algorism

Calculating-Table by Gregor Reisch: Margarita Philosophica, 1508

Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This system largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude and in some cases required a device such as an abacus.

Starting with the integer arithmetic developed in India using base 10 notation, Arabian mathematicians documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point.

The word algorism comes from the name al-Khwarizmi ("the one from Khwarizm") of an early 9th century Persian mathematician, possibly from what is now Khiva in western Uzbekistan. In English, it was first used about 1230 and then by Chaucer in 1391^[1]. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus:

Haec algorismus ars praesens dicitur, in qua Talibus Indorum fruimar bis quinque figuris.

"Algorism is the art by which at present we use those Indian figures, which number two times five."

The word algorithm derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts.

See also

• Positional notation
• Hindu-Arabic numeral system
• History of the Hindu-Arabic numeral system

References

1. ^ Oxford English Dictionary (first quote c1230CE, Chaucer c1391, and later quotes showing continuing usage since then)