Li Chunfeng's main contribution in mathematics was the compilation and annotation of the famous Ten Arithmetic Classics. These ten arithmetic classics were later used as mathematics teaching materials in the Imperial Academy of Arithmeticology in the Tang Dynasty. "Sui Shu Baiguan Zhi" records: "Guozi Temple offers wine, governs Guozi, Taixue, Simen, calligraphy (study), and arithmetic, and each has doctors, teaching assistants, students and other staff." This is a national specialized mathematics At the beginning of education, the Tang Dynasty continued to organize mathematics education on the basis of the Sui Dynasty, and selected scholars based on calculation. In the first year of Xianqing's reign (656), a library of arithmetic was set up in the Imperial College, and at the same time, the selection and compilation of arithmetic textbooks began. According to "The Biography of Li Chunfeng" in Volume 79 of the "Old Tang Book": "First, the eunuch Wang Sibian said that the "Wu Cao" and "Tzu" ten calculation classics had many refutations, and Chunfeng returned to the Imperial Academy's calculation school Doctor Liang Shu, Taixue assistant Wang Zhenru and others were ordered to annotate the "Wucao" and "Sunzi" ten calculation classics. On the 19th day of the second lunar month, Shangshu Zuo Pushe sent a memorial to Zhining and ordered Xi Li Chunfeng and others to annotate ten calculation classics such as "Wucao" and "Sunzi" and divide them into twenty volumes for practical use. "
Ten Suanjing, also known as the Ten Books of Suanjing, refers to "Zhou Bi Suan Jing", "Jiu Zhang Suan Shu", "Haidao Suan Jing", "Sun Zi Suan Jing", "Xiahou Yang Suan Jing", "Zhang Qiu Jian" There are ten mathematical works including "Sushu Jing", "Zu Shu", "Wucao Suan Jing", "Five Classics Arithmetic" and "Ji Gu Arithmetic". They are major mathematical works before the Tang Dynasty and represent the glorious achievements of ancient Chinese mathematics. The passed version of "Zhou Bi Suan Jing" contains Zhao Shuang's annotations and Zhen Luan's annotations. Although it was called "Suan Jing" at that time, the original text and the annotations by Zhao Shuang and Zhen Luan are not perfect. Li Chunfeng's work corrected the shortcomings of this book and made it closer to perfection. Li Chunfeng's annotation pointed out three important errors in "Zhou Bi":
First, the author of "Zhou Bi" believed that the north and south were a thousand miles apart, and the shadow of the eight-foot-high measuring pole in the sun often differed by one inch. , and use this as the basis for the algorithm, which is divorced from reality;
Secondly, Zhao Shuang used the arithmetic series interpolation method to calculate the surface shadow size of the twenty-four gases, which does not conform to the actual measurement. Result;
Third, Zhen Luan had various misunderstandings about Zhao Shuang's "Pythagorean Square Diagram Theory". Li Chunfeng corrected the above errors one by one and put forward his own correct opinions.
More importantly, while Li Chunfeng criticized the Rigao formula in "Zhou Bi" for being inconsistent with the "Gaitian theory", he revised it again based on the bold assumption of the oblique plane, thus successfully The problem of measuring the heavy difference at different heights was transformed into the general daily height formula on the plane to deal with, and for the first time the problem of general similar shapes appeared in the Chinese arithmetic classics, and Liu Hui's theory of heavy differences was developed, making "Gaitian theory" "The mathematical model was close to "perfect" under the understanding conditions at that time. In the "Linder Calendar", the shadow length in the 24-day period was re-measured, and a secondary interpolation algorithm was introduced for the first time to calculate the daily shadow length.
