15377
[Commentary:
On this folio Harriot appears to be searchng for a formula for the sequence 1, 6, 20, 50, ...
of sums of square-pyramidal numbers (see Add MS 6782
f. ), or rather, for those numbers multiplied 24, that is, 24, 144, 480, ... .
Examples on the left hand side of the page test the polynomial (note that 8 + 4 + 10 + 2 = 24). This is evaluated for , giving 144 (as required) and for , giving 492 (too large).
Examples in the bottom left hand corner rearrange the same coefficients in different orders: (2, 10, 8, 4), (8, 10, 2, 4), (8, 2, 10, 4), etc.
In examples further to the right, the fifth-degree polynomial , represented by the coefficients 24, 50, 35, 10, 1, is evaluated for , giving 640, and for giving 2520. ]
Examples on the left hand side of the page test the polynomial (note that 8 + 4 + 10 + 2 = 24). This is evaluated for , giving 144 (as required) and for , giving 492 (too large).
Examples in the bottom left hand corner rearrange the same coefficients in different orders: (2, 10, 8, 4), (8, 10, 2, 4), (8, 2, 10, 4), etc.
In examples further to the right, the fifth-degree polynomial , represented by the coefficients 24, 50, 35, 10, 1, is evaluated for , giving 640, and for giving 2520. ]