re not generally used in Germany until the beginning of the
fourteenth century; but in general the forms of the ciphers were not
permanently fixed there till after the year 1531. The Russians were
strangers to them, before Peter the Great had finished his travels in
the beginning of the last century.

The origin of these useful characters with the Indians and Arabians is
attributed to their great skill in the arts of astronomy and of
arithmetic, which required more convenient characters than alphabetic
letters for the expressing of numbers.

Before the introduction into Europe of these Arabic numerals, they used
alphabetical characters, or _Roman numerals_. The learned authors of the
Nouveau Traite Diplomatique, the most valuable work on everything
concerning the arts and progress of writing, have given some curious
notices on the origin of the Roman numerals. Originally men counted by
their fingers; thus, to mark the first four numbers they used an I,
which naturally represents them. To mark the fifth, they chose a V,
which is made out by bending inwards the three middle fingers, and
stretching out only the thumb and the little finger; and for the tenth
they used an X, which is a double V, one placed topsy-turvy under the
other. From this the progression of these numbers is always from one to
five, and from five to ten. The hundred was signified by the capital
letter of that word in Latin, C--centum. The other letters, D for 500,
and M for a 1000, were afterwards added. They subsequently abbreviated
their characters, by placing one of these figures before another; and
the figure of less value before a higher number, denotes that so much
may be deducted from a greater number; for instance, IV signifies five
less one, that is four; IX ten less one, that is nine; but these
abbreviations are not found amongst the ancient monuments.[77] These
numerical letters are still continued by us in the accounts of our
Exchequer.

That men counted originally by their fingers, is no improbable
supposition; it is still naturally practised by the people. In
semi-civilized states small stones have been used, and the etymologists
derive the words _calculate_ and _calculations_ from _calculus_, the
Latin term for a pebble-stone, and by which they denominated their
counters used for arithmetical computations.

Professor Ward, in a learned dissertation on this subject in the
Philosophical Transactions, concludes that it is easier to falsi