Li Chunfeng's annotation of "Nine Chapters on Arithmetic" is based on Liu Hui's annotation, but the background and environment of Li Chunfeng and Liu Hui's annotation are different. The purpose of Li's annotations is to provide an appropriate textbook for the Ming Dynasty. The annotations are aimed at beginners and focus on explaining the meaning of the questions and algorithms. For places where the meaning of Liu Hui's annotations is very clear, there will be no additional annotations. There are no annotations by him in the chapters such as "Insufficiency of Profit" and "Equations". However, some people think that it is due to the incomplete copying by later generations. For example, Bao Huanzhi of the Southern Song Dynasty said: "Li Chunfeng's annotations can be found in nine volumes of Tang Zhifan, but now there are not enough, and the equations chapter is Xianque Chunfeng's annotation. It means that this book has been passed down for a long time. The recording is full of errors and omissions." Li Chunfeng and others cited the correct calculation formula for the volume of a sphere proposed by Zu Xun when annotating Shao Guang's chapter on "Nine Chapters of Arithmetic" and introduced the theoretical basis of the formula for the volume of a sphere, that is, "the power potential is both If we are the same, we will not be different." This is the famous "ancestral principle". After "Zhu Shu" was lost, this outstanding research result of Zu Chongzhi and his son was passed down to this day only because of Li Chunfeng's citation. "Haidao Suan Jing" is the original result of Liu Hui's mathematical research, but the original text, problem-solving methods and text of Liu Hui's work are very concise and difficult to understand. The annotations by Li Chunfeng and others list the calculation steps in detail, thus opening the door of convenience for beginners.
Li Chunfeng and others' annotations on the "Ten Books of Suanjing" also have shortcomings. It is unfair to underestimate the great significance of Liu Hui's circle-cutting technique when understanding pi.
The Ten Arithmetic Classics became the mathematics textbooks of various dynasties after the Tang Dynasty, and had a huge impact on the development of mathematics after the Tang Dynasty, especially creating conditions for the high development of mathematics in the Song and Yuan Dynasties. After the ten arithmetic classics, "Han Yan's Arithmetic" of the Tang Dynasty, "Nine Chapters of the Yellow Emperor's Algorithm and Fine Grass" by Jia Xian of the Song Dynasty, Yang Hui's "Nine Chapters of Arithmetic Compilation", Qin Jiushao's "Nine Chapters of the Book of Arithmetic", etc. The problems in the ten arithmetic classics were quoted, and new mathematical theories and methods were developed based on the ten arithmetic classics. Later generations spoke highly of Li Chunfeng's contribution to the compilation and annotation of ten mathematical classics. For example, the famous British scholar Dr. Joseph Needham said: "He is probably the greatest annotator of mathematical works in the entire history of China." Tang Dynasty In the second year of Emperor Wude's reign (619), Fu Renjun's "Wuyin Yuanli" was promulgated. "Wuyin Yuanli" adopted Dingshuo for the first time, which was a major reform in the history of Chinese calendar. Before the "Wuyin Yuanli", the calendar used Pingshuo, that is, the average value of the sun and moon conjunction cycle was used to determine the synodic moon. "Wuyin Yuanli" first considers the slow movement of the moon, uses the real moment when the sun and the moon meet to determine the new moon, and then determines the new moon and the moon. It requires that "the moon is dark and cannot be seen in the east, and the new moon cannot be seen in the west."
Due to problems with some calculation methods of the Wuyin Yuan Calendar, one year after its promulgation, the eclipses of the sun and moon were frequently reported incorrectly. In the sixth year of Wude, Zu Xiaosun, a doctor in the Ministry of official affairs, "omitted those who were particularly sparse", and later corrected them by Cui Shanwei, the minister of Dali, and Wang Xiaotong, a doctor of calendar calculation. In the early years of Zhenguan, Li Chunfeng wrote about eight things in the "Wuyin Yuanli". Emperor Taizong of the Tang Dynasty ordered Cui Shanwei to evaluate the gains and losses of the two families, and Li Chunfeng's seven opinions were adopted. Li Chunfeng made contributions to improving the "Wuyin Yuanli" and was awarded the title of General Shilang. In the 14th year of Zhenguan (640), Li Chunfeng said that the "Wuyin Yuanli" method "reduced a little too much" and the time of conjunction and lunar New Year was earlier than the actual time. He suggested that it should be corrected, and this opinion was adopted. In the 18th year of Zhenguan, Li Chunfeng also pointed out: "Wuyin Yuanli" stipulates that there are three big months and three small months. However, according to Fu Renjun's calculation, after September of the 19th year of Zhenguan, there will be four consecutive big months. This is considered to be the number of big months in the calendar. Undue phenomenon. So Emperor Taizong of the Tang Dynasty had to issue an edict to restore Pingshuo. After switching to Pingshuo, "Wuyin Yuanli" has more problems, and reform is imperative.
