The book First Lessons in Geometry was written by author Thomas Hill Here you can read free online of First Lessons in Geometry book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is First Lessons in Geometry a good or bad book?
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(One half) How long is the radius of the cycloid at the top of the arch ? How long at the bottom ? What is the evolute of a cycloid ? Explain what you mean by this ? 9T If I want to slide anything from A down to B, there is no curvOj nor straight line, down which a thing would slide so quickly as down the cycloid. If a hill was hollowed out in that shape, sleds would run down it faster than they could down any other shaped hill of the same height and the same breadth at the bottom. 6. The secon...d curious thing about sliding on the inside of a cycloid is, that it takes always exactly the same time to slide to the bottom, how- ever high up or low down you start. If A, in the last figure, is the top of such a hill, and c the lowest point, it will take a sled exactly as long to go from B to c, as to go from A to c. But this, you must remember, is only when we imagine the hill and the runners of the sleds to be, both of them, perfectly slippery ; so that there shall be no rubbing. In that case, if the road from A to c was two miles long, it would only take a sled twenty-eight seconds to come down the whole length.
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