From the late Ming, Western science arrived step by step: Ricci at Zhaoqing, Euclid's Elements, and the Tongwen Guan school of 1862.

Late Ming to early Republic
1583 · OriginIn 1583 Matteo Ricci settled in Zhaoqing, Guangdong, showing scholar-officials Western science and world maps, which began the eastward transmission of Western learning.1607 · EvolutionXu Guangqi and Ricci published their translation of the first six books of Euclid's Elements, introducing Euclidean geometry to China.1862 · ImpactIn 1862 the Qing founded the Tongwen Guan in Beijing, bringing Western learning into state-run modern education.
Sources (3)
  1. Wikipedia: Matteo Ricci
  2. Britannica: Xu Guangqi
  3. MacTutor: Xu Guangqi

"Western learning" means the learning that came from the West, mainly mathematics, physics, chemistry and the other natural sciences, together with new fields of study. "Spreading east" means that it came in gradually from the west.

In 1583 (Wanli 11 of the Ming) Matteo Ricci settled in Zhaoqing, Guangdong, and showed scholar-officials Western science and world maps; the eastward transmission of Western learning began from this.

In 1607 (Wanli 35) Xu Guangqi and Ricci published their translation of the first six books of Euclid's Elements, and Euclidean geometry was introduced to China.

In 1862 (Tongzhi 1 of the Qing) the Tongwen Guan was founded in Beijing, and Western learning began to enter state-run modern education.

Western Learning is the class in the chapter on Education on the coming in of foreign learning. It covers how Western mathematics, the natural sciences and new fields of study entered China from the late Ming to the early Republic: Matteo Ricci settled at Zhaoqing in 1583, the first six books of Euclid's Elements were published in translation in 1607, and the Tongwen Guan was founded in Beijing in 1862.