Li Chunfeng compiled a new calendar in the second year of Linde (665) based on his many years of research and long-term observations on astronomical calendars. Recommended by Si Li Nangong Ziming, Taishi Ling Xue Yi, and Guozi Jijiu Kong Yingda, Emperor Gaozong of the Tang Dynasty issued an edict to promulgate it and named it "Linder Li". The main contributions of "Linder Calendar" are twofold:
First, for the first time in the history of the Chinese calendar, the law of Zhang and Li eras was abolished, and the "General Law" 1340 was established as a method for calculating various cycles (such as tropical years, synodic moons, etc.) , Peripheral month, etc.) The common *** denominator of the odd zero part. The "day" of the ancient Chinese calendar begins at midnight, the "month" begins with the new moon, and the "year" begins with the winter solstice. The ancient calendar called the cycle in which the winter solstice and the conjunction of the new moon fall on the same day as "Zhang", and the cycle in which the conjunction of the winter solstice and the winter solstice fell on the same day in the middle of the night was called "蔀". The ancient calendar uses ten "Heavenly Stems" and twelve "Earthly Branches" to record the years and days. If the Winter Solstice and the New Year's Day fall at midnight on the same day, and the calendar stems and branches are restored, then this cycle is called "Ji" ; If even the stems and branches of the year are restored, this cycle is called "Yuan". These cycles were calculated in ancient calendar making, but these cycles were not necessary for calendar calculation. Instead, they became a burden to the calendar. Li Chunfeng resolutely abolished them. Various calendars before the "Linder Calendar" used fractions with different denominators to represent the odd zero parts below the integers of various cycles. These cycles, such as period (tropical year), lunation (synodic month), lunar period (periconon month), synodic period (nodal month), etc., are all important data that must be measured and calculated in advance for calendar calculations. Because these periods are uneven, the calculation is very cumbersome, and it is inconvenient to compare various data. Li Chunfeng established a "general method" of 1340 as the common denominator of the odd-zero parts of various periods. In this way, numerical calculations are much faster than before. The calendar is much simpler. "Chou Ren Zhuan" spoke highly of this: "Gai Huitong's theory is no different from the ancient times, and the operation is simple and simple, which is the best. The masters follow it, and it is followed by the Song and Yuan Dynasties, and the three unifications and four divisions are divided into three parts." Since then, the laws of the Zhang and Li era have been abolished. The cleverness of his legislation is better than that of Daduan, one of the ancients."
Secondly, Dingshuo was adopted again. Although the "Wuyin Yuanli" used Dingshuo for the first time, it fell back to using Pingshuo because the relevant calculation methods were not completely solved. In order to make the Dingshuo method tenable, "Linder Li" improved the method of calculating Dingshuo. In his early years, Li Chunfeng carefully studied Huangji Li by Liu Zhuo of the Sui Dynasty and wrote another volume of Huangji Li. Based on Zhang Zixin's observations of the daily movements of the sun and the moon in the Northern Qi Dynasty, Liu Zhuo created the "Zhaocai technique", which is the interpolation formula of the quadratic function, to calculate the degrees of the sun and the moon. Li Chunfeng summarized Liu Zhuo's interpolation formula and used it to calculate the correction number for the slow and slow movement of the moon and the waxing and waning of the daily movement, so as to calculate the correction number for the fixed lunar hour. In order to avoid the phenomenon of four consecutive big months on the calendar, he also created the method of "accommodating the new moon". The "Lindé Lijing" contained in Volume 26 of "New Book of Tang" says: "The day names of Dingshuo and Cishuo are bigger if they are the same, and smaller if they are different." The day name here refers to the "stem" in the stems and branches that record the day. It also stipulates: "If there is a cross on the first day and should be seen in the extra time, the size will be determined one or two months before and after the news, so that the loss will be in the dark and the second, and the string and hope will also follow the news." News means reduction and increase. According to this regulation, it can be achieved that "the first day of the new moon is extremely full, but the frequency is no more than three. If it is more than three times, it can be measured by observing the small remaining time near midnight." That is to say, the carry method of changing the fraction of less than one day in a month (i.e., the small remainder) is used to avoid the appearance of four consecutive big or small months on the calendar. However, it should be pointed out that this "Advanced New Year" method is an artificial accommodation method to avoid the appearance of four consecutive big months in the almanac, and is not a correct reflection of the movement patterns of the sun and the moon. According to modern calculation methods, it is possible that four big months will appear in a row if Dingshuo is used.
