Answer:
The act of performing surgery may be called a surgical procedure, operation, or simply "surgery". In this context, the verb "operate" means to perform surgery. The adjective surgical means pertaining to surgery; e.g. surgical instruments or surgical nurse.
James Madison, the author of the paper "Federalist #51" call the US a "compound republic" to describe the complexity of the government system comprised of several parts that form a substance. The consequence of having a government system that is complex and divided is that the federals check on the states, and the states check on the federals. That is what he refers to as "double security". This generates more insecurity about how the rights of the people are handled, and the feeling that the power of the government is independent of them.
D. to inform. It's informing you that the library will be closed.
I'd say this means he wants forgiveness or reconciliation :)