The Nine Chapters on the Mathematical Art

1. Rule of Three for Proportional Problems

   A large class of practical problems is solved by arranging known quantities into a proportion and finding a fourth: multiply the two cross-related known values and divide by the third. This single procedure, applied across pricing, taxation, and material exchange, reduces diverse real-world situations to one computational template.

2. Fangcheng Elimination for Linear Systems

   Systems of multiple unknowns are solved by laying coefficients in columns on a counting board and systematically subtracting multiples of one column from another to eliminate entries, reducing the array until each unknown is isolated. The method also admits negative numbers as intermediate quantities, handled by explicit sign rules for addition and subtraction.

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