**John and I**
The common noun in the given sentence is "library" and the proper noun is "Springville".

**Library as a Common Noun**
A common noun is a general name given to a person, place, thing, or idea. In this sentence, "library" is a common noun because it refers to a general place where books and other resources are stored and made available for borrowing or reading. It does not refer to a specific or particular library.

**Springville as a Proper Noun**
A proper noun, on the other hand, is a specific name given to a particular person, place, or thing. In this sentence, "Springville" is a proper noun because it is the specific name of a place. It refers to a particular town or city named Springville.

**John and I as Personal Pronouns**
In the given sentence, "John and I" is not a noun, but rather a pronoun. Pronouns are words that are used to replace nouns in a sentence. "John and I" is a personal pronoun because it is used to replace the names of individuals (John and the speaker, in this case). It is used to indicate that both John and the speaker will be going to the library together.

In summary, the common noun in the sentence is "library" because it refers to a general place, and the proper noun is "Springville" because it is the specific name of a town or city. "John and I" is a personal pronoun used to replace the names of individuals.