 While consideration of Clavius’s construction of the quadratrix offers some reason to accept Descartes’ distinction between the different sorts of pointwise constructions, there remains the controversial claim that curves described by “generic” pointwise constructions are curves that can be constructed by continuous motion. This identification allows Descartes to establish Pappus curves as “geometric” curves, but he offers no proof of the identity, and thus, there is question of whether Descartes has in fact demonstrated that the Pappus curves are “geometric” by his own standards. (See Grosholz 1991 and Domski 2009 for alternative ways of addressing this tension.)