The traditional branches of arithmetic are:
* Addition: Combining numbers to find their sum.
* Subtraction: Finding the difference between two numbers.
* Multiplication: Repeated addition of a number.
* Division: Splitting a number into equal parts.
It's possible that Carroll explored these concepts in a unique way through his writings, but he didn't formally define four specific branches. If you have a specific passage from his work in mind, I might be able to provide more context.