Footnotes to New Mechanics...

1 The terms "content", "mass" and "matter" are equal in their meaning.

2 "All bodies are heavy" means that they appear; that they have increments dm or dl.

3 The only substance is that upon on which all descriptions of changes exist, while it is itself cannot be represented if it does not change. Existence in time appertains to the nature of substance and in the nature of objects two or more substances may not be granted the same nature of existence in changes. (Spinoza)

4

5 Poincare J., "The Foundations of Science", The Science Press, Lancaster, 1946

6 A plane is a surface of constant changing negative curvature; where any path-line of any object's motion can be imagined as a cross line of two surfaces of constant changing negative curvature..

7 The One is something that cannot be characterized because it does not change -- the simpe substance itself.

8 The observation of an event from two different frames of reference moving with a relative velocity v along the z axis would be related by the Lorenz transformation: where the Lorenz transformations confirm that activities of objects mean changes in their forms or contents.

9 Hegel, "The Encyclopedia Logic"

10 Cantor defined the cardinal number of a set as that property of it which remains after abstracting the qualitative nature of its elements and their ordering: if A is a closed set of apeirons at rest containing n apeirons, then card A = 0.

11 Theatetus; [157b]

12 where because time is continuous -- it is the infinitum itself -- movement must be continuous, given that it is impossible there should be time without movement; time, then, is the number of a particular continuous movement, or circular movement therefore. However, the number of objects is finite.

13 There are three kinds of points: -- objects; all objects are accumulation points (an accumulation point of a set of points is a point P such that there is at least one point of the set distinct from P in any neighborhood of the given point) and they have three measures: form, matter and the existence in the infinitum of time; -- objects-in-themselves; objects-in- themselves are points of the whole accumulation that contain all objects from their neighborhoods in themselves and that have two measures: form and matter; -- solids; they are points of absolute accumulation or, what is the same, the endlessly remote points; which points do not have objects in their neighborhoods and which points have only one measure: the existence in the eternity of immovability.

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