two new sciences summary

Thus the effect of the fifth is to produce a tickling of the ear drum such that its softness is modified with sprightliness, giving at the same moment the impression of a gentle kiss and of a bite. . The image on the left is from the original Italian version while the one on the right is from a 1730 English translation.

Let A denote a cylinder of diameter DC and the largest capable of sustaining its own weight: the problem is to determine a larger cylinder which shall be at once the maximum and the unique one capable of sustaining its own weight. This done, imagine the larger polygon to roll uponEdition: NatlEd; Page: [69] the line AS, carrying with it the smaller polygon. . wanted him to say, so that he can make the analogy between what happens on Earth Therefore DE represents the time occupied by the body in passing from E to F, after fall from A to E and after reflection along EB.

And thus we have a continuous quantity built up of an infinite number of indivisibles.

Let the solid be cut by a plane CO parallel to the plane AD.

Place a heavy body upon a yielding material, and leave it there without any pressure except that owing to its own weight; it is clear that if one lifts this body a cubit or two and allows it to fall upon the same material, it will, with this impulse, exert a new and greater pressure than that caused by its mere weight; and this effect is brought about by the [weight of the] falling body together with the velocity acquired during the fall, an effect which will be greater and greater according to the height of the fall, that is according as the velocity of the falling body becomes greater. wish to apply our proven conclusions to distances which, though finite, are very large, it is necessary for us to infer, on the basis of demonstrated truth, what correction is to be made for the fact that our distance from the center of the earth is not really infinite, but merely very great in comparison with the small dimensions of our apparatus. When I take a hard substance such as stone or metal and when I reduce it by means of a hammer or fine file to the most minute and impalpable powder, it is clear that its finest particles, although when taken one by one are, on account of their smallness, imperceptible to our sight and touch, are nevertheless finite in size, possess shape, and capability of being counted. This undulation expands through the air and sets into vibration not only strings, but also any other body For let CD be to CE as A is to B; then, from the preceding, it follows that the time required to complete the distance CD at speed A is the same asEdition: NatlEd; Page: [194] the time necessary to complete CE at speed B; but the time needed to traverse the distance CE at speed B is to the time required to traverse the distance CD at the same speed as CE is to CD; therefore the time in which CD is covered at speed A is to the time in which CD is covered at speed B as CE is to CD, that is, as speed B is to speed A. Besides, I may add, that it is impossible for lines which maintain this same ratio and which are drawn from the terminal points, A and B, to meet at any point either inside or outside the circle, CEG.

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