#### 6. Verbiest and the Mathematical Sciences

##### Geometry and Surveying

The direction of Jesuit mathematical publication in Chinese was set by Matteo Ricci. Six translations accomplished in collaboration with the Chinese scholars Xu Guangqi and Li Zhizao appeared between 1607 and 1614. All of them were based on Latin texts written or edited by the leading Jesuit mathematician Christoph Clavius, with whom Ricci had trained in Rome.

The first of these works to appear were an edition of Euclid and a work on the astrolabe, the one providing the rigorous basis for the problems in astronomy, timetelling and measurement of the other. For Ricci and his successors, skill in practical mathematics was vital in securing acceptance from Chinese scholars and officials. In particular, surveying and mapmaking - considered as both intellectually pleasurable and useful to the state - remained activities which excited Chinese admiration.

##### Mixed Mathematics

In Renaissance Europe, arithmetic and geometry were commonly considered the foundations of a much broader range of mathematical arts. These mixed mathematical disciplines were not purely theoretical but dealt with both practical problems and natural effects.

Machines, sundials and navigational instruments all fell within the responsibility of the mathematician. Not only did Verbiest direct the construction of the new instruments of the observatory but he was given the task of overseeing the casting of lightweight cannon for the Kangxi Emperor's military campaigns. Verbiest initially refused - but on religious grounds rather than as a matter outside his mathematical competence.

##### Astronomy

The telescope is often seen as the emblem of 17th-century astronomy. But it plays little part in Verbiest's presentation of the science. Its limited role is not due to Galileo's problems with the Church and the controversy over Copernicus's heliocentric doctrine. Rather, the early telescope was largely irrelevant to Verbiest's project.

He was concerned with the astronomy that mattered in China, and that meant the calendar and the prediction of events such as eclipses. He needed accurate observations and adequate mathematical models. His point of reference was therefore the great Danish observer Tycho Brahe rather than Galileo Galilei. In addition to his data, which were incorporated into the best available astronomical tables, Tycho also provided a wealth of instrument designs. These served as Verbiest's starting point for his own observatory instruments.