Equivocation can have a few different ways in which it is formulated, but, Enotes' general definition of equivocation is:
Equivocation is classified as both a formal and informal fallacy. It is the misleading use of a term with more than one meaning or sense (by glossing over which meaning is intended at a particular time).
Enotes also provides some great examples of the different types of equivocation: puns; fallacious reasoning; semantic shift; metaphors; etc. Please use the link below for more on equivocation and examples of these and the other types listed on that page.
When you mentioned equivocation in Act III, my mind immediately went to Macbeth's scene i soliloquy. He has already murdered Duncan, and while that act was performed after much agonizing and soul-searching, this soliloquy (which begins, "To be thus is nothing/But to be safely thus.") is one in which Macbeth is beginning to develop an easy rationalization for his murderous ways. He is explaining to the audience why it is necessary for him to kill Banquo.
Before, in Act I, he admitted that there was no good reason to kill Duncan. He did so only to appease his "vaulting ambition." Here, in Act III, he uses a bit of equivocation to create an "argument" for the necessity of killing Banquo.
His equivocating goes like this:
- Macbeth has murdered to become King of Scotland.
- The witches prophesied that Banquo's issue would be kings of Scotland.
- Therefore, Macbeth has murdered Duncan, only to have Banquo's son follow him as king of Scotland.
Which, of course, doesn't necessarily follow. There could be many generations of kings between Macbeth and Banquo's future relations. Macbeth has assumed that the witches meant that Fleance (Banquo's son) would succeed Macbeth as king. This is fallcious (or faulty) reasoning.
Here are the lines of text that give this reasoning:
When first they put the name of king upon me,
. . .then prophet-like
They hail'd him father to a line of kings:
Upon my head they put a fruitless crown,
. . .No son of mine succeeding. If't be so,
For Banquo's issue. . .
. . .the gracious Duncan have I murder'd
. . .To make them kings, the seed of Banquo kings!
There are certainly more possible instances of equivocation in this Act. I hope that this answer and the links below will help you find them.