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

INTRODUCTIO1N.

5

A comparison of the Greek with the Hebrew numerical letters will
suggest at once their common origin, and that the alphabets of both
languages are derived from the same source, or that one is derived
from the other. The fact of the correspondence of the order, the
powers, and the names of the letters of both alphabets, is an argument in favour of this opinion. But the difference in form of the
characters presents a difficulty, and it is uncertain whether the
Greeks derived their numeral system from the same source as their
alphabet. The system of the Greeks possesses an interest which
does not attach either to that of the Romans or of the Hebrews, both
from the improvements and extensions it received. A knowledge of
these is essential for every one who may wish to read and understand
the mathematical and astronomical writings of the Greeks.
The founders of the Roman name in Italy appear to have derived
their descent from a colony of Pelasgi, who transported their language
thither in its earliest and rudest form. For many ages, among a
people incessantly occupied with war and conquest, their dialect continued almost unchanged till after the Punic wars, and the structure
of the Latin language carries us back to a period anterior to any
distinct vestige of the Greek language. The names of numbers must
necessarily have been formed before any regular system of abbreviated
numerical notation could have existed. There are no ancient writings
extant which afford any satisfactory account of the origin of the
Roman numerical symbols. From the large existing remains of
Roman literature, besides monumental and other inscriptions, there is
ample evidence of their universal use wherever the Roman arms and
Roman language prevailed. Niebuhr informs us (vol. i. p. 134) that
"what we call the Roman numerals are Etruscan, and they frequently
occur on their monuments. They are remnants of a hieroglyphical
mode of writing, which was in use before the age of the alphabetical,
and like the numerals of the Aztecans, they represent certain objects
that were associated with particular numbers. They are indigenous,.
and belong to the time when the west was subsisting with all itsa
original peculiarities, before it received any influence from Asia."'
Notwithstanding this opinion of Niebuhr, that the Etruscan signs of'
numbers existed prior to the age of alphabetical writing, it must beconsidered doubtful, as little beyond conjecture can be attempted in
the absence of evidence with respect to their origin and primary
meaning. It is scarcely possible to discover what alterations in the;
signs took place after their adoption, or what additions or substitutions were made, except so far as they appear in the inscriptions on
ancient monuments. The Romans employed seven elementary charac —
ters, as the primary signs of number, whose values are successively
increased fivefold and twofold, beginning with unity. This was
probably suggested by the two hands and the five fingers on each,
hand; or, as it is expressed by Ovid, Fast. iii., 126,
"Seu quia tot digiti per quos numerare solemus."
These seven characters are I, V or A, X, L, 0, D or 10, M: denoting
respectively 1, 5, 10, 50, 100, 500, 1000. Other numbers are expressed
in different ways by means of these seven symbols. A symbol
repeated two or three, &c., times, denotes the double or treble of its
value, as III stands for 3, and XX for 20. The symbols I, X, 0
are in general found repeated not more than four times; but in