Theorems

[23]**

10. Hence every motion in a plenum is circular, or returns into itself in a closed line. For if body A moves into the place of B, then B must move into the place of C, and so on, until some body moves into the place vacated by A. 11. From this it follows that no body is moved alone, but the whole system of the plenum is affected by the motion of any single part. 12. The swiftest motion is that of the Aether, which, because of the smallness of its parts and the frequency of its endeavors, penetrates all things and acts as the universal motor.

13. From the different circulations of the aether, different species of things arise, such as gravity, light, and magnetism. 14. Gravity is nothing other than the pressure of the aether tending toward the center of the earth, as was explained in the Theory of Concrete Motion. 15. Light is the most rapid vibration or endeavor of the aether propagated in straight lines. 16. All these things are performed mechanically, without any need for “occult qualities” or “substantial forms,” which are but names for our ignorance. 17. If two bodies of the same magnitude and speed strike each other from opposite directions, they both rest; for their endeavors are extinguished by equality.

[24]**

…if they are unequal, the smaller is moved by the larger; if equal, both are moved.

¹⁹ If a body is moved, and its endeavor (conatus) is stronger than the obstacle, it will cross it; if it is not stronger, it will be reflected or its motion will be diverted, but with its speed always preserved.

²⁰ If two bodies of the same magnitude and equal speed concur directly, both are reflected with the same speed with which they came.

²¹ If they are of unequal magnitude but equal speed, the larger carries the smaller with it; the speed of both will be the difference of their magnitudes divided by their sum.

²² If they are of equal magnitude but unequal speed, the faster carries the slower; the speed will be the difference of the speeds.

²³ If they are unequal in both magnitude and speed, it is resolved through the ratio of the magnitudes and speeds joined together.

²⁴ From these [principles], the reasons for all the motions in the whole of nature are sought. For since all things are full of bodies [a plenum], and any body is an aggregate of smaller ones, and these again of others, it follows that no motion exists which is not composed of countless smaller motions, and no impact which is not the result of countless endeavors (conatuum).

This is that Mechanical Labyrinth which has hitherto been inaccessible, but which is now made plain through the laws of abstract motion.

[25]**

These laws show that the nature of things is not a dead mass, but is everywhere living and acting through the aether.

For as a point is the beginning of a line, so is the endeavor the beginning of motion.

As the mind is the beginning of the body, so is God the beginning of the World.

²⁵ It is established that the laws of nature are the laws of Reason.

For since nothing is without reason, and the greatest possible harmony must always be preserved, it follows that the motions of bodies must be directed so that the greatest amount of motion is preserved with the least possible change of direction.

This is the Supreme Law of Mechanics, which is also the Law of Divine Wisdom acting in the world.

The End.

26]**

Some people that it is in vain to seek the quadrature of the circle and so many other things which, even if found, would bring no relief to human affairs; since we already have more exact mechanical proportions than those which can be attained with instruments.

Nor shall I speak of the greatest pleasure which, once detected, a certain new harmony of things affects minds accustomed to this music (so that at least a place must be left for this kind of doctrine among the mental arts, which for painters, poets, and musicians—add also the Appicii [gourmets] and Petronian judges of pleasure—cannot be seen as inferior to corporal arts). For unless it can be persuaded to those unexperienced in these matters, it seems to them that the sweetness of such sterile and dry things is non-existent.

But even if I were to show that the greatest controversies concerning the finite and the infinite, the vacuum and the plenum, the composition of the continuum, and the motion or rest of the earth, cannot be defined except by properly understanding the abstract reasons of motion, these things will not be, I think, of such great value among these censors. What then? Unless we experience the ultimate things, and show that at some point one cannot ascend to solid demonstrations concerning GOD and the Mind, and to the confirming of the greatest mysteries of faith (to which task I, if anyone ever has, have applied myself with the greatest contention of spirit, and have left almost nothing of others unexamined, and nothing of my own untried). Those who make nothing of these things can, I confess, lack a great part of the sciences. For thus, by divine and human right…

27]**

…and whatever in these matters builds a step in Philosophy, once the old histories are abolished (whose chief use among the prudent is to bear testimony to the truth of religion, unless when it is used for pomp, the truth is neglected); there will remain for these men only two arts: one for leading a life as long and pleasant as possible, the other for most skillfully turning others to one’s own use. The latter is Politics, the former Medicine. The rest they either publicly despise or, since they have only learned them for appearance, they laugh at them inwardly. But how safely, they shall see for themselves.

I return to those for whom not all these things seem to be despised, who perhaps will acknowledge with me that a part of Phoronomics [the science of motion], Elemental, abstract, and purely rational (for the other part is mechanical and experimental, or simple, consisting only of observations; or mixed, built from a combination of the consequences of observations and regular abstract ones) has nowhere as yet, as far as has become known, existed as a demonstrated science. No one has rendered a reason for Cohesion, a quality so obvious: what does it profit to devise branches, hooks, crooks, rings, and other entanglements of bodies, when there will be need for hooks of hooks unto infinity? Indeed, many have denied that there are any Curves in the nature of things; I will name only those who occur to me now: Lubin, Basso, Regius, Bonart, and I am not far from adding Hobbes…

30]**

…so that it [the truth] might be clearer and simpler. I hope also that at some time something can be brought forward which, by present use, may strike the eyes.

As for the rest, I bear witness that there is almost none of those whom I have named in this place—even those from whom I have professed to depart—whom I do not highly esteem. Certainly, I judge that to most of them, immortality is owed by posterity, statues by the Republic, and panegyrics by us. But one person does not see all things: even in thoughts there is a certain fortune, which offers some things to some people, and often some things to those of mediocre talent. To have erred, I hope, will be no disgrace in such a great multitude of things to be thought upon; it will have been enough for a few things, correctly and newly said, to be seen by candid and learned men; the rest, even when they are disapproved of, may be excused.

FINIS.