The Square Pyramidal Number and other Figurate Numbers

The articles presented here they originated from my research, carried out in the eighties in the field of elementary number theory, which produced the second article, the most important, in which is proved the Archimedes theorem on the quadrature of the parabolic segment, without the aid of integral calculus, but using only the Square Pyramidal Number and criteria for convergence of numerical sequences. This proof has heuristic value, since there are no previous works that correlate the Parabola to the Square Pyramidal Number.