Page:Indian mathematics, Kaye (1915).djvu/35

 (generally abbreviated to yā and kā) in one system suggests the possibility of a mixed origin. It is possible that the former is connected with Diophantus' definition of the unknown quantity, plēthos monádon aoriston, i.e., 'an undefined (or unlimited) number of units.' To pass from 'an unlimited number' to 'as many as' requires little imagination. Diophantus had only one symbol for the unknown and if the use of yāvat tāvat were of Diophantine origin the Indians would have had to look elsewhere for terms for the other unknowns. With reference to the origin of the use of colours for this purpose we may point out that the very early Chinese used calculating pieces of two colours to represent positive and negative numbers. As neither the Greeks nor the Indians used any sign for addition they had to introduce some expression to distinguish the absolute term from the variable terms. The Greeks used M° an abbreviation for monádes or 'units' while the Indians used rū for rūpa, a unit. The commoner abbreviations used by the Indians are as follows:— It is hardly appropriate to discuss Sanskrit mathematical terminology in detail here but it will not be out of place to mention a few other terms. To denote the fourth power varga varga is used but it occurs only once within our period. In more modern times varga ghana ghāta denoted the fifth power, varga ghana, the sixth and so on.