 We see in these remarks that the precision and exactness of geometry is intimately tied with the geometer’s consideration of motions that can be precisely and exactly traced. Namely, the geometer is justified in using simple curves as well as more complex curves, so long as the construction of these curves proceeds by “precise and exact” motions. Descartes clarifies how a complex curve “can be conceived of as described by a continuous motion or by several successive motions, each motion being completely determined by those which precede” by presenting the mesolabe compass that he first developed in 1619: