Mathematical table

Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation.

Tables of common logarithms were used until the invention of computers and electronic calculators to do rapid multiplications, divisions, and exponentiations, including the extraction of nth roots.

Early digital computers were developed during World War II in part to produce specialized mathematical tables for aiming artillery.

For tables with greater precision (more digits per value), higher order interpolation may be needed to get full accuracy.

[3] In the era before electronic computers, interpolating table data in this manner was the only practical way to get high accuracy values of mathematical functions needed for applications such as navigation, astronomy and surveying.

To understand the importance of accuracy in applications like navigation note that at sea level one minute of arc along the Earth's equator or a meridian (indeed, any great circle) equals one nautical mile (approximately 1.852 km or 1.151 mi).

Prior to Napier's invention, there had been other techniques of similar scopes, such as the use of tables of progressions, extensively developed by Jost Bürgi around 1600.

[9][10] The computational advance available via common logarithms, the converse of powered numbers or exponential notation, was such that it made calculations by hand much quicker.