Breaking a ``viscous circle'': Unscrambling A.-C. Clairaut's iterative method of 1743 (Q1105572)

In 1743 Alexis-Claude Clairaut (1713-1765) applied an iterative method to calculate the ellipticity of an infinitesimally flattened, homogeneous ellipsoid of revolution in equilibrium, taken to represent the earth. Some readers could not understand the sense of Clairaut's calculation and they erroneously thought that Clairaut was going around in circles. The author discusses Clairaut's explanation of that calculation, published in 1760. A comparison of Clairaut's approach with the Newton-Raphson method is presented as well.