Negative Größen bei Diophant? Teil II

Abstract.

In this second part of “Negative Größen bei Diophant?” we start, as announced, by giving 33 places where Diophantus uses negative quantities as intermediate results; they appear as differences a − b of positive rational numbers, the subtrahend b being bigger than the minuend a; they each represent the (negative) basis $(\pi\lambda\varepsilon\upsilon\rho\acute{\alpha})$ of a square number $(\tau\varepsilon\tau\rho\acute{\alpha}\gamma\omega\nu o \zeta)$, which is afterwards computed by the formula (a - b)² = a ² + b ² - 2ab. Finally, we report how the topic “Diophantus and the negative numbers” has been dealt with by translators and commentators from Maximus Planudes onwards.