Historical definitions of group

Refer history of groups for more about the history of the definition and concept of group, and funky definitions of group for a list of weird definitions of group.

Jordan
In a paper in 1869 titled Commentaire sur Galois, Jordan defines a group as follows:

In his book Traité des substitutions, Jordan defines a permutation (he calls it a substitution) and then goes on to define a group:

Cayley (1854)
Cayley attempted the first general definition of a group, in his paper On the theory of groups, as depending on the symbolic equation $$\theta^n = 1$$. This definition is not precisely the same as the modern definition, though it is equivalent. Cayley states:

This definition is today summarized as saying that a group is an associative quasigroup. It is equivalent to the modern definition of group.

Weber (1882)
Heinrich Weber gave this definition in a paper on quadratic forms.

Weber's definition is equivalent to the modern definition of finite group.