On Friction: Why No Perfect Circle Can Be Drawn
The compass point wears as it turns, so absolute geometric exactness is impossible.
Under the heading 'On friction', Leonardo argues that anything wholly consumed by long friction begins consuming itself at the very start of that motion. From this he concludes that no work of perfect exactness can be made: if the point of a compass wears away over a long stroke, then it must also wear in each part of the time, so that even the indivisible instant initiates some wear while tracing a circle. He notes that the opposite point of the compass, pivoting on the center, likewise gains wear at every degree of motion. A small circle diagram at the upper right accompanies the argument.
On this page
Wear begins in the first instant of motion
Leonardo reasons that whatever is entirely consumed by a long rubbing motion must consume a portion of itself at the very beginning of that motion. If the whole wears away over a whole span of time, then a part wears in a part of the time, and the indivisible instant initiates the consumption. The pivoting point of the compass on the center likewise gains wear at every degree of its turning.
The impossibility of a perfectly exact circle
The friction argument is used to deny that any figure of perfect exactness can be drawn: because the compass point tracing the circle is consumed as it moves, the traced circle cannot be truly perfect. A small circular figure sketched at the upper right of the page illustrates the compass and its traced circle. The point wearing away means each degree of rotation departs slightly from the ideal path.