I consider the Theorem of Pythagoras as understood by ancient Chinese mathematicians based on texts dated to the 3rd-century AD. I have attempted to reproduce the diagrams that are indicated by the text to have existed, but are no longer extant. Through an analysis of the Chinese 'Gou-gu Rule' and its use in the context of a mathematical problem, it can be seen that the diagram was an essential component of the communication and development of ancient Chinese mathematics. By comparison with the Greek proof as given by Euclid in his Elements, this study explores the different modes of mathematical reasoning employed by these two independent civilisations.