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Newton's Calculus in Lixiang Kaocheng Houbian

Lu Dalong (Beijing, China)

It was revealed that Dai Wei Ji Shiji, which was translated by Li Shanlan (1811-1882) and Alexander Wylie (1815-1887) from Elias Loomis' Elements of Analytical Geometry and of the Differential and Integral Calculus (8 vo., pp. 278. New York, 1851) and published in 1859, is the earliest book by which Newton's calculus was generally introduced into China. However, in 1742, Isaac Newton's theory of the Moon's motion, which was expatiated in the second edition of his Magisterial Philosophiae Naturalis Principia Mathematica, was introduced and applied in Lixiang Kaocheng Houbian, sequel to the Compendium of Observational and Computational Astronomy and one of the Chinese astronomical theories and Chinese calendars, which had been put into use in China from 1742 to 1911. Newtonian scholar has discovered that the Portsmouth mathematical papers show that by 1687 Newton had developed an alternative approach which corresponds to the method of variation of orbital parameters developed many years later by Euler, Lagrange and Laplace, by which Newton required the inequalities and perturbations of the Moon's motion in the 2nd edition of Principia, among which four inequalities were originated with Newton. The data above mentioned were mostly compiled into Lixiang Kaocheng Houbian. Furthermore, in the section of "It is required to find Second Average" of Yue Li Shuli, volume 2 of Lixiang Kaocheng Houbian, there was an expression about the calculation of Second Average, i.e., which is proportional to the cube of the distance of the current Sun from Earth, which was a direct application of Newton's calculus. Probably, the conclusion is that Newton's calculus was introduced into China in the first half of the 18th century, just at the same time when Newton's theory of the Moon's motion, as well as his celestial mechanics began to play an important role in the compiling of the last "ancient" Chinese calendar.

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