Okay, here is the translation following your instructions: Arithmetic and Practical Arithmetic

Author: Lao Hansheng
Publisher:
Publish Date: 2000-02-01
Features: To make this book somewhat unique, the author pays special attention to the following issues in the writing, targeting the difficulties:
1. Based on the developmental patterns of ancient calculating devices and algorithmic languages, the origin of the abacus is divided into several stages: germination (Han–Song), establishment (Song–Yuan), and popularization (Ming). The book strives to elucidate the gradual evolution process from counting rods to the abacus, and seeks evidence in literary works.
2. A systematic study is conducted on important works and prominent abacus scholars from the Han to the Qing dynasties. Special emphasis is placed on the establishment of Ming Dynasty abacus methods, with the maximum use of archaeological and cultural relics to enrich and explain related issues.
3. A systematic study is carried out on the state of traditional Chinese practical mathematics, and the era's mathematics is reevaluated from the perspectives of practicality, sociality, and economics. The view is proposed that Ming Dynasty mathematics represents the peak of ancient Chinese practical mathematics.
4. From the perspective of mathematical society, the socio-economic background of the era is examined to clarify the relationship between the failure of traditional Chinese mathematics to develop into modern mathematics in the Ming Dynasty and the unsuccessful transition from feudal society to capitalist society. The aim is to broaden the readers' horizons and provide them with new thinking space.