"Linder Li" made an important contribution to the completion of the reform of adopting Dingshuo in Chinese history. "Those who are precise in modern times are all using the pure style and Yixing method, which has lasted through the ages without any difference. Later generations will update it and set new standards, and nothing can exceed its precision." Although this statement is laudable, it can be seen from this that the Linde Calendar had a significant impact on later calendars. As one of the outstanding calendars of the Tang Dynasty, it was used for sixty-four years (665 to 728). "Lindokuli" was also spread eastward to Japan, and was adopted in the fifth year of Emperor Tenmu (667) and renamed "Yiholi".
The biggest shortcoming of "Linder Calendar" is that it does not consider precession. After Yu Xi of the Jin Dynasty discovered the precession of equinox, Zu Chongzhi first used it to make calendars, which greatly improved the accuracy of the calendar. Since then, Zhang Zhouxuan's "Daye Li" in the Sui Dynasty, Liu Zhuo's "Huangji Li", and Fu Renjun's "Wuyin Yuan Li" in the early Tang Dynasty all considered precession.
However, Li Chunfeng took advantage of the inherent contradiction in the four stars in the "Yao Canon" to deny the existence of precession at all. Together with the mathematician Wang Xiaotong, he criticized the "Wuyin Yuanli" for considering precession, which resulted in "the art of precession being no longer possible." Later, in 728, when Zhang Sui (and his party) compiled the Dayan Calendar, he reconsidered the precession of equinox. The armillary sphere is an important instrument in ancient times for observing the position and movement of celestial bodies. According to research, the "Pre-Qin Armillary Sphere" was made as late as 360 BC. Luo Xiahong and Geng Shouchang of the Western Han Dynasty and Jia Kui and Zhang Heng of the Eastern Han Dynasty all made armillary spheres. In the sixth year of Zhao Guangchu BC (323), Kong Ting made major reforms to the armillary sphere. The armillary sphere he created consisted of two rings, the Liuhe Yuan and the Siyou Yuan as Li Chunfeng called them. During the Northern Wei Dynasty, Chao Chong and Huo Lan used iron to cast an armillary sphere, and its structure was roughly the same as Kong Ting's. These armillary spheres are all equatorial devices. Only Jia Kui's zodiacal bronze sphere adds a zodiac ring to the equatorial device. In the early years of Zhenguan, Emperor Taizong of the Tang Dynasty "tested the seven rays and followed the equator. Now we have tested the winter solstice in the extreme south and the summer solstice in the extreme north, and the equator should be in the middle. There is no difference between north and south. How can we get the truth by measuring the seven rays?" In calculations, it is necessary to calculate the movement of the sun, moon and five stars according to the ecliptic degree, so that important data such as the time of the new moon and the length of the tropical year can be easily and accurately calculated. Therefore, based on summarizing historical experience and practical problems, he proposed to create an ecliptic observation system The armillary sphere in which the sun, moon and five stars move.
