or Aristotle's Wheel, denotes a celebrated problem in mechanics, concerning the motion or rotation of a wheel about its axis, so called because Aristotle was the first who took notice of it.

The difficulty of it may be represented in the following manner. While the circle makes one revolution on its centre, advancing at the same time in a right line along a plane, it describes on that plane, a right line which is equal to its circumference. Now, if this circle carry with it another smaller circle, concentric with it, like the nave of a coach wheel; then this smaller circle or nave, will describe a line in the time of the revolution, which shall be equal to that of the large wheel or circumference itself, because its centre advances in a right line as fast as that of the wheel does, being in reality the same with it.

Aristotle attempted to solve this problem, but his solution can only be regarded as a good account of the difficulty.

It was next attempted by Galileo, who had recourse to an infinite number of infinitely small vacuities in the right line described by the two circles, and imagined that the little circle never applies its circumference to those vacuities; but in reality only applies it to a line equal to its own circumference, though it appears to have applied it to a much larger. This, however, is nothing to the purpose.

According to Tacquet, the little circle making its rotation more slowly than the great one, does, on that account, describe a line longer than its own circumference; yet without applying any point of its circumference to more than one point of its base. This is no more satisfactory than the former.

After the fruitless endeavours of many great men, M. Dortous de Meyran, a French gentleman, had the good fortune to hit upon a solution which, after being fully examined by a committee of the Academy of Sciences, was declared to be satisfactory. The following is his solution.

The wheel of a coach is only acted on, or drawn in a right line; its rotation or circular motion arises purely from the resistance of the ground. Now this resistance is equal to the force which draws the wheel in a right line, as it defeats that direction, and therefore the causes of the two motions are equal. The wheel therefore describes a right line on the ground equal to its circumference.

On the contrary, the nave is drawn in a right line by the same force as the wheel, but it only turns round because the wheel does so, and can only turn in the same time with it. Hence, its circular velocity is less than that of the wheel, in the ratio of the two circumferences, and therefore its circular motion is less than the rectilinear one. Since it must describe a right line equal to that of the wheel, it can only do it by partly sliding and partly revolving, the sliding part being more or less as the nave itself is smaller or greater.