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Crystallography before the Discovery of X-Ray Diffraction

This paper presents a brief description of the prevailing ideas and hypothesis about the nature of matter from antiquity to the end of XIX century. It shows how gradually, since the Hauy proposal of the existence of the unit cell, the crystal lattice and symmetry and subsequent derivation of the 14 crystal classes by the French Physicist A. Bravais, the 32 point groups by the German mathematician A. Shoenfliess and the 230 space groups independently deduced by the Russian mathematician E. S. Fedorov and A. Shoenflies confirmed the atomic theory suggested by the Greek philosopher Democritus. These empirical and theoretical findings, conducted by several scientists, are one of the most brilliant theoretical predictions of all time in Science, fully confirmed after von Laue discovery of X-ray diffraction by crystals in 1912 and its application on the determination of molecular and crystalline structure by the English physicists W. H. Bragg (1862-1942) and his son W. L. Bragg (1890-1971).