Tang Taizong adopted this suggestion and ordered the manufacture of the armillary sphere designed by Li Chunfeng. In the seventh year of Zhenguan (633), this ritual was made. According to the records in Volume 31 of "New Book of Tang", the armillary sphere is made of copper, and its basic structure is: "Three layers on the outside and inside, with the bottom according to the base, shaped like a cross, with a tree at the end of the foot to open the four tables." The cross shape of the armillary sphere " The "standard base" is a device for correcting the level of the instrument. It is made based on the "cross level" on the armillary sphere invented by Chao Chong and Hu Lan in the later Wei Dynasty. Using this device can improve the observation accuracy of the instrument. The outer part of the three layers of the Armillary Sphere is called the Six-in-one Sphere, which includes the celestial meridian, the golden and the Hunluo latitudes, and the golden regular rules, namely the meridian ring, the horizon ring, and the outer equatorial ring. The twenty-eight constellations, ten days, twelve celestial bodies, and three hundred and sixty longitudes and latitudes are listed above. Fifth degree; Nei Zhong calls it Siyouyi, "Xuanshu is the axis, connecting the Yuheng travel cylinder and running the rules. There is also a tree in the north of Xuanji, Beichen, and the axis of the earth is in the south, turning inside. The Yuheng is between Xuanshu. When traveling north and south, look up to observe the stars in the sky, and look down to see the dial of the instrument. "It can be seen that the four-wheel instrument includes a four-wheel ring that can rotate around the axis of the red pole and a watch tube (i.e., a jade scale). It can rotate east-west and north-south with its four-wheel circle, and can point to any position in the sky to determine the equatorial coordinates of stars. The basic structure of these two layers is already present in Kong Ting's armillary sphere. Li Chunfeng's major reform of the Armillary Sphere was that a new first level - the Three-Chen Yi was embedded between the external Liuhe Yi and the internal Siyou Yi. The Three-Chen Instrument has a "round diameter of eight feet, with the lunar calendar, the zodiac, the lunar calendar, the distance between the heavens and the constellations, and the paths of the seven rays. They are prepared here and transferred within the Liuhe". Shen Kuo of the Northern Song Dynasty said: "The so-called celestial being, the yellow equator belongs to Yan." It can be seen that there are ecliptic rings, inner equatorial rings, and white zodiac rings in the three-chen ritual, which are the lunar orbit rings. The three-star instrument can also rotate. It was added to realize the observation of "the movements of the seven rays" according to the ecliptic.
Li Chunfeng’s armillary sphere is still an equatorial device. In addition to measuring the extreme declination, the ascension degree (i.e., the right ascension difference), and the stars at midnight, it can also measure the ecliptic longitude difference and The longitude of the moon is different, but the measured ecliptic degree is inaccurate, so it can only partially solve the problem of observing the seven celestial bodies according to the ecliptic.
For the first time in Chinese history, Li Chunfeng divided the Armillary Sphere into three parts: Liuhe Sphere, Sanchen Sphere and Siyou Sphere. His influence was far-reaching. In the eleventh year of Kaiyuan of the Tang Dynasty (721), Yi Xing and Cao Liang Ling Zan, who led the army, made a zodiacal armillary sphere, which was also a three-layer system. Although one line said that Li Chunfeng's Armillary Sphere "is quite complex in usage, and its technique is very poor", as Shen Kuo pointed out, Liang Lingzhan and others "added new ideas because of Chunfeng's method"③. The "Huangyou Armillary Sphere" (1050) made by Zhou Cong, Su Yijian and Yu Yuan in the Northern Song Dynasty was basically designed and made according to Li Chunfeng. At the end of the Northern Song Dynasty, Su Song and Han Gonglian made an astronomical instrument (1096) that included three parts: an armillary sphere, an armillary image, and a time-telling device. The armillary sphere was roughly the same as Li Chunfeng's. Although Li Chunfeng's armillary sphere has its advantages, it is too complex. It has as many as eleven rings. It is very difficult to ensure that these rings are concentric, so center differences are inevitable. There are too many rings, and they often block each other's line of sight during observation, which is very difficult. inconvenient. After the Northern Song Dynasty, the armillary sphere gradually developed from complex to simple. "Book of Jin"
In the fifteenth year of Zhenguan (641), Li Chunfeng was ordered to "pre-write the Book of Jin and the History of the Five Dynasties". "The astronomy, laws and calendars, and the Five Elements Chronicles were all written by Chunfeng." also". "History of the Five Dynasties" is the history of the five dynasties of Liang, Chen, Zhou, Qi and Sui. Later, the "Ten Chronicles" were merged into the "Book of Sui", so "History of the Five Dynasties" is the "Chronicle" in the "Book of Sui". When Li Chunfeng wrote the Astronomical and Legal Chronicles, he made a relatively comprehensive collection and arrangement of the important achievements in astronomy, calendar and mathematics during the historical period from the Wei and Jin Dynasties to the Sui Dynasty.
