In this paper it is proposed that the techniques employed by Diophantus is his solutions of the equations with two unknowns can be explained by means of the theory of proportions. At the same time, a number of arguments are advanced against interpreting the same techniques through modern algebraic geometry. The interpretation by means of proportions was proposed for the first time by Maximus Planudes (ca. 1255–1305) in his commentary on problem II.8 of the Arithmetica. Finally, an appendix presents letters received by the author from R. Rashed, I. G. Bashmakova, J. Høyrup, D. Fowler and S. Unguru, in which these historians express their views on the proposed interpretation.