 According to Clavius’s commentary of 1589, this pointwise construction of the quadratrix was an improvement over that offered by Pappus, because it was more accurate: Since the pointwise construction allowed one to identify arbitrarily many points along the curve, one could trace the quadratrix with greater precision than if one had to consider the intersection of two moving lines. To support his case, Clavius relates his pointwise construction of the quadratrix with the pointwise construction of conics proposed by the “great geometer” Apollonius and claims that “unless someone wants to reject as useless and ungeometrical the whole doctrine of conic sections” proposed by Apollonius, “one is forced to accept our present description of the [quadratrix] as entirely geometrical” (cited in Bos 2001, 163). However, in his later Geometria practica (1604), Clavius tempers his assessment of both the quadratrix and the conics. He maintains that these more complicated curves could be constructed by pointwise methods that offered greater precision, but the curves thus generated were no longer presented as absolutely geometrical. Instead, they were presented as “more accurate,” “easier,” and geometrical “in a certain way” (Bos 2001, 164–5).