What books advanced the development of the Chinese calendar?

During the Eastern Han Dynasty, Liu Hong, an astronomer, wrote the Qianxiang Calendar in 206, which made new progress in the study of the moon's movement, proposing for the first time the movement of the moon's perigee, thus calculating the length of the perigee month and compiling a table of lunar departures day by day in a perigee month; proposing for the first time that the angle of intersection between yellow and white is 6 degrees; and proposing for the first time the method of calculating the eclipses' limits in the calculation of intersecting eclipses, which had a great impact on the calendars of the future generations.

"Five Stars" is a silk book in the Mawangdui Han Tomb in Changsha, written around the time of Emperor Wen of the Han Dynasty, specializing in the movement of the five planets and some astronomical knowledge, **** there are nine parts, 8000 words. The book has a detailed description of the movement of the five planets, and became the forerunner of the work of "step five stars" in the calendar of later generations.

The "Five Stars" is more accurate in determining the conjunction cycle of Venus and Saturn, and the dynamics of the three stars of Wood, Earth and Venus during the 70-year period from 246 B.C.E. to 177 B.C.E. is documented on a year-by-year basis, which is an important source of information for the study of the ancient planetary problems.

Two other important astronomical works of the Han Dynasty are the Book of Heavenly Officials and the Zhou Thigh Calculations. The Book of the Heavenly Officials, one of Sima Qian's Records of the Grand Historian, can be regarded as a summary of the knowledge about astronomy at that time. In particular, the stellar part recorded the stars recognized at that time in the whole day, *** more than 90 groups of names and more than 500 stars, which is the earliest complete document about the stars in the whole day. It influenced the naming of many later stars.

The content of the Book of Heavenly Officials, in addition to the stars, there are planets, the division of the field, the sun and the moon to occupy the weather, strange celestial phenomena, clouds, the age of the star chronicle, celestial records and accounted for the test, etc., is the study of the Qin and Han astronomy and even the pre-Qin astronomy of an authoritative document. It is an authoritative document for the study of astronomy in the Qin and Han dynasties and even in the pre-Qin era. The Book of Heavenly Officials" created the tradition of writing astronomical records in the history books of later generations. There are more than a dozen astronomical records in the "Twenty-four Histories", which provide systematic and comprehensive information for the study of the history of astronomy in China.

The Zhou Thigh Calculation Classic was written in the late Western Han Dynasty, the author is not available, is the "Calculation of ten books" in one of the name of the book of calculations, in fact, it is mainly an astronomical work. There are two volumes in the book, focusing on a theory of the structure of the universe at that time, "Gaitian", elaborating in detail the method of calculating the structure of heaven and earth, the size of the sun's orbit, the number of miles in the circumference of the heavens, the North Pole Xuangui, and the production of a circular Gaitian-type star map and so on, which is a systematic and exhaustive book on the "Gaitian". It is a systematic and detailed book on the "Gaiten Sermon".

The astronomical calendar of the Sui Dynasty also made many achievements. Yang Guang, the son of Emperor Wen of Sui Dynasty, enlisted the calendar experts of the whole country, all of them were concentrated in the East Palace, **** with the discussion of the calendar. Liu Zhuo was among those summoned by the Crown Prince, and this time he presented the Emperor's Extreme Calendar, which had been researched for decades.

The Imperial Calendar takes into account the uneven movement of the sun and the moon to calculate the moment of the sun and the moon's conjunction, and creates the method of interpolating the equidistant quadratic difference. In order to find the corrected value of the fixed solstice at any time, it also created the formula of the arbitrary interval quadratic difference interpolation method. This is an important position in the history of astronomy and mathematics in our country, and the interpolation method used in the calculation of the movement of the sun, moon and five stars in future calendars is mostly inherited from the method of the "Imperial Calendar" and has been developed.

The achievement of astronomical calendar in Tang Dynasty was another progress compared with the Huangji Calendar. In 727, Emperor Xuanzong of the Tang Dynasty ordered the astronomer monk Yixing to write the Dayan Calendar, which was later organized into a text by Zhang Shuo and Chen Xuanjing, and was promulgated in 729 and used until 751. It was introduced to Japan in 733 and was used in Japan for nearly a century.

