The Collaborative International Dictionary
Algorism
Algorism \Al"go*rism\, Algorithm \Al"go*rithm\, n. [OE. algorism, algrim, augrim, OF. algorisme, F. algorithme (cf. Sp. algoritmo, OSp. alguarismo, LL. algorismus), fr. the Ar. alKhow[=a]rezm[=i] of Khow[=a]rezm, the modern Khiwa, surname of Abu Ja'far Mohammed ben Mus[=a], author of a work on arithmetic early in the 9th century, which was translated into Latin, such books bearing the name algorismus. The spelling with th is due to a supposed connection with Gr. ? number.]
The art of calculating by nine figures and zero; computation with Arabic figures.

the Arabic system of numeration.
Syn: decimal system
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
Wikipedia
Algorism
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 This positional notation system largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus.
Wiktionary
algorism
n. 1 (obsolete spelling of algorithm English) 2 Computing in, or using, Arabic numerals.
WordNet
algorism
n. the Arabic (or decimal) system of numeration
computation with Arabic figures
Usage examples of "algorism".
Ever since Solomon had shown him the basis of algorism, the methods of alKhwarizmi, he had been seeking problems to turn it on.
Fly, make lenses, invent algorism, make fire devices, alkuhl, aljabr, alkimiya, alqili.
His Almagest, and books both great and small, His astrolabe, belonging to his art, His algorism stones all laid apart On shelves that ranged beside his lone bed's head.
All I know is, I was showing them how to program some new algorisms for the computer when"