 Notice that these constructions illustrate the sort of “single motion” constructions to which Descartes refers in his 26 March 1619 letter to Beeckman: His new compasses generate curves by the single motion of a designated arm of the compass, and thus, the curves generated in this manner meet the standard of geometrical intelligibility—the standard by which to distinguish geometrical from imaginary curves—that is alluded to in the brief outline of the “entirely new science” that Descartes envisions. That such motions are completed by instruments does not threaten the constructed curve’s geometrical status. (As we saw above, Viète had leveled this charge against the instrumental, pointwise constructions provided by Clavius.) And moreover, we already notice in the mathematical research of 1619 Descartes’ focus on the intelligibility of motions as a standard for identifying legitimately geometrical curves. This theme will reemerge in Book Two of La Géométrie.