 In the later tradition, Plato is reported to have criticized Archytas’ solution for appealing to “constructions that use instruments and that are mechanical” (Plutarch, Table Talk VIII 2.1 [718e]; Marc. XIV 5–6). Plato argued that the value of geometry and of the rest of mathematics resided in their ability to turn the soul from the sensible to intelligible realm. The cube with which geometry deals is not a physical cube or even a drawing of a cube but rather an intelligible cube that fits the definition of the cube but is not a sense object. By employing physical instruments, which “required much common handicraft,” and in effect constructing machines to determine the two mean proportionals, Archytas was focusing not on the intelligible world but on the physical world and hence destroying the value of geometry. Plato’s quarrel with Archytas is a charming story, but it is hard to reconcile with Archytas’ actual solution, which, as we have seen, makes no appeal to any instruments or machines. The story of the quarrel, which is first reported in Plutarch in the first century AD, is also hard to reconcile with our earliest source for the story of the Delian problem, Eratosthenes. Eratosthenes had himself invented an instrument to determine mean proportionals, the mesolab (“mean-getter”), and he tells the story of the Delian problem precisely to emphasize that earlier solutions, including that of Archytas, were in the form of geometrical demonstrations, which could not be employed for practical purposes. He specifically labels Archytas’ solution as dysmêchana, “hardly mechanical.” Some scholars attempt to reconcile Plutarch’s and Eratosthenes’ versions by focusing on their different literary goals (Knorr 1986, 22; van der Waerden 1963, 161; Wolfer 1954, 12 ff.; Sachs 1917, 150); some suggest that the rotation of the semicircle and the triangle in Archytas’ solution, might be regarded as mechanical, since motion is involved (Knorr 1986, 22). It may be, however, that Plutarch’s story of a quarrel between Plato and Archytas over the use of mechanical devices in geometry is an invention of the later tradition (Riginos 1976, 146; Zhmud 1998, 217) and perhaps served as a sort of foundation myth for the science of mechanics, a myth which explained the separation of mechanics from philosophy as the result of a quarrel between two philosophers. In the Republic, Plato is critical of the solid geometry of his day, but his criticism makes no mention of the use of instruments. His criticism instead focuses on the failure of solid geometry to be developed into a coherent discipline alongside geometry and astronomy (528b-d). This neglect of solid geometry is ascribed to the failure of the Greek city-states to hold these difficult studies in honor, the lack of a director to organize the studies, and the arrogance of the current experts in the field, who would not submit to such a director. Since Archytas’ duplication of the cube shows him to be one of the leading solid geometers of the time, it is hard to avoid the conclusion that Plato regarded him as one of the arrogant experts, who focused on solving charming problems but failed to produce a coherent discipline of solid geometry. Since Archytas was a leading political figure in Tarentum, it is also possible that Plato was criticizing him for not making Tarentum a state which held solid geometry in esteem. 