion by no lesser force, however swiftly it may be applied.

62. When a solid body is thus transferred from a fluid, it is not therefore moved

If we pay attention to the true and absolute nature of motion, which consists in the translation of the moved body from the vicinity of other contiguous bodies, and in both bodies that touch each other

even though it may not always be named in the same way, we will clearly recognize that

A hard body is not so properly moved when it is carried by the containing fluid as when it is not carried by it;

In the latter case, it does not recede as much from the neighboring particles of that fluid.

63. Why are some bodies so hard that they are not easily divided by our hands?

This seems to strongly contradict the rules of motion just discussed.

We should be able to cut a nail with our hands since:

• the parts of bodies adhere to each other by no other glue other than the fact that each rests next to its neighbor
• every body at rest can be impelled to motion by another body in motion

But why can’t we divide an iron nail into 2 parts by the force of our hands alone?

The middle part of this nail is one body which is smaller than our hand. We should be able to move it by force and separate it from the other middle part.

This does not happen because our hands are very soft, resembling the nature of fluid bodies more than hard ones.

Therefore, they do not usually act entirely together on the body that they are moving.

Instead, they only act on the part of them that touches the body and bears down on it.

The part of our hand that touches the nail closely is smaller than the part of that nail.

This small part of our hand is more easily separated from the rest of the hand than the part of the nail from the rest of the nail.

This is why trying to separate the nail with our hand produces a sense of pain.

But if we equip our hand with a hammer, file, pliers, or another instrument so that its [larger] force for dividing the body is applied to the smaller body it uses for dividing, it can overcome its hardness no matter how great.

64. The principles of Physics are based in Geometry and Abstract Mathematics.

These explain all the phenomena of nature through definite demonstrations.

I will add nothing here about shapes, nor how from their infinite variety countless variations of motion follow, because these will become clear enough by themselves whenever it becomes necessary to discuss them.

I assume that my readers already know the first elements of geometry or at least have a mind sufficiently apt to understand mathematical demonstrations.

I recognize no other material of corporeal things than that which is entirely divisible, shapeable, and moveable, which geometers call quantity and take as the object of their demonstrations.

I consider nothing in it except these divisions, figures, and motions.

I admit nothing about them as true that is not so clearly deduced from those common notions, the truth of which we cannot doubt, that it should be considered as a mathematical demonstration.

All the phenomena of nature can be explained in this way. And so I think that no other principles of physics are to be admitted, nor even desired.