he Greek [Greek: pempazein], to count by fives, and
a few kindred words which certainly do hint at a remote antiquity in which
the ancestors of the Greeks counted on their fingers, and so grouped their
units into fives. The Roman notation, the familiar I., II., III., IV.
(originally IIII.), V., VI., etc., with equal certainty suggests quinary
counting, but the Latin language contains no vestige of anything of the
kind, and the whole range of Latin literature is silent on this point,
though it contains numerous references to finger counting. It is quite
within the bounds of possibility that the prehistoric nations of Europe
possessed and used a quinary numeration. But of these races the modern
world knows nothing save the few scanty facts that can be gathered from the
stone implements which have now and then been brought to light. Their
languages have perished as utterly as have the races themselves, and
speculation concerning them is useless. Whatever their form of numeration
may have been, it has left no perceptible trace on the languages by which
they were succeeded. Even the languages of northern and central Europe
which were contemporary with the Greek and Latin of classical times have,
with the exception of the Celtic tongues of the extreme North-west, left
behind them but meagre traces for the modern student to work on. We presume
that the ancient Gauls and Goths, Huns and Scythians, and other barbarian
tribes had the same method of numeration that their descendants now have;
and it is a matter of certainty that the decimal scale was, at that time,
not used with the universality which now obtains; but wherever the decimal
was not used, the universal method was vigesimal; and that the quinary ever
had anything of a foothold in Europe is only to be guessed from its
presence to-day in almost all of the other corners of the world.

From the fact that the quinary is that one of the three natural scales with
the smallest base, it has been conjectured that all tribes possess, at some
time in their history, a quinary numeration, which at a later period merges
into either the decimal or the vigesimal, and thus disappears or forms with
one of the latter a mixed system.[323] In support of this theory it is
urged that extensive regions which now show nothing but decimal counting
were, beyond all reasonable doubt, quinary. It is well known, for example,
that the decimal system of the Malays has spread over almost the entire
Poly