The way was now paved for a new theory of planetary motions. Nicolaus Copernicus (1473-1543) a Pole, developed the astronomical system bearing his name, as a result of suggestions gained by studying the works of the Greek astronomer Hicetas, and Plutarch's Lives of Greek Scientists. His great work was entitled "De Revolutionibus Orbium Celestium, or the Movements of Heavenly Bodies," which treated the sun as the center of the planetary system. Weather forecasting was improved by Tycho Brahe (1546-1601), and many fine astronomical observations were made by him. He greatly improved astronomical instruments and built and splendidly equipped a great observatory in Uraniborg, Denmark. Numerous important observations were made there. John Kepler, the discoverer of the ellipticity of the planetary orbits and the laws of their movements, was a student under Brahe, and continued his master's researches. His observations on the movements of the planet Mars led to his discovery that the planets travel in ellipses and not in circles. Besides his numerous works on astronomy he wrote valuable books on optics and other scientific subjects. Galileo (1564-1642) took up the work of Tycho Brahe and Kepler and carried it forward to new triumphs. He made the first telescope ever used for astronomical observation, and with it was able to discern that the Milky Way was composed of aggregations of innumerable stars; that the surface of the moon was covered with plains and mountains, that there were four moons revolving around the planet Jupiter, that the planet Venus showed phases like those of the moon as she moved around her orbit, and that there were black spots, at times, upon the sun, which revealed its rotation on its axis. Galileo did equally fundamental work in developing the laws of motion, and the principles of mechanism and physics. The development of modern mathematics began with three intellectual feats--the invention of the Arabic notation, of decimal fractions, and of logarithms. The notation was derived by the Arabs from India about 700 A. D. They had used numerals long before, but the old system was crude like the systems employed by the Egyptians and Greeks. The Textbook on Mathematics by Mohammed ibn Musa, published at Bagdad about 825 A. D., contained the first notable exposition of modern numerals. This important work gave rise to many more Arabic treatises, some of which showed improved methods. Decimal fractions were used by the early peoples of central Asia and were transmitted by them to the Babylonians. Their system was based, apparently, upon a sexagesimal scale. Simon Stevin (1548-1620), a Belgian, made great improvements in decimals. He adopted the plan of William Buckley, of England, and other mathematicians, and made the base 100,000, instead of 60.