The subjoined proof is not given in the current text books, but is handed on by oral tradition.

The usual proof requires in general the assumption of an infinite series of operations (with the consequent limit theorems involved), as all the n given numbers tend to equality. Let us take an arithmetical example, and let us tabulate the sequences involved in the way suggested in my paper on “The Teaching of Limits and Convergence to Scholarship Candidates” in the May (1911) issue of the Mathematical Gazette.