Mei tried to situate the new European knowledge properly within the historical framework of Chinese astronomy and mathematics. In his view, Chinese astronomical knowledge had advanced following the adoption of the new, more accurate Jesuit calendar following the reform initiated by Xu Guangqi in 1629. In his historical studies, Mei stressed that Chinese astronomy had improved from generation to generation, progressing from coarseness to accuracy. He gave precisely the same description for the development of Western astronomy. In other words, he believed that progress was a universal historical pattern. This was Mei's historical rationale for synthesizing Western and Chinese knowledge.

Errors in the astronomical texts, he argued, jeopardized the development of the discipline; he then developed an evidential method to analyse traditional Chinese mathematics and astronomy. His methods involved correcting and reconstructing texts while preserving questions that he had been unable to solve. Mei argued that all sorts of errors in the ancient mathematical and astronomical texts had seriously impaired their transmission regardless of whether they were the corruption of printing boards, or mistakes in coping with a text, or commentating on a text without a proper understanding. In reviving the Chinese mathematical and astronomical traditions, collecting and collating ancient texts was a crucial first step.

Mei Wending argued, moreover, that calendrical studies were at the core of the Confucian pursuit of 'gewu qiungli' (investigating things so as to fathom the principle thoroughly).The eternity of 'li' guaranteed the status of the ancient sages, a status profoundly important to the cultural identity of Confucian scholars. The innate capacity of the heart/mind was such that the ultimate 'li' could be attained through mathematical investigations of each ancient calendar. From this angle, Mei Wending suggested the possibility of integrating calendrical study into the newly emerging evidential scholarship and contended that the investigation of ancient calendars and ancient remains were of equal importance for understanding 'li'. In addition, he claimed that the new Western calendar was only a variant of the Chinese calendar, anticipated by the wisdom of the ancient sages. This emphasis on the great importance of astronomy led Mei to reject the claims of Confucian scholars such as Yang Guangxian who were satisfied with understanding the 'li' of astronomy without bothering with detailed calendrical calculations. According to Mei, without engaging in complicated calendrical computation, 'li' simply could not be attained.

You only know that I am versed in mathematics. But you do not know why I study mathematics. When I was young, the Chinese officials and the Westerners at the Board of Mathematics were on unfriendly terms with each other. They accused each other. It almost came to capital punishment. Yang Guangxian and Adam Schall von Bell measured the length of the sun's shadow in front of the Wu Men gate. Unfortunately among those leading ministers there was no one who understood the method. I realised that if I did not know it myself, I could not judge true from false. So I was eagerly determined to study mathematics.

'Fangcheng' is one of the 'jiushu' (Nine Subjects Concerning Number) emphasised in Confucian education in the pre-Qin period (before 211 B.C.). When he finished writing this book, Mei Wending wrote to one of his friends saying that "I am disgusted by those Western missionaries who exclude traditional Chinese mathematics, and therefore I wrote this book about which even Matteo Ricci could not possibly say a bad word". Indeed, Western missionaries who went to China in the 16th and 17th centuries did not mention simultaneous linear equations because the subject was then only in its infancy in the West. Mei Wending clearly wished to demonstrate the superiority of early Chinese mathematics over the methods Western scholars had brought to China, and at least in this case, the example of simultaneous linear equations was an excellent one to stress.

In his various works, Mei Wending compiled ancient mathematical material and studied a number of almost forgotten topics. For example, the gougu theorem (referred to in the West as the Pythagorean Theorem) was a well-known and important focus of ancient Chinese geometry, but since the time of Liu Hui and Zhao Shang, two brilliant mathematicians of the 3rd century, no proof of the gougu theorem had been given in any mathematical books. Mei Wending, however, proposed two proofs, along with other applications of the theorem in his 'Gougu juyu' (Illustration of the Right-Angled Triangles) (written before 1692).

Number and principle are united. [In this respect] China and the West do not differ. Therefore rites can be retrieved from Barbarians, administration can be enquired about from Tanzi. Refusing this learning just because it is Western would be a short-sighted attitude, and not the way to what is excellent. Furthermore, if we look for it in the past, we will probably find something similar.