P. HISTORY OF ' AATHEMATICAL - School of Mathematics

36 A HISTORY OF MATHEMATICAL NOTATIONS
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
vise 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 undue. The abstract fraction f 3 wrts
called deuna (=de uncia, i.e., as [1] less uncia [,%I). Each duodecimal
subdivision had its own name and symbol. This is shown in the following
table, taken from Friedleinll in which S stands for semis or "half"
of an as.
TABLE
-
89 .............. 1 1 1 ...........................
deunx ...........
;!:;:) ........
dodrans. .........
bes ..............
septunx. .........
sem18 ............
quincunx. ........
triena. ...........
quadrans. ........
....................
(de uncia 1 - &)
' (de sextans 1 -4)
~(decem unciae)
(de quadrans 1 - 4)
(duae assis sc. partes)
(septem uncise)
...................
(quinque unciae)
sextans. ......... 4 = or Z or : ....................
sescuncial+ ...... l = -Ij-LPL ....................
uncia. .......... "', ' 1 - or a
or on bronze abacus e
In place of straight lines - occur also curved ones -.
' OP. cil., Plate 2. No. 13; Bee also p. 35.
I