When Graham Jagger, a tutor at The Open University with a particular interest in logarithms was sent the puzzle in January 2004, he used historical detective work to find the tables that Banneker probably used. The logarithms used above are to base 10; i.e. Briggsian, or common, logarithms. Briggs’s logarithm tables were more or less freely copied by later printers and formed the basis of all subsequent tables until the beginning of the nineteenth century.
The following tables, all derived from those of Briggs, may have been available in the new State of Maryland in 1788 and hence could have been used by Banneker in 1798, the year of the page in his journal:
Henry Briggs |
Arithmetica Logarithmica |
1624 |
London |
Logarithms of numbers from 1 to 20,000 and from 90,000 to 100,000 (to 14 figures). |
Henry Briggs |
Arithmetica Logarithmica |
1628 |
Gouda |
A second edition of the above published by Adrian Vlacq, who calculated the additional logarithms from 20,000 to 90,000 (to 10 figures), and the logarithms of sines, tangents and secants (to 10 figures). |
Henry Briggs |
Trigonometria Britannica |
1633 |
London |
Logarithms of sines and tangents (to 14 decimal places). |
John Newton |
Tabulæ Mathematicæ |
1654 |
London |
Logarithms of numbers and trigonometric functions taken from Briggs (to 6 decimals). |
William Oughtred |
Trigonometria |
1657 |
London |
Logarithms of numbers (to 7 decimals) and trigonometric functions (to 6 decimals) taken from Briggs. |