"The geometrical algebra of the Greeks has been in evidence all through our history from Pythagoras downwards, and no more need be said of it here except that its arithmetical application was no new thing to Diophantus. It is probable, for example, that the solution of the quadratic equation, discovered first by geometry, was applied for the purpose of finding numerical values for the unknown as early as Euclid, if not earlier still. In Heron the numerical solution of equations is well established, so that Diophantus was not the first to treat equations algebraically. What he did was to take a step forward towards an algebraic notation."
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Thomas Little Heath, A History of Greek Mathematics (1921) Vol. 2, From Aristarchus to Diophantus p. 448
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Diophantus
Diophantus of Alexandria (c. 201 - 285 AD) sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica (c. 250 AD), many of which are now lost. Diophantus was the first Greek mathematician who recognized fractions as numbers, thus allowed positive rational numbers for the coefficients and solutions.
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