The Dayan Calendar is well-structured and organized, with 7 chapters on calendar techniques and specific calculation methods. There are also 12 articles on the calendar, the theoretical aspects of the calendar, a paper written for the Dayan Calendar, commonly known as the Dayan Calendar. The formulation of the Dayan Calendar began with the manufacture of instruments and the determination of basic astronomical data through actual observation, which was the scientific method. After the formulation of the Dayan Calendar, the phenomenon of uneven movement of the sun and the moon was understood correctly and comprehensively. Through actual observation, the fallacy of "the difference of an inch by a thousand miles", which had been circulating for 1,000 years, was dispelled. In terms of calculation methods, the Dayan Calendar creates the formula of unequal spacing second difference interpolation, which is much more advanced than the method of the Huangji Calendar.

The 120-volume Kaiyuan Chamjing, written by Gautama Siddhartha in the Tang Dynasty, was written between 718 and 726, so it is also known as the Great Tang Kaiyuan Chamjing. Lost after the Tang Dynasty, in 1616, Anhui Shexian Cheng Mingshan in the ancient Buddha statue found by chance in the belly, so that once again circulated to the present day. Kaiyuan Cham Ching" is a complete list of astronomical and astrological writings before the Tang Dynasty, which can be seen at that time more than 70 kinds of ancient astronomical and astrological books according to the content of the compilation of extracts, the contents of which involves astronomical and astrological phenomena, climate, and strange phenomena and other aspects. Astronomical aspects of the nomenclature, the theory of the universe, the movement of the sun, moon and planets, the twenty-eight hosts distance, Gander, Shi Shen, Wuhan three on the name of the stars throughout the day, the number of stars, the position of the description and occupation of the test, including Shi's sidereal catalog.

Because of the compilation of the Kaiyuan Chamjing, the contents of many ancient astronomical and astrological writings that had been lost were preserved intact, and for this reason, the Kaiyuan Chamjing is also an extremely valuable book.

The Tang Dynasty, there is also an astronomical astrology work, "Yisi Zhanshan", is Li Chunfeng, which excerpts from many ancient astrology works that have long been lost, including astronomy, meteorology, astrology, the content is also very broad.

During the Yuan Dynasty, Guo Shoujing made the Calendar of the Time in 1280, which was published the following year. The calendar was published in the Yuan Shi? The upper and lower chapters of the Calendar were reorganized by Guo Shoujing on the basis of Wang Xun's first draft. At that time, although the Calendar had already been promulgated, the various data tables and the push-step algorithm had not been finalized. After the death of Xun Wang, Guo Shoujing presided over the completion of the work. He "compared and organized, neatly divided into seconds, cut into two volumes".

The "Calendar of the Time" **** has seven parts, the content is similar to the "Dayan Calendar", but the use of equidistant three-difference interpolation method to calculate the position of the sun, the moon and the five-star, and the use of the arc-vector cut circle and similar spherical triangle method based on the sun's ecliptic to find its ruddy meridian ruddy latitude and longitude, the two methods in the history of astronomy and the history of mathematics have an important position.

In the Ming Dynasty, Liu Ji entered the Daitong Calendar at the beginning of the Ming Dynasty. To the Hongwu years of 1384, set up in Nanjing Jiming Mountain Observatory, Dr. Yuan Tong repair calendar, still with the "Daitong" as the name, and the integral whole of the Yuan Dynasty, "time calendar" method of number, before and after the *** use of more than 360 years, is the ancient calendar in the line with the longest, but also in the calculation of astronomical data to the peak of the development of a calendar. This is the end of the classical system of calendar in China, and later on, there will be western astronomical knowledge imported and influence on the calculation of the calendar. In addition, the Ming Dynasty, "Observation and play occupation" and "Chongzhen calendar" is worth mentioning. The author of the "Observation and play occupation" is not available, is also a valuable book of astronomy and astrology. It through a large number of astronomical phenomena and strange celestial records, you can understand the history of many valuable astronomical events, such as the outbreak of nova-supernova, the comet and the split, meteor showers change, variable stars of light change, solar eclipse scene, the black son of the sun and the corona of the changes in the history of the age, planetary movements, the Earth and the Moon system changes, which is a great value to the theoretical study of modern astronomy.