241121
[Commentary:
On the right hand side of the page are three partial difference tables from earlier pages;
the first and third tables are from page 10 (Add MS 6782
f. ) while the second is from page 11 (Add MS 6782
f. ). In each case, Harriot has also listed the first entries of the columns of the original difference table, denoted by , , , and .
On the left hand side are algebraic versions of the same partial difference tables. The first table gives formulae for successive second entries of the column beginning with , together with successive differences.
The second table gives formulae for successive third entries of the column beginning with , together with successive differences. The third table gives formulae for succesive th entries of the column beginning with .
The final table shows the th-entry formulae multiplied out, with differences calculated between them. This demonstrates that the constant difference, in a table constructed from every th entry of the original table, is . ]
On the left hand side are algebraic versions of the same partial difference tables. The first table gives formulae for successive second entries of the column beginning with , together with successive differences.
The second table gives formulae for successive third entries of the column beginning with , together with successive differences. The third table gives formulae for succesive th entries of the column beginning with .
The final table shows the th-entry formulae multiplied out, with differences calculated between them. This demonstrates that the constant difference, in a table constructed from every th entry of the original table, is . ]
hoc
[Translation: that ]
[Translation: that ]
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