Page:A History Of Mathematical Notations Vol I (1928).djvu/56

numeration for the membranes of their Rolls, the numerals assuming a degraded form which in its later stages is practically unreadable. In Figure 15 the first three forms show the number 147 as it was written in the years 1421, 1436, and 1466; the fourth form shows the number 47 as it was written in 1583.

57. At the present time the Roman notation is still widely used in marking the faces of watches and clocks, in marking the dates of books on title-pages, in numbering chapters of books, and on other occasions calling for a double numeration in which confusion might arise from the use of the same set of numerals for both. Often the Roman numerals are employed for aesthetic reasons.

58. A striking feature in Roman arithmetic is the partiality for duodecimal fractions. Why duodecimals and not decimals? We can only guess at the answer. In everyday affairs the division of units into two, three, four, and six equal parts is the commonest, and duodecimal fractions give easier expressions for these parts. Nothing definite is known regarding the time and place or the manner of the origin of these fractions. Unlike the Greeks, the Romans dealt with concrete fractions. The Roman as, originally a copper coin weighing one pound, was divided into 12 unciae. The abstract fraction was called deuna (= de uncia, i.e., as [1] less uncia [1/1 2]). Each duodecimal subdivision had its own name and symbol. This is shown in the following table, taken from Friedlein, in which S stands for semis or "half" of an as.

as.. deunx. dextans (decunx) dodrans... bes.... septunx. semis... quincunx. triens.... quadrans... sextans .... sescuncia 1.. uncia.. 1 11 ... 2000/204/0 11 1 S S == or S:: S Sor Sor S: 11 1 TABLE 1 - or S ::. S or S. S or S1 or S. 1 . . or = == or = or 1 or :. = or Z or : 12=1-LELEL or or on bronze abacus In place of straight lines occur also curved ones. = or ::. Sor :: ¹ Op. cit., Plate 2, No. 13; see also p. 35. (de uncia 1-1) ((de sextans 1-1) (decem unciae) (de quadrans 1-4) (duae assis sc. partes) (septem unciae) (quinque unciae)