Predecessors
The Babylonians sometime in 2000–1600 BC may have invented the quarter square multiplication algorithm to multiply two numbers using only addition, subtraction and a table of squares. However it could not be used for division without an additional table of reciprocals. Large tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of computers.
Michael Stifel published Arithmetica integra in Nuremberg in 1544, which contains a table of integers and powers of 2 that has been considered an early version of a logarithmic table.
In the 16th and early 17th centuries an algorithm called prosthaphaeresis was used to approximate multiplication and division. This used the trigonometric identity
or similar to convert the multiplications to additions and table lookups. However logarithms are more straightforward and require less work. It can be shown using complex numbers that this is basically the same technique.
Famous quotes containing the word predecessors:
“No philosopher understands his predecessors until he has re-thought their thought in his own contemporary terms.”
—Sir Peter Frederick Strawson (b. 1919)
“I recognize in [my readers] a specific form and individual property, which our predecessors called Pantagruelism, by means of which they never take anything the wrong way that they know to stem from good, honest and loyal hearts.”
—François Rabelais (1494–1553)
“Human development is a form of chronological unfairness, since late-comers are able to profit by the labors of their predecessors without paying the same price.”
—Alexander Herzen (1812–1870)