1845).

DIVISION (from Lat. _dividere_, to break up into parts, separate), a
general term for the action of breaking up a whole into parts. Thus, in
political economy, the phrase "division of labour" implies the
assignment to particular workmen of the various portions of a whole
piece of work; in mathematics division is the process of finding how
many times one number or quantity, the "divisor," is contained in
another, the "dividend" (see ARITHMETIC and ALGEBRA); in the musical
terminology of the 17th and 18th centuries, the term was used for rapid
passages consisting of a few slow notes amplified into a florid passage,
i.e. into a larger number of quick ones. The word is used also in
concrete senses for the parts into which a thing is divided, e.g. a
division of an army, an administrative or electoral division; similarly,
a "division" is taken in a legislative body when votes are recorded for
and against a proposed measure.

In logic, division is a technical term for the process by which a
_genus_ is broken up into its _species_. Thus the genus "animal" may be
divided, according to the habitat of the various kinds, into animals
which live on land, those which live in water, those which live in the
air. Each of these may be subdivided according to whether their
constituent members do or do not possess certain other qualities. The
basis of each of these divisions is called the _fundamentum divisionis_.
It is clear that there can be no division in respect of those qualities
which make the genus what it is. The various species are all alike in
the possession of the generic attributes, but differ in other respects;
they are "variations on the same theme" (Joseph, _Introduction to
Logic_, 1906); each one has the generic, and also certain peculiar,
qualities (_differentiae_), which latter distinguish them from other
species of the same genus. The process of division is thus the obverse
of classification (q.v.); it proceeds from genus to species, whereas
classification begins with the particulars and rises through species to
genus. In the exact sciences, and indeed in all argument both practical
and theoretical, accurate division is of great importance. It is
governed by the following rules. (1) _Division must be exhaustive_; all
the members of the genus must find a place in one or other of the
species; a captain who selects for his team skilful batsmen and bowlers
only is guilty of an incomplete division of the whole