"Sui Shu·Lu Li Zhi 1·Bishu" says: "Things are blurred, and if you control them with speed, you will not follow their original principles. Therefore, hidden feelings and subtle changes can be obtained. "Rate" is the most basic quantitative "relationship" studied by ancient Chinese arithmetic. It has extremely wide applications in arithmetic and is the basis of many theories and algorithms in Chinese arithmetic. Li Chunfeng recorded "rate" in the history of official revision for the first time and gave it a prominent position, which shows Li Chunfeng's profound understanding of the true meaning of the theory of calculation.
Li Chunfeng further elaborated on this as follows: "What I call leaders, there are nine streams: the first is square fields, which are used to control the boundaries of fields; the second is corn, which is used to control changes in exchange quality; the third is declining points, which is used to control taxes on the rich and the poor; The fourth is Shao Guang, to control the accumulation of power in a square circle; the fifth is Shang Gong, to control the progress of work and accumulation; the sixth is All Loss, to control the labor and expense of far and near; the seventh is Yingshu, to prevent hidden things from being seen; the eighth is Equation, to prevent mistakes. Mix the positive and negative; the ninth is called Pythagorean, to control the high, deep, wide and far. They are multiplied by the scattered ones, divided by the gathered ones, and brought together to connect them. Now that they are connected, the calculation is done.
There is also the following description in a section of "Sui Shu·Lu Li Zhi · Preparing Numbers": "The ancient nine numbers, the circumference ratio is three, the diameter ratio is one, and its technique is sparse. Since Liu Xin, Zhang Heng, Liu Disciples of Hui, Wang Fan and Pi Yanzong each set up new rules without reaching compromise. At the end of the Song Dynasty, Southern Xuzhou engaged in Shi Zuchong's new secret method, which used a circle diameter of 100 million as one foot and a circumference of three feet, one foot and four inches. One minute, five centimeters, two seconds, seven seconds, one minute, five centimeters, two seconds, six seconds, three feet, one foot, four inches, one minute, five centimeters, two seconds, six seconds. The positive number is between the two limits of the density, and the circle diameter is one hundred and thirteen. , circle three hundred and fifty-five. Approximate ratio, circle diameter seven, Tuesday twelve. "This is the earliest record of Zu Chong's pi in current Chinese history books. Expressed in modern mathematical language, Zu Chongzhi calculated: 3.1415926<π<3.1415927, the circumferential density is 355/113, and the approximate ratio is 22/7. Zu Chongzhi's pi is accurate to the seventh decimal place. His "density" is the best approximate fraction of pi with the numerator and denominator within 1,000. It took more than 1,100 years for Europeans to obtain this result. Zu Chongzhi's "Zhushu" has been lost for a long time. This glorious achievement of his has been included in the history books by Li Chunfeng and has been passed down to this day.
In "Book of Jin·Lu Li Zhi", Li Chunfeng described in detail the method of "Qianxiang Calendar" written by Liu Hong. Liu Hong actually measured the rate of lunar delay and created an interpolation formula for calculating the linear function of fixed moon and fixed moon. He measured the intersection angle of yellow and white to be more than five degrees, and measured the periapsis month to be 27.55336 days, which is similar to today's measured values. These values All are important achievements in ancient Chinese astronomy. Liu Hong's "Qianxiang Calendar" was a key stage in the calendar reform after the "Sifen Calendar". However, the "Song Book" written by Shen Yue of the Liang Dynasty, which was written before the "Book of Jin", was omitted out of prejudice. contains no mention of Liu Hong's scientific achievements. Li Chunfeng recorded Liu Hong's scientific achievements in detail in "Book of Jin·Lü Li Zhi".
In "Tianwenzhi", Li Chunfeng created a format that encompasses all aspects of ancient astronomy: explaining the importance of astronomy and the traditions of the past dynasties, and introducing theories about the structure of the heaven and earth. Research, astronomical instruments, stars and their measurements, various astronomical records, etc. When introducing the various theories of Yantian, briefly explain their theories, quote more of the original words rather than paraphrase, and write a brief introduction to the author and the names and opinions of those who argued with him, so that future generations can have a clear idea of ??the debate on the structure of heaven and earth at that time.
