Starting from the premise that mythology and legend preserve at least a nucleus of historical fact, Bachofen argued that women were dominant in many ancient societies. His work was based on a comprehensive survey of references in the ancient sources to Amazonian and other societies with matrilineal customs – societies in which descent and property rights are traced through the female line. Some support for his theory can be found in evidence such as that drawn from Herodotus, the Greek "historian" of the fifth century B. C. Nonetheless, this assumption that the first recorders of ancient myths have preserved facts is problematic. Ancient Greek descriptions of those societies were meant not so much to represent observed historical fact – real Amazonian 15 societies – but rather to offer "moral lessons" on the supposed outcome of women's rule in their own society. The Amazons were often characterized, for example, as the equivalents of giants and centaurs, enemies to be slain by Greek heroes; thus, their customs were presented not as those of a respectable society, but as the very antitheses of ordinary Greek practices.