The Compendious Book on Calculation by Completion and Balancing

The Compendious Book on Calculation by Completion and Balancing is a foundational mathematical text by al-Khwarizmi, written in the 9th century. It systematically introduces methods for solving algebraic problems, including step-by-step techniques for rewriting equations (completion) and balancing both sides to find unknowns. The book effectively formalizes algebra, making complex problem-solving more structured and accessible. Its principles laid the groundwork for modern algebra and algorithms, bridging arithmetic and advanced mathematics. Overall, it represents a significant step toward developing systematic methods for resolving equations and understanding mathematical relationships.