Chapter 1

Theory of Concrete Motion

Leibniz was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is a prominent figure in both the history of philosophy and the history of mathematics.

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A Hypothesis on the Phenomena of our Globe

  1. Let there be assumed at the beginning a Solar Globe, a Terrestrial Globe, and an intermediate space which is at rest.

This space we shall call aether.

It is filled as much as is sufficient (for the universal fullness of the state of the world, which we perceive, does not allow for a vacuum, as demonstrated elsewhere).

  1. It is necessary, therefore, that there be a certain motion, above all, both in the solar globe and in the terrestrial globe.

For since these two globes must have coherent parts—lest they be dissolved or punctured by the slightest impact of even a tiny thing—and since no cohesion of a resting body exists (as per the things said in the Abstract Theory of Motion, th. 20, which we shall give in its proper place), some motion must be assumed in them.

This is perhaps the unique and primary demonstration of the necessary motion of the earth. Although, as will be advised below in § 35, it matters nothing to the sum of our hypothesis whether the circulation of the earth is admitted, along with the Circulation of Light or the aether…

..of the aether around the earth, which we primarily utilize, see § 9, [it] could easily prove itself to all, unless I am mistaken.

  1. Let us suppose, therefore, if you please, both in the sun and in the globe of the earth, a motion around their own centers; for the same things that occur in our earth can occur in proportion in other large and small globes interspersed in the same aether, moved around their own centers—that is, not only the planets which we see, but also certain innumerable little worlds [mundulos], as it were, which we do not see, and which we do not consider now.

  2. But in the sun, another motion must also be supposed, by which it acts outside of itself, from which the cause of motion in the world—which does not return into itself—is derived. For motion around its own center does not act outside itself; for as the illustrious men Torricelli and Hobbes established, the rotation of the sun alone around its own center would cause the whole aether with the planets to be carried around the sun, to ferment, and to produce light. Indeed, it would project the matter thus moved away from itself along a tangent—the thinner [tenuiora] more so, the thicker [craffiora] less so.

Since there is a similar motion in the earth, it follows that thicker things succeed into the place of thinner things that have been rejected, and hence are heavy [gravia]. I cannot admit that it follows that just as a stone tends toward the earth, so the earth and other planets tend toward the sun; nor can it be said that distance diminishes efficiency, when on the contrary in this hypothesis, it is increased because of the larger circle of a larger radius. Nor is it permitted here to appeal to experience…

Page 7 [7] …of a resting liquid moved solely by the rotation of a solid within it around its own center, just as a stick in a jar moved around its own center sets the whole water in motion. For it has been shown in the Abstract Theory of Motion that most phenomena of repercussions do not arise from the notions of motion in liquids, but have causes far different from the economy and motion of the invisible system—such as gravity, attraction, the restoration of bends [elasticity], and others of that kind.

Specifically, the stick moves the water with it because it rests upon it by its own gravity and internal [intestino] motion; which cannot be said of the aether, in which no cause of motion other than the sun is supposed to exist. Since our liquids, even with the stick removed, would then be in perpetual motion. To say nothing of the rotations around their own centers, which we are accustomed to establish, [they] for the most part waver greatly.

Therefore, so that the sun may be able to radiate or act in all directions, it is necessary that there be a certain motion in its parts, distinct from the motion of the whole around its own center. And having conceded with Copernicus many large Orbs, there will be the same or a proportional reason for each of its suns.

  1. This motion of the parts of the sun (or of any radiant thing) cannot tend directly outward; otherwise they would all have flown away long ago. Therefore, a motion of the parts must be supposed in addition to the rotation of the whole, which is variously circular, or otherwise returning into itself, from the concurrence of which…

8] …expelled outward, as per problem 7 of the Abstract Theory of Motion. And indeed, so many [are expelled] that there cannot be a sensible point around the sun all the way to the earth and beyond, to which at any sensible instant some radius of the sun—that is, an agitation of the aether sent from the sun in a straight line—does not reach. This matter, on account of the divisibility of any continuum into parts however small to infinity, is not difficult to explain. Moreover, let me advise by the way, that it can be necessarily demonstrated that it is impossible for the sun to have shone from eternity, unless there be a source from which it is perpetually replenished.

  1. Now, these rays of light act upon the terrestrial globe. Let it be supposed that the terrestrial globe was initially entirely homogeneous, and thus neither as rare as air is, nor as thick as earth is, but—as Sacred Scripture also intimated—of a nature approaching water. And this [the chemist] Van Helmont would not deny, who places water as the principle of things and makes the earth the sediment of water.

  2. This state of the globe will be wonderfully changed by the rays of the sun (or before the sun, by the primigenial light later collected into the sun, for according to our hypothesis it is the same) rushing in. For since, according to the doctrine of abstract motion (th. 19), no cohesion of a body occurs at the same time across its entire face, the globe of the earth, having been struck where it does not cohere, will gape open [dehiscet] and admit the aether. For in the natural state, such as is first supposed, or in the abstract, there is no cohesion of a rotating homogeneous globe…

Page 9 [9] …cohesion, except in lines parallel to the equator. Therefore all sensible parallels, and their concentric [parts], will be able to depart from each other, and with light rushing in from most directions, they will gape. Furthermore, by many blows, most things will go toward the center; the greater part of the material, collected at the bottom, will give Earth; the water will float above [supernatabit]; the air will spring forth [emicabit]: INTRUSIVE AETHER. (This is perhaps that Spirit of the Lord which was borne over the waters and was digesting them; from them, by its own ventilation, it precipitated the thicker things, sublimated the thinner things, and by the removal of which all things are reduced into an inert, non-coherent, dead powder). And it pervades all things within, and is intercepted here and there into bubbles [bullas]…

…These things are not to be understood as if it were necessary that our globe actually arose in this way, although they wonderfully agree with the traditions of Sacred Scripture; but it suffices that some cause of the beginning (as if of a perpetual beginning) can be understood to be imagined; and therefore [it serves as] an aid to the imagination in perceiving the hypothesis of origin, at least in present causes.

  1. Moreover, it is not the place here to declare the origin of other similar globes (especially since every great Orb seems to have its own sun); such things pertain to the doctrine of the System of the World; just as this also: by what reason from the rotation of the sun…

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