an equal distance to the whole circle so that when the line BH comes to K, the circumference ZΓ will be ZΛ, and the whole circle will be unrolled. In the same way, when I move the large circle, fitting the small one to it, their centre being the same, AB will be perpendicular and at right angles simultaneously with AΓ, the latter to ZI, the former to HΘ. So that, when the one will have completed a line equal to HΘ, and the other to ZI, and ZA becomes again perpendicular to ZΛ, and HA to HK, so that they will be as in the beginning at Θ and I. The problem is then stated: Now since there is no stopping of the greater for the smaller so that it [the greater] remains for an interval of time at the same point, and since the smaller does not leap over any point, it is strange that the greater traverses a path equal to that of the smaller, and again that the smaller traverses a path equal to that of the larger. Furthermore, it is remarkable that, though in each case there is only one movement, the center that is moved in one case rolls a great distance and in the other a smaller distance. In the Scientific Revolution The mathematician Gerolamo Cardano discusses the problem of the wheel in his 1570 Opus novum de proportionibus numerorum, taking issue with the presumption of its analysis in terms of motion. Mersenne further discussed it in his 1623 Quaestiones Celeberrimae in Genesim, where he suggests that the problem can be analysed by a process of expansion and contraction of the two circles. But Mersenne remained unsatisfied with his understanding, writing:Indeed I have never been able to discover, and I do not think any one else has been able to discover whether the smaller circle touches the same point twice, or proceeds by leaps and sliding. In his Two New Sciences, Galileo uses the wheel problem to argue for a certain kind of atomism. He begins his analysis by considering a pair of concentric hexagons, as opposed to circles. Imagining this hexagon "rolling" on a surface, Galileo notices that the inner hexagon "jumps" a little space with each roll of the outer onto a new face. He then imagines what would happen to the limit as the number of faces on a polygon