you can read it online at https://archive.org/stream/mothergooseinpro00baum#page/n5/mode/2up
The volume begins with an historical overview written by Baum himself, in which he notes that the first use of the name "Mother Goose" was by the great French author of fantasies, Charles Perrault -- the inventor of Sleeping Beauty, Little Red Riding Hood, Cinderella and Puss in Boots. Each tale begins with the nursery rhyme, and then a tale that illustrates the rhyme follows -- told in Baum's charming, natural fashion. Mother Goose in Prose is a delight for children of all ages. The book's last selection features a girl named Dorothy who can talk to animals — an anticipation of the Oz books.
Old king Cole seems to be a favorite of Parrish, who did all 3 of these variations on the story. The bottom one, the original painting, hangs in the St Regis Hotel, it's been appraised between 5 and 10 million dollars.
by the way, there was a companion volume:
Parrish also illustrated a couple other significantly famous books (that I've only just learned of)