Geocentric model coelestium" ("On the Revolutions of the Heavenly Spheres"), which posited that the Earth and the other planets instead revolved around the Sun. The geocentric system was still held for many years afterwards, as at the time the Copernican system did not offer better predictions than the geocentric system, and it posed problems for both natural philosophy and scripture. The Copernican system was no more accurate than Ptolemy's system, because it still used circular orbits. This was not altered until Johannes Kepler postulated that they were elliptical (Kepler's first law of planetary motion). With the invention of the telescope in 1609,
Central limit theorem possible values. The law of large numbers as well as the central limit theorem are partial solutions to a general problem: "What is the limiting behaviour of as approaches infinity?" In mathematical analysis, asymptotic series are one of the most popular tools employed to approach such questions. Suppose we have an asymptotic expansion of : Dividing both parts by and taking the limit will produce , the coefficient of the highest-order term in the expansion, which represents the rate at which changes in its leading term. Informally, one can say: " grows approximately as ". Taking the difference between and