Chinese proof, step 04


Thus the (four) outer half-rectangles of width 3, length 4, and diagonal 5, together make two rectangles (of area 24); then (when this is subtracted from the square plate of area 49) the remainder is of area 25. This (process) is called 'piling up the rectangles' (chi chu).

From the Chou pai suan ching, quoted in Swetz and Kao, 1877.


Ralph H. Abraham, 26 April 1996.