 Nonetheless, according to Viète, if a problem could not be solved by neusis, then questions of legitimacy remained. For instance, neither the spiral nor the quadratrix—curves used to square the circle by Archimedes and Pappus, respectively—could be constructed in the same obvious and “not difficult” way as the neusis. Viète appears to grant that the pointwise construction of the quadratrix, such as that presented by Clavius, was in fact more precise than other constructions of the curve, but, Viète claims, this greater precision does not legitimize its status as genuinely geometrical. Indeed, such precise descriptions relied on instruments and, thus, on the mechanical arts and, as such, were not geometrical. Moreover, Viète claimed that, in general, curves not constructed by the intersection of curves, such as the Archimedean spiral, were “not described in the way of true knowledge” (Bos 2001, 177). Therefore, just as the quadratrix, these curves were not legitimately geometrical, which left the problem of squaring the circle an open problem for Viète.