English Mechanic and World of Science: With which are Incorporated "the Mechanic", "Scientific Opinion," and the "British and Foreign Mechanic.", Volume 38

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E. J. Kibblewhite, 1884 - Industrial arts
 

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Page 56 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.
Page 55 - A more extended experience and more accurate measurements would teach them that the axioms were each of them false; and that any two lines if produced far enough each way, would meet in two points: they would in fact arrive at a spherical geometry, accurately representing the properties of the two-dimensional space of their experience. But their original...
Page 141 - ... only for the reason that there are certain countries in the world where pure science has been and is cultivated, and where the study of nature is considered a noble pursuit. But such countries are rare, and those who wish to pursue pure science in our own country must be prepared to face public opinion in a manner which requires much moral courage. They must be prepared to be looked down upon by every successful inventor whose shallow mind imagines that the only pursuit of mankind is wealth,...
Page 102 - Lightly they'll talk of the spirit that's gone, And o'er his cold ashes upbraid him ; But little he'll reck, if they let him sleep on In the grave where a Briton has laid him ! But half of our heavy task was done When the clock struck the hour for retiring, And we heard the distant and random gun That the foe was sullenly firing.
Page 34 - Over long periods of time and many lines of being we have a nearly continuous chain, and if this does not show the tendency desired, the fault is as likely to be in the theory as in the record. On the other hand, the abrupt and simultaneous appearance of new types in many specific and generic forms and over wide and separate areas at one and the same time, is too often repeated to be accidental. Hence palaeontologists, in...
Page 56 - I said that I would speak to you, not of the utility of mathematics in any of the questions of common life or of physical science, but rather of the obligations of mathematics to these different subjects. The consideration which thus presents itself is in a great measure that of the history of the development of the different branches of mathematical science in...
Page 34 - ... one hand, any geological map whatever suffices to show that the general outline of the existing land began to be formed in the first and oldest crumplings of the crust. On the other hand, the greater part of the surface of the land consists of marine sediments which must have been derived from land that has perished in the process, while all the continental surfaces, except perhaps, some high peaks and ridges, have been many times submerged. Both of these apparently contradictory statements are...
Page 129 - ... under military discipline, which he enforced himself. He also ate and drank as they did. The men were kept on single articles of food, coffee and water. Among these articles were beans, beef, bread, chicken, crackers, fish, lobster, mutton, potatoes, rice, turkey, oatmeal. The blood, urine and faeces of the animals were carefully examined microscopically and chemically daily without any preconceived idea to develop, but simply to ascertain facts and develop ideas from those facts. In this manner...
Page 55 - We measure distance, say, by a yard measure or a foot rule, anything which is short enough to make the fractions of it of no consequence (in mathematical language, by an infinitesimal element of length); imagine, then, the length of this rule constantly changing (as it might do by an alteration of temperature), but under the condition that its actual length shall depend only on its situation on the plane and on its direction: viz. if for a given situation and direction it has a certain length, then...
Page 56 - But if it' were said that the problem had " so many imaginary solutions," the word " imaginary " would here be understood to be used in opposition to real. I give this explanation the better to point out how wide the application of the notion of the imaginary is — viz. (unless expressly or by implication excluded), it is a notion implied and presupposed in all the conclusions of modern analysis and geometry. It is, as I have said, the fundamental notion underlying and pervading the whole of these...

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