division 
baninse, etc.), also for the purpose of impaling two shields 
together, or in quartering, (c) The separation ol members 
in a legislative house in order to ascertain the vote. This 
is effected in the British House of Commons by the pass- 
ing of the affirmative and negative sides into separate lob- 
bies, to be counted by tellers ; in American legislatures, 
by their rising alternately, or, as is frequently done in the 
House of Representatives, by passing between tellers stand- 
ing in front of the Speaker's desk. In the British House 
of Commons the usual method of voting on any contested 
measure is by division ; in the United States, by ayes and 
noes, or affirmative and negative answers on a call of the 
roll. 
The motion passed without a division. Macaulay. 
2. In math. : (a) The operation inverse to mul- 
tiplication: the finding of a quantity, the quo- 
tient, which, multiplied by a given quantity, 
the divisor, gives another given quantity, the 
dividend. In elementary arithmetic division is often de- 
nned as, for example, "the partition of a greater summe 
by a lesser" (Records, 1540); but such a definition applies 
only when the quotient is an abstract number and an in- 
teger. Division is denoted by various signs. Thus, a di- 
vided by b may be written in any of the following ways : 
~r> alb, a-'.b. 
b 
ab 
Where multiplication is not commutative (that is, where 
xy is not generally equal to yx) there are two kinds of 
division ; for if xy = z, x may be regarded as the quotient 
uiviaiuu , lui 11 ;*</ , M> may uc legal ucvi as nio igwnBW 
of z divided by y, or y as the quotient of z divided by x. 
These two kinds of division are denoted as follows : 
Division is one of the fundamental operations in arithme- 
tic, common algebra, and quaternions ; but in other forms 
of algebra it generally gives an indeterminate quotient, 
and so loses its importance. (J) A rule or method 
for ascertaining the quotient of a divisor into 
a dividend : as, long division, (c) A section ; 
the separation of a geometrical figure into two 
parts. 3. The state of being divided; sepa- 
ration of parts : as, an army weakened by di- 
vision; divisions among Christians. 
Hate is of all things the mightiest divider ; nay, is di- 
vision itself. Milton, Divorce, ii. 21. 
4. That which divides or separates ; a dividing 
line, partition, or mark of separation ; any sign 
or cause of separation or distinction. 
I will put a division between my people and thy peo- 
ple. Ex. viii. 23. 
5. A part separated or distinguished in any 
way from the rest ; a minor part or aggregate ; 
a distinct portion : as, the divisions of an or- 
ange ; a division of mankind or of a country ; 
the divisions of a book or of a discourse. 
Express the heads of your divisions in as few and clear 
words as you can. Swift. 
Specifically (a) A definite part of an army or of a fleet, 
consisting of a certain number of brigades or of vessels 
under a single commander. 
For his divisions, as the times do brawl, 
Are in three heads ; one power against the French, 
And one against Glendower ; perforce, a third 
Must take up us. Shak., 2 Hen. IV., i. 3. 
(b) A part of a ship's company set apart for a certain ser- 
vice in action. Those who serve at the guns are classed as 
tbejirst, second, third, and/owr(A divisions; the powder di- 
vinon provide the guns with ammunition ; the master's 
division steer the ship and work the sails ; and the engi- 
neer's division manage the engines and the boilers, (c) 
A geographical military command, consisting of two or 
more departments. Thus, the Military Division of the 
Missouri consists of the department of Dakota, the de- 
partment of the Platte, the department of the Missouri, 
and the department of Texas. The United States is di- 
vided for military purposes at the present time (1889) into 
three divisions the divisions of the Atlantic, the Mis- 
souri, and the Pacific, (d) In nat. hist. : (1) In zoological 
classification, any group of species forming a part of a 
larger group : in entomology, sometimes specifically ap- 
plied to a group smaller than a suborder and larger than a 
family, as the division Oymnocerata of the Heteroptera. A 
section may be equivalent in value to a division, or a group 
subordinate to it ; a series is a division in which the minor 
groups show a regular gradation in structure. (2) In bo- 
tanical classification, one of the higher grades in the se- 
quence of groups, equivalent to mbkingdom or series, as the 
phtenogamous and cryptogamous divisions of plants. It 
is also often used as subordinate to class, as the polypet- 
alous, ape tul i n is. etc., divisions ot dicotyledonous plants. 
By some authors it has been used to designate a grade 
between tribe and order. 
6. The state of being divided in sentiment or 
interest; disunion; discord; variance; differ- 
ence. 
There was a division among the people. John vii. 43. 
Betwixt these two 
Division smoulders hidden. 
Tennyson, Princess, iii. 
Earth, these solid stars, this weight of body and limb, 
Are they not sign and symbol of thy division from Him ? 
Tennyson, The Higher Pantheism. 
7. In music, a rapid and florid melodic passage 
or phrase, usually intended to be sung at one 
breath to a single syllable : so called because 
originally conceived as the elaboration of a 
phrase of long tones by the division of each 
1708 
into several short ones. It was common in the 
music of the eighteenth century. 
