What makes Montag think he can realistically memorize the Book of Ecclesiastes before handing his Bible over to be burned in Fahrenheit 451 by Ray Bradbury?

Montag attempts to memorize the Book of Ecclesiastes in the Bible because he has a copy of the Old and New Testament at home that he stole from a fire. He calls Faber, the retired professor who keeps track of books, and asks him how many copies of the Bible are left in their part of the country. Montag already knows Faber will say there are no copies left because Montag has seen the firehouse listings. Montag tries to memorize the Book of Ecclesiastes because he believes he has the only existing copy. At the end of the book, when he is hiding out with Granger, Montag finds out another man named Harris has memorized the Book of Ecclesiastes but that he, Montag, will become the book if anything happens to Harris.