The Hindu-Arabic Numerals c11.130

c11.130

Bernelinus⁴ states that the abacus is a well-polished board (or table), which is covered with blue sand and used by geometers in drawing geometrical figures. We have previously mentioned the fact that the Hindus also performed mathematical computations in the sand, although there is no evidence to show that they had any column abacus.⁵ For the purposes of computation, Bernelinus continues, the board is divided into thirty vertical columns, three of which are reserved for fractions. Beginning with the units columns, each set of three columns (*lineae* is the word which Bernelinus uses) is grouped together by a semicircular arc placed above them, while a smaller arc is placed over the units column and another joins the tens and hundreds columns. Thus arose the designation *arcus pictagore*¹ or sometimes simply *arcus*.² The operations of addition, subtraction, and multiplication upon this form of the abacus required little explanation, although they were rather extensively treated, especially the multiplication of different orders of numbers. But the operation of division was effected with some difficulty. For the explanation of the method of division by the use of the complementary difference,³ long the stumbling-block in the way of the medieval arithmetician, the reader is referred to works on the history of mathematics⁴ and to works relating particularly to the abacus.⁵