= Diophantus
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<Diophantus> studied algebraic problems seeking numerical solutions, preserved in the Arithmetica. Many of those problems ask for positive <rational numbers>; their scope therefore differs from the exclusively integer formulation often associated with modern <Diophantine equations>.<Diophantus of Alexandria: A Study in the History of Greek Algebra by Thomas Little Heath (1910)>[Translated Arithmetica and introductory account of its problem conventions]{ref}
Book II, Problem 8 asks for a square to be split into two squares. In modern notation, $16=(12/5)^2+(16/5)^2$ gives a concrete rational example. The problem connects algebraic manipulation with the search for <rational points> on a curve, through exact algebraic relations.<Diophantus of Alexandria: A Study in the History of Greek Algebra by Thomas Little Heath (1910)>[Arithmetica II.8]{ref}
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