The Book of Squares
The Book of Squares, ' is a book on algebra by Leonardo Fibonacci, published in 1225. It was dedicated to Frederick II, Holy Roman Emperor.
The Liber quadratorum has been passed down by a single XV century-manuscript, the so-called ms. E 75 Sup. of the Biblioteca Ambrosiana, ff. 19r-39v. During the XIX century, the work has been published for the first time in a printed edition by Baldassarre Boncompagni Ludovisi, prince of Piombino.
Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication, appears in it. The book anticipated the works of later mathematicians like Fermat and Euler. The book examines several topics in number theory, among them an inductive method for finding Pythagorean triples based on the sequence of odd integers, the fact that the sum of the first odd integers is, and the solution to the congruum problem.
