Anaphora is a rhetorical device in which words are repeated at the beginnings of neighboring clauses. It is used to create emphasis.
In the given excerpt from Lincoln's Second Inaugural Address, the word <em>with </em>is repeated at the beginning of each clause. Besides creating emphasis, this device is often used to appeal to the emotions of the audience in order to persuade and motivate them. This is present in the given case as well.
