In theory these successive approximations may be carried as far as we please, but in practice the labour of executing each approximation is so great that we are obliged to stop when the solution is so near the truth that the outstanding error is less than that of the best observations.
In actual practice, however, decimals only represent approximations, and the process has to be modified (§ 111).
When a first approximation has been obtained in this way, further approximations can be obtained in various ways.
Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.
The following table gives the values of this constant and several expressions involving it Useful fractional approximations are 22/7 and 355/113.