XIV

Measuring and Writing

The art of measuring brings the world into subjection to man;
the art of writing prevents his knowledge from perishing along
with himself; together they make man--what nature has not made
him--all-powerful and eternal. It is the privilege and duty of
history to trace the course of national progress along these paths
also.

Italian Measures

Measurement necessarily presupposes the development of the several
ideas of units of time, of space, and of weight, and of a whole
consisting of equal parts, or in other words of number and of
a numeral system. The most obvious bases presented by nature for
this purpose are, in reference to time, the periodic returns of
the sun and moon, or the day and the month; in reference to space,
the length of the human foot, which is more easily applied in
measuring than the arm; in reference to gravity, the burden which
a man is able to poise (-librare-) on his hand while he holds
his arm stretched out, or the "weight" (-libra-). As a basis for
the notion of a whole made up of equal parts, nothing so readily
suggests itself as the hand with its five, or the hands with their
ten, fingers; upon this rests the decimal system. We have already
observed that these elements of all numeration and measuring
reach back not merely beyond the separation of the Greek and Latin
stocks, but even to the most remote primeval times. The antiquity
in particular of the measurement of time by the moon is demonstrated
by language;(1) even the mode of reckoning the days that elapse
between the several phases of the moon, not forward from the phase
on which it had entered last, but backward from that which was
next to be expected, is at least older than the separation of the
Greeks and Latins.

Decimal System

The most definite evidence of the antiquity and original exclusive
use of the decimal system among the Indo-Germans is furnished by
the well-known agreement of all Indo-Germanic languages in respect
to the numerals as far as a hundred inclusive.(2) In the case of
Italy the decimal system pervaded all the earliest arrangements: it
may be sufficient to recall the number ten so usual in the case of
witnesses, securities, envoys, and magistrates, the legal equivalence
of one ox and ten sheep, the partition of the canton into ten curies
and the pervading application generally of the decurial system, the
-limitatio-, the tenth in offerings and in agriculture,