"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.