Open main menu

Page:Carroll - Notes by an Oxford Chiel.djvu/22

This page has been validated.
12
THE EVALUATION OF π.

(A.P.)S entered into the above process, in various forms.

The experiment was therefore tried of transforming (A.P.)S into a new scale of notation: it had hitherto been, through a long series of terms, entirely in the senary, in which scale it had furnished many beautiful expressions: it was now transferred into the denary.

Under this modification, the process of division was repeated, but with the old negative result: the attempt was therefore abandoned, though not without a hope that future mathematicians, by introducing a number of hitherto undetermined constants, raised to the second degree, might succeed in obtaining a positive result.


IV. Elimination of J.


It had long been perceived that the chief obstacle to the evaluation of π was the presence of J, and in an earlier age of mathematics J would probably have been referred to rectan-