Sweet as ditties highly penn'd, 
Sung by a fair queen in a summer's bower, 
With ravishing division, to her lute. 
Shak., 1 Hen. IV., iii. 1. 
Music, advance thee on thy golden wing, 
And dance division from sweet string to string. 
Middleton, Blurt, Master-Constable, i. 1. 
Now that the manager has monopolized the Opera- 
house, haven't we the signers and signoras calling here, 
sliding their smooth semibreves, and gargling glib divi- 
sions in their outlandish throats? 
Sheridan, The Critic, i. 1. 
8. The precise statement of the points at issue 
in any dispute. [Bare.] 
The devision is an openyng of thynges wherein we agree 
and rest upon, and wherein we stick and stand in travers, 
shewing what we have to saie in our owne behalfe. 
Sir T. Wilson, Rhetoric (1553). 
9. See the extracts. 
At the University of Cambridge, England, each of the 
three terms is divided into two parts. Division is the 
time when this partition is made. 
B. H. Hall, College Words. 
The terms are still further divided, each into two parts ; 
and, after division in the Michaelmas and Lent terms, a 
student who can assign a good plea for absence to the Col- 
lege authorities may go down and take holiday for the rest 
of the time. C. A. Bristed, English University, p. 87. 
Accidental division, a division of a subject according 
to its accidents : as, good things are, according to Aris- 
totle, either qualities of mind, qualities of body, or acci- 
dents of fortune. Centesimal division. See centesimal. 
Complementary division, a method of division given 
by Boethius. The smallest round number larger than the 
divisor is used, and also the complement of the divisor, or 
the remainder after subtracting it from the round number. 
The first figure of the quotient is set down, from the divi- 
dend is subtracted the product of this by the round num- 
ber, and to the remainder is added the product of the same 
figure of the quotient by the complement of the divisor. 
The sum is treated as a new dividend. Complex or com- 
pound division, the division of a complex or compound 
number either by a number of the same sort or by an ab- 
stract number, as the division of 3 days 13 hours 17 minutes 
by 1 day 18 hours 28 minutes 36 seconds, or by 7. Direct 
division, (a) Division not complementary. (6) A rule 
for dividing one number by another, so as to obtain the 
entire period of the circulating decimal of the quotient. 
Both dividend and divisor are multiplied by the same 
number so as to make the last significant figure of the di- 
visor 9. By striking off from the divisor so multiplied the 
9, together with any ciphers which may follow it, and in- 
creasing the truncated remnant by 1, a number is obtained 
called the current multiplier. The last figure of the mul- 
tiplied dividend is now struck off, multiplied by the cur- 
rent multiplier, and the product added to the truncated 
dividend. The sum is treated as a new dividend ; and this 
process is continued until the dividends begin to repeat 
themselves. The successive figures struck off from the divi- 
dend from last to first are now written down from left to 
right as a whole number, and subtracted from the circulat- 
ing part of the same figures repeated indefinitely into the 
decimal places. The remainder, after shifting the decimal 
point as many places to the left as there were zeros struck 
off from the divisor along with the 9, is the quotient sought. 
Division by circulating decimals, a method of di- 
viding by means of a table of circulating decimals. Divi- 
sion by factors, the process of dividing successively by 
factors of the divisor. Division by logarithms, a meth- 
od of dividing based on the fact that the logarithm of the 
quotient is the logarithm of the dividend diminished by 
the logarithm of the divisor. Division Of a ratio, the 
reduction of a proportion from a:b = c:d to b a:a = d 
- c:c. Division Of labor, in polit. econ., the dividing 
np of a process or an employment into particular parts, 
so that each person employed can devote himself wholly 
to one section of the process. Division Of the ques- 
tion, in a legislative body, the division of a complex propo- 
sition or motion into distinct propositions, in order that 
each may be considered and voted upon separately: a 
course resorted to, upon motion or demand, when any of 
the members favor parts but not the whole of the mea- 
sure. The presiding officer usually has the power of de- 
ciding whether such division is admissible. Division 
Viol. SeetiiW. General Of division. See general, n. 
Golden division!, arithmetical division not complemen- 
tary. Harmonic division of a line. See harmonic. 
Iron divisiont. Same as complementary division. 
Logical division, any division not a partition, being 
either a nominal, substantial, or accidental division. 
Long division, the common modern method of arith- 
metical division when the divisor is a number larger 
than 10. The greatest number of times that the divisor 
is contained in the first figures of the dividend, beginning 
with the left (a sufficient number being taken to make a 
number greater than the divisor), is set down to the right 
of the dividend, as the first figure of the quotient ; the di- 
visor is then multiplied by this quotient, and the product 
is subtracted from the left-hand part of the dividend ; to 
the remainder the next figure to the right in the dividend 
is then annexed, and the number thus formed is treated 
as a new dividend ; and so on. The same method is ex- 
tended in algebra to the division of polynomials in gen- 
eral. The rule is of Italian origin. See scratch division. 
- Nominal division, an enumeration of the different 
senses of an equivocal word or expression ; a distinction. 
