Elementary arithmetic, with brief notices of its history... by Robert Potts.

6

INTRODUCOTION.

inscriptions I is found repeated six times, as IIIIrIVIR, for sevir or
sextumvir. V and L are not found repeated. A symbol of less value
postfixed to one of greater value increases the greater by that value,
as VI means 5 increased by 1; and LX, 50 increased by 10; but if
prefixed, it diminishes the greater by that number, as IV stands for 5
diminished by 1; and XL, 50 diminished by 10. This mode of notation by deficit was peculiar to the iRomans, and is in accordance with
the forms of their numerical words. Instead of octodecim for 18,
their writers use duodeviginti, and undeviginti instead of novendecim.
The letter M, the initial of mille, denoting 1000; 2000, 3000, 4000,
&c., were denoted by IIM, IIM, IVYM, &c.; and by placing a line
over the symbols their value was increased a thousand times, thus:
1, L, C, MlV, &c., denote respectively 1000, 50,000, 100,000, 1,000,000, &c.
The latest improvement in the Roman notation was devised at a
late period for the expression of large numbers. The method of proceeding was perfectly analogical. Talking the symbol C for 100, and
ID for 500, by postfixing 0 once, twice, thrice, &c., to ID; the symbols
I00D I000, I0000, &c., were assumed to denote 5000, 50,000,
500,000, &c, respectively; and by prefixing C once, twice, thrice, &c.,
to IDO IO0, I000, &c., respectively, their values become doubled, and
the symbols CID, CIO, CCCI0001000, CCI0000, &c., denoted 1000,
10,000, 100,000, 1,000,000, &c.
The Roman numerals are incapable of any material improvement.
They could serve to register numbers, but could not afford the slightest
aid in performing numerical calculations. In fact, they never were
employed for that purpose. In the calculations which their accountants
(calculatores, rationarii) had occasion to make, they were obliged to
have recourse to a mechanical process, employing pebbles or counters.
A box (loculus) of pebbles (calculi), and a board (tabula) on which the
pebbles were placed in rows, formed their instruments of calculation.
(Hor. Lib. I. Sat. vi. 74.) The terms calculate, calculation, are closely
related to calculus, and in their primary meaning had reference to counting by means of pebbles. The board on which arithmetical operations
were performed was also called abacus, and was divided from the right
to the left by lines or grooves, on which the pebbles were placed to
denote units, tens, &c. The operations of the abacus were rendered
more commodious by substituting small beads strung on parallel
threads, and sometimes by pegs stuck along grooves. With such an
instrument, it is not difficult to perceive how addition and subtraction
might be performed with ease and expedition, but to perform multiplication and division must have been a work of tedious labour.
The Roman notation was employed throughout the extent of the
Empire for recording all accounts, whether fiscal or mercantile, and
continued in use in Europe after its dissolution. The Roman notation was sanctioned by the almost universal employment of the Latin
language in all subjects of literature and science, which for ages continued to be the language of the learned. It was employed in
England from the time the Romans held possession of the island, and
during the rule both of the Saxon and the Norman. The accounts in
the Domesday Book are registered in the Roman characters. The
dotation of the colleges of Oxford and Cambridge, and the annual
accounts, were all recorded in the Roman characters long after the
Indian notation had been introduced. It still continues to hold a