See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

DIVISION (from See also:

• LAT

Lat. dividere, to break up into parts, See also:

• SEPARATE

separate)  , a See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general See also:

• TERM

term for the See also:

• ACTION

action of breaking up a whole into parts . Thus, in See also:

• POLITICAL

political See also:

• ECONOMY

economy, the phrase " See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

division of labour " implies the See also:

• ASSIGNMENT, ASSIGNATION, ASSIGNEE

assignment to particular workmen of the various portions of a whole piece of See also:

• WORK

work; in See also:

• MATHEMATICS (Gr. /saBnµar1Kil, Sc. vOcvn or E7rlQTt'µn; from p iN.La, "learning" or "science ")

mathematics division•is the See also:

• PROCESS

process of finding how many times one number or quantity, the " divisor," is contained in another, the " See also:

• DIVIDEND (Lat. dividendum, a thing to be divided)

dividend " (see See also:

• ARITHMETIC (Gr. apeOµ7run7, sc. TEXVn, the art of counting, from (ipLBµos, number)

ARITHMETIC and See also:

• ALGEBRA (from the Arab. al-jebr wa'l-mugabala, transposition and removal [of terms of an equation], the name of a treatise by Mahommed ben Musa al-Khwarizmi)

ALGEBRA); in the musical terminology of the 17th and 8th 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 See also:

• QUICK

quick ones . The word is used also in See also:

• CONCRETE
• CONCRETE (Lat. concretes, participle of concrescere, to grow together)

concrete senses for the parts into which a thing is divided, e.g. a division of an See also:

• ARMY
• ARMY (from Fr. armee, Lat. armata)

army, an administrative or electoral division; similarly, a "division" is taken in a legislative See also:

• BODY

body when votes are recorded for and against a proposed measure . In See also:

• LOGIC (Xoy1K7, sc. rixvrt, the art of reasoning)

logic, division is a technical term for the process by which a genus is broken up into its See also:

• SPECIES

species . Thus the genus "See also:

• ANIMAL
• ANIMAL (Lat. animalis, from anima, breath, soul)

animal " may be divided, according to the See also:

• HABITAT (a French word derived from habiter, Lat. habitare, to dwell)

habitat of the various kinds, into animals which live on See also:

• LAND

land, those which live in See also:

• WATER

water, those which live in the See also:

• AIR (from an Indo-European root meaning " breathe," " blow ")
• AIR, or ASBEN

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 divisions . 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 See also:

• POSSESSION
• POSSESSION (Lat. possessio, possidere, to possess)

possession of the generic attributes, but differ in other respects; they are " See also:

• VARIATIONS
• VARIATIONS, CALCULUS
• VARIATIONS, CALCULUS OF

variations on the same theme " (See also:

• JOSEPH
• JOSEPH, COMTE DE (1785-1870)
• JOSEPH, FATHER (FRANCOIS LECLERC DU TREMBLAY) (1577-1638)

Joseph, Introduction to Logic, 1906); each one has the generic, and also certain See also:

• PECULIAR

peculiar, qualities (differentiae), which latter distinguish them from other species of the same genus . The process of division is thus the obverse of See also:

• CLASSIFICATION (Lat. classis, a class, probably from the root cal-, cla-, as in Gr. icaMce, clamor)

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 See also:

• ARGUMENT

argument both See also:

• PRACTICAL

practical and theoretical, accurate division is of See also:

• GREAT

great importance . It is governed by the following rules .

(1) Division must be exhaustive; all the members of the genus must find a See also:

• PLACE (through Fr. from Lat. platea, street; Gr. IrAar6s, wide)

place in one or other of the species; a See also:

• CAPTAIN (derived from Lat. ca put, head, through the Low Lat. capitanus)

captain who selects for his team skilful batsmen and bowlers only is guilty of an incomplete division of the whole See also:

• FUNCTION

function of a See also:

• CRICKET
• CRICKET (Gryllidae)

cricket team by omitting to provide himself with See also:

• GOOD, JOHN MASON (1764-1827)

good fielders . Rectilinear figures cannot be divided into triangles and quadrilaterals because there are rectilinear figures which have more than four sides . On the other See also:

• HAND
• HAND (a word common to Teutonic languages; cf. Ger. Hand, Goth. handus)
• HAND, FERDINAND GOTTHELF (1786-185r)

hand, triangles can bedivided into equilateral, isosceles and scalene, since no other See also:

• KIND (O. E. ge-cynde, from the same root as is seen in " kin," supra)

kind of triangle can exist . (2) Division must be exclusive, that is, each species must be See also:

• COMPLETE

complete in itself and not contain members of another species . No member of a genus must be included in more than one of the species . (3) In every division there must be but one principle (fundamentum divisions) . The members of a genus may differ from one another in many respects, e.g. books may be divided according to See also:

• EXTERNAL

external See also:

• FORM (Lat. forma)

form into See also:

• QUARTO

quarto, See also:

• OCTAVO

octavo, &c., or according to binding into See also:

• CALF
• CALF, THE GOLDEN

calf, See also:

• CLOTH

cloth, See also:

• PAPER
• PAPER (Fr. papier, from Lat. papyrus)

paper-backed and so on . They cannot, however, be divided logically into quarto, paper-backed, novels and remainders . When more than one principle is used in a division it is called " See also:

• CROSS

cross division." (4) Division must proceed gradually (" Divisio non facit saltum "), i.e. the genus must be resolved into the next highest (" proximate ") species . To go straight from a summum genus to very small species is of no scientific value . It is to be observed that logical division is concerned exclusively with universals or concepts; division is of genus and species, not of particulars . Two other kinds of division are recognized:—metaphysical division, the separation in thought of the various qualities possessed by an individual thing (a piece of See also:

• LEAD
• LEAD (pronounced iced)

lead has See also:

• WEIGHT

weight, See also:

• COLOUR (Lat. color, connected with celare, to hide, the root meaning, therefore, being that of a covering)

colour, &c.), and See also:

• PHYSICAL

physical division or See also:

• PARTITION

partition, the breaking up of. an See also:

• OBJECT

object into its parts (a See also:

• WATCH (in O. Eng. wcecce, a keeping guard or watching, from wacian, to guard, watch, wacan, to wake)

watch is thought of as being composed of See also:

• CASE
• CASE, JOHN (d. 1600)

case, See also:

• DIAL

dial, See also:

• WORKS

works, &c.) .

Logical division is closely allied with logical See also:

• DEFINITION (Lat. definitio, from de-finire, to set limits to, describe)

definition (q.v.) .