Partible division, the mental division of a whole into 
its parts, as of the English nation into sovereign, lords, 
and commons ; partition. Real division, a division re- 
lating to facts, not a mere distinction between different 
meanings of a word, embracing substantial, partible, and 
accidental division ; the explication of a whole by its parts. 
Scratch division, the ordinary method of division be- 
fore long division came into general use, late in the seven- 
teenth century. The products were not set down at all, 
but only the remainders. The divisor was set down under 
the dividend ; the first figure of the quotient was then set 
divisor 
down and was multiplied by the first figure of the divisor, 
and the remainder was set down over the corresponding 
figures of the dividend, which were immediately canceled, 
together with the first figure of the divisor. This process 
having been repeated until the whole divisor had been 
canceled, the latter was written down again one place fur- 
ther to the left, the second figure of the quotient was set 
down, and the whole proceeding repeated until a remain- 
der was obtained less than the divisor. The following 
shows the successive stages of the division of 351 by 13 : 
The rule was derived from Arabian writers. Short di- 
vision, a process of division practised with a divisor not 
larger than 10. in which the quotient is set down directly, 
being written from left to right, usually below a line under 
the dividend without auxiliary figures. Substantial 
division, or division per se, the division of a genus into 
its species. To run divisiont, in music, to make florid 
variations on a theme. 
Running division on the panting air. 
B. Jonson, Poetaster, iv. 3. 
He could not run division with more art 
Upon his quaking instrument than she, 
The nightingale, did with her various notes 
Reply to. Ford, Lover's Melancholy, i. 1. 
She launches out into descriptions of christenings, runs 
divisions upon a head-dress. Addison, Lady Orators. 
= Syn. 1. Demarcation, apportionment, allotment, distri- 
bution. 5. Section, Portion, etc. (see part, n.), compart- 
ment, class, head, category, detachment. 6. Disagree- 
ment, breach, rupture, alienation. 
divisional (di-vizh'on-al), a. [< division + -al.~\ 
1. Pertaining to or serving for division; noting 
or making division : as, a divisional line. Also 
divisionary. 2. Belonging to a division, as of 
an army, or to a district constituting a division 
for any purpose ; having to do with a division : 
as, a divisional general (that is, a general of 
division in the French service); a divisional 
surgeon of police. 
Stem soldier as Davoust was, the correspondence shows 
him to have been on friendly, if not indeed affectionate, 
terms with his divisional generals. 
Edinburgh Rev., CLXIV. 202. 
Divisional bonds. See bondi. 
divisionary (di-vizh'on-a-ri), a. [< division + 
-aryi.] Same as divisional, 1. Imp. Diet. 
divisionert (di-vizh'on-er), n. One who divides. 
division-mark (di-vizh'on-mark), . In musi- 
cal notation, a horizontal curve inclosing a nu- 
meral which is placed over or under notes that 
are to be performed in a rhythm at variance 
with the general rhythm of the piece. The nu- 
meral indicates the desired rhythm. See trip- 
let, guintole, sextolet, etc. 
division-plate (di-vizh'on-plat), . In a gear- 
cutting lathe, a disk or wheel perforated with 
circular systems of holes, representing the divi- 
sions of a circumference into a certain number 
of parts. 
divisive (di-vi'siv), a. [= F. divisif = Pr. di- 
viziu = Sp. Pg. It. divisive, < L. as if *divisivus. 
< divisus, pp. of dividere, divide : see divide.] 
1. Forming or expressing division or distribu- 
tion. 
Those numbers which the grammarians call distributive 
or divisive, terni, quaterni, . . . &c. 
J. Mede, On Daniel, p. 12. 
2. Creating division or discord: as, divisive 
courses. 
In this discharge of the trust put upon us by God, we 
would not be looked upon as sowers of sedition, or broach- 
ers of national and divisive motions. 
Milton, Articles of Peace with the Irish. 
There is nothing so fundamentally divisive as superficial 
misunderstanding. Contemporary Rev., LI. 198. 
Divisive descent. See descent, 13. Divisive difference. 
Same as specijic difference (which see, under difference). 
Divisive members, the parts which come into view 
by the division of a whole. Divisive method, Galen's 
method of treating a subject by successive definitions and 
divisions : otherwise called the definitive method. 
divisively (di-vi'siv-li), adv. In a divisive man- 
ner ; by division. Hooker. 
divisiveness (di-vi'siv-nes), . The state or 
quality of being divisive ; tendency to split up 
or separate into units. 
So invincible is man's tendency to unite with all the in- 
vincible divisiveness he has. 
Carlyle, French Rev., III. iii. 1. 
divisor (di-vi'zpr), n. [= G. Dan. Sw. divisor, 
< F. diviseur = Sp. Pg. divisor = It. divisore, < 
L. divisor, a divider, distributor, < dividere, pp. 
divisus, divide: see divide.'] In arith.: (a) A 
number or quantity by which another number 
or quantity (the dividend) is divided. (6) A 
number which, multiplied by an integer quo- 
tient, gives another number of which it is said 
to be a divisor Common divisor, or common mea- 
sure, in math., a number or quantity that divides each 
of two or more numbers or quantities without leaving 
