A multiplicity of circumstances - including geographic and political isolation, and differences of social organization and customs - has led different groups of people to develop mathematical knowledge independently of each other. Yet history has shown us again and again that by some necessity these separate groups often encounter the same problems. The solutions they propose, however, are often different. This suggests a series of questions. First of all: what is the relationship between the solutions? Is one solution an alternative (...) to the other, and if so, how to account for their differences? Or, on the contrary, are the solutions complementary? Both of these configurations can be found in the history of mathematics: in the following article we will investigate two elementary examples of these phenomena and trace the historical circumstances under which different solutions have come into contact. (shrink)