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By Celletti A., Chierchia L.

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It consists of thirteen books dealing with the basic properties of rectilinear figures and circles, the theory of proportion, the theory of numbers, the classification of incommensurables, and solid geometry. The style of the book, consisting entirely of definitions, axioms, theorems and proofs, determined the nature of all subsequent Greek mathematical works and, indeed, much mathematics that is written today still bears the hallmark of this early Greek paradigm. The contents of the Elements show that in the three centuries since the beginnings of deductive mathematics in Ionia, the Greeks had made great progress in mathematics.

Thoren (1971)) do not share his view. Eudoxus’ system of concentric spheres 29 Earth a Fig. 2. Eudoxus’ scheme for the motion of the planets. the greatest apparent diameter of which is 14 per cent larger than its smallest. Simplicius was well aware that, even judged by the astronomical knowledge of Eudoxus’ day, the system of concentric spheres had serious deficiencies. Nevertheless the theories of Eudoxus and his followers fail to save the phenomena, and not only those which were first noticed at a later date, but even those which 8 were before known and actually accepted by the authors themselves.

Such changes were, however, not observed. There are many theories, all very speculative, of why the heliocentric theory did not catch on and was superseded so completely by geocentric astronomy. Perhaps the most plausible is the simple fact that the geometrical skill of the Greeks allowed them to devise ingenious constructions that modelled accurately the motions of all the heavenly bodies without having to take the drastic step of removing the Earth from its privileged position at the centre of the Universe.

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KAM stability for a three-body problem of the solar system by Celletti A., Chierchia L.

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