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A comparison between Mei Wending's Zheng Xing (�鸃�) and the western trigonometry

Kong Guoping (Science Press, Beijing)

In 16-17 century, because of the work of J. Regiomontanus, G.H. Rheticus and F. Vieta, the trigonometry of the West had become an independent subject and developed rapidly. However, their questions of spherical trigonometry were all solved on the spherical surface, so the methods were complicated. Based on the Western trigonometry, Mei Wending wrote a book named "A Ruler in the Ring". He used the method of projection in order to turn the spherical triangles to plane triangles. the vertical projection of a spherical triangle in the plane passing the center of a sphere was called zheng xing (�鸃�) of the spherical triangle. On the figure of zheng xing, the segments representing the trigonometric functions of a spherical triangle can be measured by a ruler, so the book was named "A Ruler in the Ring". Obviously, to study the figure of zheng xing is much easier than to study spherical triangles directly. This method of projection is an outstanding creation by Mei Wending. However, at that time the communication between the East and the West was little. So this advanced method was not spread to the West in time.

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