According to Napier, logarithms express ratios: formula_7 has the same ratio to formula_8, as formula_9 to formula_10 if the difference of their logarithms matches. Mathematically: formula_11. At first, base e was used (even though the number had not been named yet). Henry Briggs proposed to use 10 as a base for logarithms, such logarithms are very useful in astronomy.