These two pages are from the *Zhoubi suanjing* (*Arithmetical Classic of the Gnomon and the Circular Paths of Heaven*), a Chinese book on astronomy and mathematics dated to approximately 100 BCE. These images are from a Ming dynasty copy printed in 1603. These diagrams were added to the original text at some point in an attempt to illustrate a dissection proof of the "Pythagorean Theorem," known by the Chinese as the *Gougu* theorem. A complete English translation and analysis of the *Zhoubi suanjing* is given by Christopher Cullen in his *Astronomy and Mathematics in Ancient China: the Zhou bi suan jing* (Cambridge University Press, 1995). See, in particular, Appendix 1.

On these pages, the diagram on the right is usually called the "hypotenuse diagram" and illustrates the proof of the *Gougu* (or Pythagorean) theorem in the 3-4-5 case. The diagram on the left shows how a square of side 3 fits into a square of side 5.

This diagram illustrates a square of side 4 fitting into a square of side 5.