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DYNAMICS
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DYNAMICS , See also:ANALYTICAL; GYROSCOPE; See also:HARMONIC See also:ANALYSIS; See also:WAVE; See also:HYDROMECHANICS ; See also:ELASTICITY; See also:MOTION, See also:LAWS OF; See also:ENERGY; See also:ENERGETICS; See also:ASTRONOMY (See also:Celestial See also:Mechanics) ; See also:TIDE. Mechanics (including dynamical astronomy) is that subject among those traditionally classed as " applied " which has been most completely transfused by mathematics—that is to say, which is studied with the deductive spirit of the pure mathematician, and not with the covert inductive intention overlaid with the superficial forms of See also:deduction, characteristic of the applied mathematician. Every See also:branch of physics gives rise to an application of See also:mathematics. A prophecy may be hazarded that in the future these applications will unify themselves into a mathematical theory of a hypothetical substructure of the universe, See also:uniform under all the diverse phenomena. This reflection is suggested by the following articles: See also:AETHER; See also:MOLECULE; CAPILLARY See also:ACTION; See also:DIFFUSION; See also:RADIATION, THEORY OF; and others. The applications of mathematics to See also:statistics (see STATISTICS and See also:PROBABILITY) should not be lost sight of ; the leading See also:fields for these applications are See also:insurance, See also:sociology, variation in See also:zoology and See also:economics. The See also:History of Mathematics.—The history of mathematics is in the See also:main the history of its various branches. A See also:short See also:account of the history of each branch will be found in connexion with the See also:article which deals with it. Viewing the subject as a whole, and apart from remote developments which have not in fact seriously influenced the See also:great structure of the mathematics of the See also:European races, it may be said to have had its origin with the Greeks, working on pre-existing fragmentary lines of thought derived from the Egyptians and Phoenicians. The Greeks created the sciences of See also:geometry and of number as applied to the measurement of continuous quantities. The great abstract ideas (considered directly and not merely in tacit use) which have dominated the See also:science were due to them—namely, ratio, irrationality, continuity, the point, the straight See also:line, the See also:plane. This See also:period lasted' from the See also:time of Thales, c. 600 B.C., to the See also:capture of See also:Alexandria by the Mahommedans, A.D. 641. The See also:medieval Arabians invented our See also:system of numeration and See also:developed See also:algebra. The next period of advance stretches from the See also:Renaissance to See also:Newton and See also:Leibnitz at the end of the 17th See also:century. During this period logarithms were invented, See also:trigonometry and algebra developed, analytical geometry invented, dynamics put upon a See also:sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the See also:differential calculus by Newton and Leibnitz and the See also:discovery of See also:gravitation. The 18th century witnessed a rapid development of analysis, and the period culminated with the See also:genius of See also:Lagrange and See also:Laplace. This period may be conceived as continuing throughout the first See also:quarter of the loth century. It was remarkable both for the brilliance of its achievements and for the large number of See also:French mathematicians of the first See also:rank who flourished during it. The next period was inaugurated in analysis by K. F. See also:Gauss, N. H. See also:Abel and A. L. See also:Cauchy. Between them the See also:general theory of the complex variable, and of the various " See also:infinite" processes of mathematical analysis, was established, while other mathematicians, such as See also:Poncelet, See also:Steiner, Lobatschewsky and von Staudt, were See also:founding See also:modern geometry, and Gauss inaugurated the differential geometry of surfaces. The applied mathematical sciences of See also:light, See also:electricity and See also:electromagnetism, ' Cf A Short History of Mathematics, by W. W. R. See also:Ball. and of See also:heat, were now largely developed. This school of mathematical thought lasted beyond the See also:middle of the century, after which a See also:change and further development can be traced. In the next and last period the progress of pure mathematics has been dominated by the See also:critical spirit introduced by the See also:German mathematicians under the guidance of Weierstrass, though fore-shadowed by earlier analysts, such as Abel. Also such ideas as those of invariants, See also:groups and of See also:form, have modified the entire science. But the progress in all directions has been too rapid to admit of any one adequate characterization. During the same period a brilliant See also:group of mathematical physicists, notably See also:Lord See also:Kelvin (W. See also:Thomson), H. V. See also:Helmholtz, J. C. See also:Maxwell, H. See also:Hertz, have transformed applied mathematics by systematically basing their deductions upon the See also:Law of the conservation of energy, and the See also:hypothesis of an See also:ether pervading space. See also:translations into French and See also:Italian). (A. N. 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