In late 2019, the present author identified a hitherto unnoticed manuscript of the Japanese version of the Jesuit Compendia of philosophy, theology and cosmology among the holdings of Herzog August Bibliothek in Wolfenbüttel, Germany. Unlike the single previously known manuscript witness it contains all three parts, allowing us for the first time to study the cosmological part in its initial Jesuit translation into Japanese. At the same time, we are now in a much more favorable position to elucidate the textual history of the Compendia by comparing the two manuscripts of the Japanese version and the single known manuscript of the underlying Latin version. This similarly applies to issues of authorship and the question of the European models behind the Compendia, for which the Wolfenbüttel manuscript offers us new insights to be discussed in this paper.

This paper presents the results of an investigation of Sufera no nukigaki (Selection on the sphere), a Japanese translation of the cosmological section of the so-called Jesuit Compendia. Although this translationʼs existence had long been suspected, no extant copy was known until a manuscript was discovered in 2019 at the Herzog August Bibliothek, Wolfenbüttel, Germany. In light of this discovery, this paper discusses (1) the general outline of the work, (2) the translation, (3) differences between De sphaera and Sufera no nukigaki, (4) revision from Sufera no nukigaki to Nigi ryakusetsu, (5) traces of later use.

The correspondence between Tang Shunzhi 唐順之 (1507–1560) and Gu Yingxiang 顧応祥 (1483–1565) in mid-sixteenth century China illuminates their contrasting views on mathematics. While Tang worked to retrieve the hidden “golden needle” of the Shoushi 授時 astronomical system (composed in 1280), Gu removed from Li Ye’s 李冶 (1192–1279) Ceyuan haijing 測円海鏡 (1248) the parts most pertinent to Tang’s endeavors. To address the stark contrast, this article examines their own correspondence and several related texts. I show that Tang and Gu held radically different views on the meaning of numbers and calculations, and indeed on the very purpose of learning mathematics. I also review the discovery of the “tianyuan 天元 procedure” in the eighteenth century, which determined how Gu was finally regarded by historians of Chinese mathematics.