This paper examines the debate in China over the shape of the earth during the seventeenth and eighteenth centuries. The main arguments are as follows. First, trust plays an important role in knowledge transmission. Second, partial communication between different woridviews is possible. In the case of the debate over the shape of the earth, partial communication was accomplished by the spread of Western astronomical instruments and calculating tools. Third, such alien concepts as the four elements and the experience of navigation did not serve as effective cultural resources to convince Chinese literati of the sphericity of the earth. Fourth, as a result, the legitimacy of the sphericity of the earth had to be reconstructed in an alien environment. The theory of the Chinese origins of Western learning was fabricated within such a context. Fifth, debate over factual knowledge bears social and cultural implications. Thus the debate over the sphericity of the earth involved not only how the phenomenon could be understood but also how the Chinese empire was to be positioned in the new cultural atlas. Finally, the sphericity of the earth eventually became a matter of common sense for the Chinese largely because of the political and cultural transformation of modern China.

The circulation of science across cultural boundaries involves the construction of various representations by the various actors, who each account for their involvement in the process. The historiography of the transmission of European science to China in the seventeenth and eighteenth centuries has long been dominated by one particular narrative: that of the Jesuit missionaries who were the main go-betweens for these two centuries. This fact has contributed to shaping Western images of China's history and science up to the present day.

To retrieve the multifaceted history of this transmission, more than one discourse needs to be taken into account. Even within the Society of Jesus, representations changed with the evolution of patronage of the mission, and the concomitant building up of state-sponsored science in Europe. Chinese sources yield different pictures, accounting for the reception of Western learning — rather than “European science” — in terms of integration rather than of conversion, and legitimizing it first by the Jesuits' status as scholars, then by the idea that Western learning was of Chinese origin. This shift corresponded to the imperial appropriation of this learning.

The “raison d'être” of this paper is my dissatisfaction with current portrayals of the place and the fate of the so-called rational sciences in Muslim societies. I approach this issue from the perspectives of West European visitors to the Ottoman and Safavid Empires during the sixteenth and seventeenth centuries. I show that these travelers encountered educated people capable of understanding and answering their visitors' scholarly questions in non-trivial ways. The travels and the ensuing encounters suggest that early modern Muslim societies and their institutions, their ways of producing knowledge, the types of their knowledge, and their material resources contributed important elements to various early modern West European approaches to gaining knowledge about nature, history, and politics.

During the later European Renaissance, some scholars began to write about the history of scientific disciplines. Some of the issues and problems they faced in constructing their narratives have had long-term effects on the history of science. One of these issues was how to relate scholars from the Islamic traditions of scientific scholarship to those of antiquity and of postclassical Europe. Recent historians of science have rejected a once-common Western opinion that the contribution of these Islamic scientists had lain mainly in their preservation of ancient texts that were then handed over to Western scholars, who mastered them and then moved beyond them as part of the scientific revolution. This article examines the first effort to write a history of mathematics, the Lives of the Mathematicians by Bernardino Baldi (1553–1617), to determine how he treated this issue in his work. Baldi's efforts are especially important here because he was also an early European scholar of Arabic.

An examination of the work shows that Baldi did not share the negative views held by later Europeans about these non-European scientists. However, despite his knowledge of Arabic he had no active contacts with ongoing mathematical scholarship in Arabic. As a consequence, his narrative does follow the chronology of those later Europeans who would limit consideration of these mathematicians to approximately the ninth to the fourteenth centuries. In Baldi's writings, then, we can see the later narrative shape used by Western historians of science until recent years, but not the subsidiary role accorded to non-European scholars.