In the middle of the sixth century, Zhang Zixin of the Northern Qi Dynasty, after more than thirty years of astronomical observation, finally discovered the phenomenon of uneven apparent motion of the sun and the five stars. Li Chunfeng recorded this in "Book of Sui Dynasty" It is a major discovery of epoch-making significance in the history of Chinese astronomy. In "Book of Sui·Lü Li Zhi", Liu Zhuo's "Huangji Calendar" method of the Sui Dynasty is also recorded, including the interpolation formula of quadratic functions created by Liu Zhuo, and the "precession of the zodiac" first proposed by Liu Zhuo ” concept and fairly accurate ecliptic precession data. The "Huangji Calendar" method includes the Dingqi method, Dingshuo method and Lisheng method (that is, the difference between the gain and contraction of the daily movement) pioneered by Liu Zhuo, as well as the calculation of the position, duration and fraction of the eclipse of the sun and moon that were not found in previous calendars. Methods such as how much to eat, whether to eat when not to eat, and how to calculate the five stars are also more precise than the previous calendar. "Huangji Calendar" is an excellent calendar, "warlocks praised it for its excellence" and had a great influence on later calendars. However, it was not promulgated due to various obstacles. Through comparative research, Li Chunfeng found that the "Huangji Li" was actually the best calendar of the Sui Dynasty, and recorded it in detail in the "Lü Li Zhi", becoming the only calendar in the history of Chinese calendars that was officially recorded but not promulgated.
The "Book of Sui Dynasty" also records the structure and use of the armillary sphere made by the former Zhao Kongting. This is the first time in Chinese history that there is an exact record of the specific structure of the armillary sphere. The same volume also records the development of the armillary sphere, the armillary image, and the inscriptions from the Han and Wei dynasties to the Sui Dynasty, as well as Jiang Ji's discovery of atmospheric absorption and extinction and He Chengtian and Zhang Zhouxuan's discovery of the Mongolian gas difference. The astronomical records of "Jin Shu" and "Sui Shu" also "collected richly and recorded very detailed records" of eclipses, meteors, meteorites, guest stars (novas), comets and other celestial phenomena during that period. Therefore, they are known as "the treasure house of astronomical knowledge". "Yi Si Zhan", 10 volumes, is an important astrology work by Li Chunfeng. Astrology, as a unique cultural phenomenon, coexists with astronomy. It can be said that excellence and dross are mixed, science and superstition coexist. Many famous astronomers in ancient China were involved in astrology. Influenced by his father, Li Chunfeng "compiled elegantly and studied extensively at a young age." He believed that "political and religious omens correspond to human principles, and auspicious changes correspond to astronomy." Therefore, he had a special liking for astronomy and astrology. "Yi Si Zhan" was Li Chunfeng's "collection of his notes, grouping them together by category, and editing them." accomplished. In the book, Li Chunfeng "collected the essence and deleted the redundant and false", and comprehensively summarized the astrology theories of various schools before Zhenguan of the Tang Dynasty. After synthesis, he retained the more consistent astrology of each school, discarded the contradictory parts, and established a very The systematic astrology system had a great influence on astrology in the Tang Dynasty and after the Tang Dynasty.
However, Lu Xinyuan, a scholar in the Qing Dynasty, has another unique insight into "Yi Si Zhan": "The theory that disasters are caused by different predictions is not sufficient. However, "Yi" says that the sky looks down to see good and bad luck, and "Zhou" "Li" Baozhang uses the sun, moon, stars, five clouds and twelve winds to distinguish good and bad luck, good fortune and famine. Although Chunfeng is named after the method, the chapter on cultivating virtues often quotes scriptures as a way to correct mistakes and improve things. "Jie, the Si Tian chapter is deeply about the mistakes of the Sui family, and Chun Chun Yu accepts admonishment and is far away from the tyrants. It is the words of a Confucian scholar and is beyond the reach of later generations of magicians."
