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The breadth and facility of these solutions added a new charm to the investigation of curves; and passing lightly by the Conic Sections, the mathematicians of that day busied themselves in finding the areas, solids of revolution, tangents, etc., of all imaginable curves, some of them remarkable enough.
With these measurements as a guide, Kepler was led to a very fanciful theory, according to which the orbits of the five principal planets sustain a peculiar relation to the five regular solids of geometry.
Various mathematical relationships are made clear in his games or trials of strength, such as distance in relation to time or strength, weight in relation to power and to balance, length and breadth in relation to materials, value of material in relation to money or work. By means of many of his toys the properties of solids have become working knowledge to him.
The water for experiment was taken from the English Channel, about fifty miles southwest of the Eddystone Lighthouse, and it was found to correspond closely with the analysis of the Atlantic published by Roscoe, viz.: Total solids 35.976, of which the total chlorides, are 32.730, representing 19.868 of chlorine.
There is suggested a theory of monads and the conception of the development from simple to more complex bodies, passing through the stages of lines, plain figures, and solids to sensible bodies. The doctrine of the four elements fire, water, earth, and air as the basis of all organisms is put forward.
He could not judge the difference between near and far, between solid and liquid; he had no experience, dating from childhood, of the apparent smallness of distant things, of the connexion between the impression given to the touch by solids and their effect on the eye. He had all these things to learn.
This transparent screen fenced out or fenced in, according to the side of the narrow counter on which the human lot was cast, the duskiest corner of a shop pervaded not a little, in winter, by the poison of perpetual gas, and at all times by the presence of hams, cheese, dried fish, soap, varnish, paraffin and other solids and fluids that she came to know perfectly by their smells without consenting to know them by their names.
When the child takes off the handkerchief, he can see by the color of the pieces of wood if he has made a mistake. A long time before this difficult exercise, and during the period when the child is working with the three sorts of geometrical solids and with the rough and smooth tablets, he can be exercising himself with a material which is very attractive to him.
Or think, if you choose, of the modern industry of book-making, wherein types are assembled, impressed upon sheets of paper, and these bound into volumes points, lines, planes, solids. The book in turn becomes the unit of another dimensional order, in the library whose serried shelves form lines, which, combined into planes, define the lateral limits of the room. These are truisms.
They, too, ate, and that with no delicate appetite, and having demolished a large portion of the solids, they proposed a "petit verre." I declined. Not so Mesdames Pelet and Reuter; each mixed herself what I thought rather a stiff tumbler of punch, and placing it on a stand near the stove, they drew up their chairs to that convenience, and invited me to do the same.
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