division (divizhon)

[ I'll make division of my present with you: Hold, there is half my coffer. Shak ., T. N., iii. 4. Specifically- (a) [L. divisio (n-), tr. of Gr. διαίρεσις.] In logic, the enumeration and naming of the parts of a whole; also distinguished as logical division. Division is mainly distinguished from cla ification in that the latter is a modern word, and supposes minute observation of the facts, while the former, as an Aristo tel i an term, denotes a much ruder proceeding, based on ordinary knowledge, and undertaken at the outset of the study of the genus divided. One of the distinctive doctrines of the Ramist school of logicians was that all division should proceed by dichotomy. New-light Divinity, names given to the New England especially, the enumeration of the species of a genus. The theology of Edwards and others, in the earlier history of its development. - New Haven Divinity, a popular title for a phase of modified Calvin ism, deriving its name from the residence of its chief founder, N. W. Taylor (1786-1858) of Yale Theological Seminary in New Haven, Connecticut. divinization (div"i-ni-za's hon), n. [= F. di vin is at i on -ation.] The act of divinizing; deification: as, the divinization of pleasure. Also divinisation. [Rare.] IMG:content-2940.png:[blocks in formation] Division is a dividyng of that whiche is more commune into those whiche are le e commune. As a def in i cion therefore dooeth declare what a thing is, so the division sheweth how many thinges are conteined in the same. Sir T. Wilson , Rule of Reason (1551). Division is the parting or dividing of a word or thing that is more generall, unto other words or things le e gen Blundeville , Arte of Logicke (1599), ii. 3. (b) In her ., the separating of the field by lines in the direction of the bend, the bar, etc. (called division bendwise , erall. IMG:content-2941.png:[blocks in formation] 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. Now that the manager has monopolized the Opera- house, haven't we the signors and signoras calling here, sliding their smooth semibreves, and gargling glib divi- sions in their outlandish throats? Sheridan, The Critic, i. 1. tient, which, the divisor hich, multiplied by a given quantity, the divisor, gives another given quantity, the dividend. In elementary arithmetic division is often de- fined as, for example, "the partition of a greater sum me by a le er" ( Recorde , 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: IMG:content-2942.png:[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors] IMG:content-2943.png:[blocks in formation] The terms are still further divided, each into two parts; and, after division in the Michael mas and Lent terms, a student who can a ign 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 acc i- dents of fortune. - Centesimal division. See centesimal. - Complementary division, a method of division given by Boëthius. 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. 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 proce 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 le than the divisor. The following shows the succe ive stages of the division of 351 by 13: 2 19 19 19 19 351 (351 (2351(2 331 (2 351 (27 351 (27 13 13 13 133 133 133 1 1. The rule was derived from Arabian writers. --Short di- vision, a proce 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. IMG:content-2944.png:[blocks in formation] There was a division among the people. John vii. 43. Betwixt these two 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 pa age 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 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. (b) 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 so multiplied the Divisional bonds. See bond1 . divisionary (di-vizh'on-a-ri), a. [ division + 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 proce is continued until the dividends begin to repeat themselves. The succe ive 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 viding by means of a table of circulating decimals. - Divi- sion by factors, the proce of dividing succe ively 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 pol it , econ., the dividing up of a proce or an employment into particular parts, so that each person employed can devote himself wholly to one section of the proce . - 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 admi ible. - Division viol. See viol. - General of division. See general , n.- Golden divisiont, 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 expre ion; 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 divisionert (di-vizh'on-ér), n. One who divides. division-mark (di-vizh'on-märk), n. In mus i- 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, quintole, sextolet , etc. division-plate (di-vizh'on-plāt), n. 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's iv), a . [= F. divis if = Pr. di- viziu = Sp. Pg. It. divisivo , divisivus , divis us , pp. of dividere , divide: see divide .] 1. Forming or expre ing division or distribu- tion. Those numbers which the grammarians call distributive or divisive , tern i, quaterni, . The Century Dictionary and Cyclopedia: The Century dictionary divisor a remainder. - Cyclotomic divisor, a divisor of a cyclotomic function. - Divisor of a form, in arith., whole number which exactly divides some number of the given form. Intrinsic (opposed to extrinsic) divisor, a суclotomic divisor which at the same time divides the index of the congruence. - Method of divisors, a method for finding the commensurable roots of an equation by first rendering them integral and then searching for them among the factors of the absolute term. - Theory of divisors, that part of the theory of numbers which relates to the divisibility of numbers, embracing the greater part of the subject.