As an important cultural history classic, " In addition to astrological methods and fulfillment situations, Yisi Zhan also retains many scientific and historical materials. Such as the record of celestial phenomena, the description of celestial phenomena, the position of the solstices, the components and structure of the armillary sphere, the calculation of precession, etc. The first volume of "Yi Si Zhan" takes "Celestial Phenomenon" as the first one, listing eight schools of thought on the celestial phenomena and taking the single one as Huntian. In the section "Second Number of Heavens", the degrees of the celestial sphere, the positions of the ecliptic and the equator, the geographical latitude (the North Pole is out of the ground) and their corresponding calculation formulas are given. Li Chunfeng did not use precession in "Linder Calendar", which was lamented by later generations as "a wise man's mistake of thousands of considerations". However, Li Chunfeng clearly discussed the existence of precession in "Yi Si Zhan". For example, "Chunfeng Note: According to Wang Fan's discussion of the two solstices of winter and summer, the two equinoxes of spring and autumn are the intersections of the sun and the sun. According to Liu Hong and Qianxiang, the current situation is not the same! The ecliptic and the sun are intersected in the Sui Dynasty. According to the current Zheng (Zheng) concept In the third year of Jichou, the winter solstice is at Dou at 12 degrees, the summer solstice is at Jing at 15 degrees, the vernal equinox is at Kui at 7 degrees, and the autumnal equinox is at Zhen at 15 degrees. There is another one degree difference every sixty years. The day travels once, that is, the day is 1,340 degrees, the year is 365 degrees, and the 1,340 degrees are 328 degrees. Each year does not circle the sky for thirteen minutes. ”
Yisizhan was written before (about 645), and Linde Li was written after. Why Li Chunfeng denied the existence of precession in Linde Li is worthy of further exploration. question.
In "Yi Si Zhan", Li Chunfeng's description of strange celestial phenomena is very distinctive. If you guess based on the meaning of the words, today's people would regard flying stars and meteors as two terms of the same celestial phenomenon. Li Chunfeng clearly explained their differences. He wrote in the book: "The light with a wake is a meteor, and the light with no wake is a flying star. "The one that reaches the ground is a falling star." "Yi Si Zhan" also gives a clear distinction between comets: "The long stars are like brooms, and the comets are round like pink catkins, and comets are comets."
Although flying streams and comets are respectively meteors and comets, the difference in one word brings out the difference in form, which is of great reference value for understanding the direction of movement and physical state of comets.
In addition to astronomical divination, the meteorological divination and wind forecasting methods in "Yi Si Zhan" also record important meteorological phenomena. Li Chunfeng introduced two types of wind direction devices in more detail in "Yi Si Zhan". One is to "set up a five-foot-long pole on a high plain, with eight taels of chicken feathers as the feather cover, which is placed on the pole to wait for the wind." Another way is: "You can make a plate at the head of the pole, and make three legs of a wood crow on the plate. Two legs are connected up, and one leg is raised (ancient mythology says that there is a three-legged crow in the sun). The feathers are tied down and turned inward. When the wind comes, the crow Turn around, turn your head towards it, hold the flower in the crow's mouth, and occupy it with the flower twist." These two wind direction devices are similar to the "伧" recorded in the historical records of the Han Dynasty (a simple symbol made of silk strips or black feathers tied to a long pole. The wind instrument) is very similar to the "Xianfeng Tongwu" (a black-shaped copper wind instrument).
"Yi Si Zhan" also retains important calendar data. Scholars have used this to verify another calendar "Yi Si Yuan Li" and "Li Xiang Zhi" written by Li Chunfeng in his early years.
Li Chunfeng’s contribution to meteorology is also reflected in his observation and research of wind. In the early days of feudal society, wind observations were more detailed than in the past. It has developed from 4 directions of wind to 8 directions, hence the name of the Eight Winds. Li Chunfeng further identified 24 wind directions based on observation, research and summarizing previous experience. He also created an eight-level wind standard based on the changes and damage caused by the wind to trees, namely: "moving leaves, singing branches, shaking branches, falling leaves, breaking small branches, breaking large branches, breaking trees and flying sand and stones," Pull out the big trees and roots."
Li Chunfeng was the first person in the world to grade the wind. More than a thousand years later, in 1805, the Englishman Francis Beaufort (1774-1857) set the wind speed at 12 levels and 13 levels. It has been revised several times since then, and the wind level has been increased to 18 since 1946. The entire book has been lost, but a small amount can be found in Daozang books.