Gu Guangguan devoted himself to the collation and research of ancient books during his medical practice. Write 22 volumes of Ancient Rhyme, Chronology of National Policy 1 Volume, Geography of Seven Kingdoms 14 Volume, and collate Huayang Guozhi, Wuyue Chunqiu, Lienv Biography and Wen Zi, all of which are attached. The books that need to be interpreted include Treatise on Febrile Diseases, Brief Notes on the Golden Chamber, Interpretation of Treatise on Febrile Diseases, Elements of Geometry, etc.
Fourteen years after Daoguang (1834), he assisted Qian Xizuo in collating Shoushan Pavilion Series and Zhihai, and assisted Qian Peiming in collating Xiaowan Juanlou Series and other famous works.
In the later period of Daoguang, he got rid of the influence of "Ganjia School" and turned from textual research on classical literature to natural science, especially interested in classical astronomy and mathematics. The Draft of the History of Qing Dynasty said that he "learned from the classics, biographies and histories of many schools of thought, and was good at astronomical calendar calculations. Because he was appointed, he could find out the reasons, but not all of them were singled out. When I repeat defects, I will search for them. " After the Opium War, western science and technology were gradually introduced to China, and he was able to accept advanced western scientific achievements and research methods and combine them with China's classical science. He believes that "the old law originated from the new law" and that "Chinese and Western laws can be mutually verified, but they cannot be abolished". He learned from the strengths of China and the West and achieved fruitful results, becoming a famous astronomical mathematician in the Qing Dynasty.
During this period, he corrected 27 mistakes in the block-printed Zhoupian and wrote a collating draft of Zhoupian. Zhouyi ·suan Jing is an astronomical work in Han Dynasty, which contains complex mathematical calculations and the application of Pythagorean theorem. After profound research, Gu Guangguang pointed out that the ancients used plan to represent round celestial bodies. The data indicating the perimeter in the book is only assumed for drawing on the plan, not measured data. The so-called "Arctic Xuan Ji" is just a metaphor for painting, not a real star. The theory of "covering the sky" reflected in the book is purely an idea made by the ancients to observe the celestial phenomena, and it is not to measure heaven and earth with this theory of flat circle. This conclusion of Gu Youguan is of great help to future generations to understand many contradictions and complicated materials in Zhou Bian Jing.
In the study of ancient astronomy, Gu Guanguang also compared the ancient calendar of China with Gregorian calendar and Hijri calendar, and explored a new numerical calculation method for calculating the error day of leap year in ancient calendar. He is the author of General Examination of Six Calendars, Interpretation of Hijri Calendar, Interpretation of Nine Calendars, Simplified Pedal Method of Jiazi Garden, Simplified Pedal Method of Guimao Garden and Simplified Pedal Method of Five Stars.
From the 26th year of Daoguang (1846) to the first year of Xianfeng (185 1), Gu mainly studied Chinese and western mathematics. I not only read through the mathematical works of contemporary scholars available at that time, but also carefully studied "all recent translations and western technologies", verified every book and every new mathematical method, and adopted its "Ming principle" to correct its "shortcomings". He is the author of several monographs, including abundant number Calculations Part I, abundant number Calculations Continuation, abundant number Calculations, Jiu Shu Wai Lu, Jiu Shu Gu Cun, etc. For example, when westerners seek a circle, they only know that half of the equilateral sides in the circle are sine, but they don't know that half of the equilateral sides are tangent. Therefore, Gu used the method of "six grids, three requirements and two transformations" in ancient mathematics to find the tangent of the circumscribed equilateral, which made up for the deficiency of the western method in finding the circle. He also thinks that Du Demei's method of finding the circle is not rigorous enough, and the solution is cumbersome and difficult to remember. Therefore, he combined the method of finding the circle by cutting the circle and connecting the proportions proposed by Dong Youcheng, a mathematician at the same time, with the method of finding the circle by Du Demei, so that the arcs and chords of a circle can be transformed into each other under certain conditions, and the number of arcs is the sum of chords.
From four to five years in Xianfeng (1854 ~ 1855), Gu Guang published a series of papers, analyzed the research results of contemporary mathematics in detail, and compared them with western methods, and put forward many supplementary opinions on finding a circle, series, logarithmic solution and making logarithmic table, which improved their research results and promoted the development of modern mathematics in China. For example, he thinks that Dai Xu and Mingda Xiang's "Fiona Fang Interchange Analytical Expression" not only affirms their achievements, but also points out that this method only "seeks the chord number of a straight line" and fails to clarify the "relationship between two lines". Li's "Finding Logarithm" uses the "sharp cone method" to deal with logarithm calculation. Although it is simpler than the western method, the calculation procedure is cumbersome, and it can only be made into tables, but it cannot be calculated directly. He proposed "using"
1855, Li translated the last nine volumes of Euclid's Elements of Geometry (the first six volumes were translated by Matteo Ricci and Xu Guangqi in the late Ming Dynasty), which was revised by Gu Xianguang. Li's translation of Re-learning is China's first mechanical translation. Shortly after the publication of 1858, most versions of this book were destroyed by the war. Before the second edition, Gu Guangguang and Zhang revised it again.
Gu Guangguang is one of the early mechanical authors in China. His Nine Numbers (published by Jiangnan Manufacturing Bureau 1874) has six articles about mathematics and four articles about mechanics. The titles of these four mechanical articles are: static gravity, dynamic gravity, liquid gravity and celestial gravity, that is, statics, dynamics, fluid mechanics and celestial mechanics. These articles introduced many topics and calculation methods of elementary mechanics, mixed with some basic concepts of mechanics, which was a valuable achievement of China at that time.
Gu Guangguang's other works include Shusheng Two Volumes, Jiushu Storing Ancient Nine Volumes, General Examination of Six Calendars, Simplified Method of Pushing Steps, Simplified Method of Pushing Steps in New Calendar, and Simplified Method of Five Stars. In mathematics, Gu Sightseeing is famous for his study of logarithms, and he has a volume called Logarithmic Face (1860).