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Influenced by their knowledge of European mathematics and mathematical astronomy, these scholars laid down new rules for verifying the authenticity of the Classical texts and, by revealing flaws in previously accepted canons, challenged the Neo-Confucian orthodoxy.
His explanations of mathematics always include optics, mathematical astronomy, harmonics, etc.
With the development of mathematical astronomy in the Seleucid period, however, it became indispensable.
Trigonometry tables had existed since antiquity, and the relations between sines and cosines were commonly used in mathematical astronomy.
The size and number of zodiacal constellations varied in antiquity and became fixed only with the development of mathematical astronomy.
The cosmology of the Timaeus had a consequence of the first importance for the development of mathematical astronomy.
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In 1713 Minggantu was appointed to the newly created Office of Mathematics, where he took part in the compilation of the imperially commissioned Lüli yuanyuan (c. 1723; "Source of Mathematical Harmonics and Astronomy"), a compendium in three sections: mathematics, astronomy, and musical harmony.
In 1712 Mei Juecheng became a court mathematician and the following year joined the Mengyangzhai (an imperial bureau created to synthesize Western and Chinese scientific knowledge) as one of the chief editors of Lüli yuanyuan (c. 1723; "Source of Mathematical Harmonics and Astronomy"), a compendium on music, mathematics, and astronomy.
Poincaré summarized his new mathematical methods in astronomy in Les Méthodes nouvelles de la mécanique céleste, 3 vol. (1892, 1893, 1899; "The New Methods of Celestial Mechanics").
But in ancient Babylonia and Greece, it was precisely because the motions of the planets could be subjected to mathematical treatment that astronomy made such rapid headway.
Thereby began his shift of interest from mathematical physics to astronomy and, in later years, led to his work on the formation of planetary systems and to his conviction that life must be of frequent occurrence in the universe.
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