4to : Or quarto. A term used generally to describe the approximate size of a book, a book that is about 10" to 12" tall and roughly squarish in shape. The term is based on the size of paper traditionally used by book printers which has been folded and cut into 16 pages.

As New : "the book is in the same immaculate condition in which it was published. There can be no defects, no missing pages, no library stamps, etc., and the dust jacket (if it was issued with one) must be perfect without any tears." Condition definition from AB Bookman's Weekly.