Das Muster: Kompakt – modern – klar by Dorothee Koch, Monika Mülhausen

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By Dorothee Koch, Monika Mülhausen

Springer necessities sind cutting edge Bücher, die das Wissen von Springer DE in kompaktester shape anhand kleiner, komprimierter Wissensbausteine zur Darstellung bringen. Damit ergänzen Springer necessities die klassischen Lehr- und Fachbücher und großen Handbücher von Springer DE um ein neues Buchformat von ca. 20-40 Seiten, das sich besonders für die Nutzung auf modernen Tablet-PCs und eBook-Readern eignet.

Mit diesem crucial stellen wir Ihnen den neuen Buchtyp vor: Auf wenigen Seiten erhalten Sie einen kompakten Überblick darüber, was once ein crucial auszeichnet, wie es aussieht und auf welche Punkte beim Aufbau zu achten ist.

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One calls a motion actual when it is no longer at its starting point, but rather when it has lasted for a time. This time between the beginning of motion and the moment when the body acts, is what makes it possible to call the motion actual. But note that this time∗ is not a fixed and determinate quantity, but is instead wholly indeterminate and can be determined at will. This means that one can suppose it to be as small as one wishes if one is to use it to denote an actual motion. For it is not this or that quantity of time that in fact makes the motion actual, but time as such that does this, however small or great it may be.

But suppose (per hypothesinh ) that the quantity of the first minute added a new dimension to the body’s force, then the quantity of two minutes would add yet another dimension to the body’s force, because this quantity involves double the conditions contained in the first minute. Thus the body that freely continues its motion would have a force of only one dimension at the starting point of its motion and a force of two dimensions after one minute had passed; but it would have a force of three dimensions after the second minute, four dimensions after the third minute, five dimensions after the fourth, and so on.

43 Motion of the second kind is no different from dead pressure. 1:29 §17. Since I actually wish to discuss motion that conserves itself perpetually in empty space, I shall briefly consider the nature of such motion in accordance with metaphysical concepts. 44 For if this aggregate were not equal to its entire force, then, in order to find a sum equal to the entire intensity of the force, one would require a time longer than infinite time, which is absurd. Now if one compares two bodies, A and B, assuming A to have two units and B one unit of velocity, from the beginning of its motion on, A perpetually pushes at the infinitely small masses of space it traverses with twice the velocity of B, but it also covers twice as much space in this infinite time as B, thus the whole quantity of the action performed by A is proportional to the product of the force with which it encounters the small parts of space and the number of these parts, while exactly the same is the case for the force of B.

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