WORD FOR THE DAY: ALGEBRA

Your word for today is: algebra, n.

algebra, n.

[‘Surgical treatment of a fractured or dislocated bone. Also (as a count noun): a fracture or dislocation. Now hist. and rare.’]

Pronunciation: Brit. /ˈaldʒᵻbrə/,  U.S. /ˈældʒəbrə/

Forms: α.   ME– algebra,   lME algabra.  β.   15–16 algeber,   16 algebre.  γ.   15 algiebar. 

Etymology: <  post-classical Latin algebra algebraic computation (12th or 13th cent.), surgical treatment of fractures (c1300) <  Arabic al-jabr <  al the + jabr restoration (of anything which is missing, lost, out of place, or lacking), reunion of broken parts, (hence specifically) surgical treatment of fractures <  jabara to restore, to reunite, (hence specifically in a medical context) to set broken bones.

The Arabic term al-jabr probably originally referred specifically to the method of solving quadratic equations by completing the square (seeto complete the square at complete v. Additions). The term achieved currency through the title of the 9th-cent. mathematical treatise by al-Ḵwārizmī, al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wal-muqābala ‘The Concise Book on Calculation by Restoration and Compensation’. This work was partially translated into Latin by the British scholar Robert of Chester (fl. 12th cent.); shortly afterwards, the Italian scholar Gerard of Cremona (fl. late 12th cent.) made a second translation of it, De jebra et almucabola. For biographical information on al-Ḵwārizmī, see algorism n. The modern Arabic term denoting the branch of mathematics is ʿilm al-jabr.
Compare Middle French, French †algebre (now algèbre) (a1376 in an apparently isolated attestation, subsequently from 1554; 1546 in Rabelais as algebra, all denoting the branch of mathematics; 1611 in Cotgrave in an isolated attestation denoting the surgical treatment of fractures), Spanish algebra (a1450 denoting the surgical treatment of fractures, 1552 denoting the branch of mathematics), Portuguese álgebra (1519 denoting the branch of mathematics; 1712 in medical use), Italian algebra (1598 in Florio denoting the surgical treatment of fractures, 1606 denoting the branch of mathematics); also Middle Dutch, Dutch algebra (1460 in an isolated attestation denoting the surgical treatment of fractures, 1612 denoting the branch of mathematics), German Algebra (1460 in puech algebra un almalcobula lit. ‘book of algebra and almacabala’ as the title of a translation of al-Ḵwārizmī's mathematical treatise; 1489 as algobre, denoting the branch of mathematics). Compare almacabala n.
In β. forms probably after Middle French algebre; in the form algeber, the word was associated by early authors with Geber, the pseudonym of a 13th-cent. European alchemist (now called Pseudo-Geber) who wrote a number of treatises using the name of the 8th-cent. Arabic alchemist Jābir b. Ḥayyān (in Latinized form, Geber).
In γ. forms apparently after the ulterior Arabic etymon.
The position of the stress probably varied in early use (compare the French parallel, which shows penultimate stress). The current first-syllable stress, exemplified e.g. in quot. 1663 at sense 2a, is attested from at least c1600.

 1.  Surgical treatment of a fractured or dislocated bone. Also (as a count noun): a fracture or dislocation Now hist. and rare.

a1400  tr. Lanfranc Sci. Cirurgie (Ashm. 1396) 63 Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate til viij daies ben goon..þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be seid in þe chapitle of algebra.

?a1425  tr. Guy de Chauliac Grande Chirurgie (N.Y. Acad. Med.) f. 1, Separate is ioyned in consolding wondes & in reducyng algebras.

?c1425  tr. Guy de Chauliac Grande Chirurgie (Paris) f. 100, Algebra, þat is strecchinge oute or restorynge of broken bones and of bones out of ioynte.

?1541  R. Copland Formularie of Helpes of Woundes & Sores in Guy de Chauliac's Questyonary Cyrurgyens sig. Xiij, The helpes of Algebra & of dislocations.

 

1999  L. H. Feldman War against Epidemics Colonial Guatemala 22 The Royal Protomedicato, a board of licensed medical examiners,..was not established in Guatemala until 1793... Its jurisdiction covered the entire field of medicine—algebra (bone setting), midwifery, phlebotomy (bloodletting), surgery, and pharmacy.

 2.  Math.

 a.  As a mass noun: (originally) the branch of mathematics in which letters are used to represent numbers in formulae and equations; (in later use more widely) that in which symbols are used to represent quantities, relations, operations, and other concepts, and operations may be applied only a finite number of times.

abstract, Boolean, matrix, quadruple, tensor algebra, etc.: see the first element

1551  R Record Pathway to Knowl. ii. Pref., Also the rule of false position, with dyuers examples not onely vulgar, but some appertaynyng to the rule of Algeber.

1570  H. Billingsley in  tr. Euclid Elements Geom. x. Introd. f. 228^v, That more secret and subtill part of Arithmetike, commonly called Algebra.

1579  L. Digges  & T. Digges Arithm. Mil. Treat. 55 This Art of Algebra or Rule of Cosse as the Italians terme it.

1612  B. Jonson Alchemist i. i. sig. B^v, Your Alchemye, and your Algebra.

1663  S. Butler Hudibras: First Pt. i. i. 10 And wisely tell what hour o' th' day The Clock does strike, by Algebra.

1709  S. Cobb tr. J. Alexander Synopsis Algebra 84  (heading) Linear Algebra in Order to the Geometric Construction of Equations.

1775  E. Burke Speech Resol. for Concil. Colonies 6 A proportion..beyond all the powers of Algebra to equalize and settle.

1782  W. Cowper Conversation in Poems 213 And if it weigh th' importance of a fly, The scales are false or Algebra a lie.

1844  W. Flagg Let. 12 Dec. in Flagg Corr. (1986) 57 There are only 2 scholars that study Algebra... I did not like it very well.

1860  J. L. Motley Hist. Netherlands III. 102 Passionless as algebra.

1928  A. Huxley Point Counter Point iv. 48 Arithmetic held a wild saturnalian kermesse; algebra cut capers.

1994  B. A. Staples Parallel Time viii. 122, I failed algebra and would spend the summer..sweating over equations.

2007 Science 7 Dec. 1534/1 Algebra is a gateway course for high school mathematics; without mastering algebra, a college degree in science or engineering is impossible.

 b.  As a count noun: a set together with operations such as addition or multiplication, typically distinguished from other such systems by the choice of axioms; spec. a ring (ring n.¹ 15) that is also a vector space over a field of scalars and has the property that multiplication of an element by a scalar commutes with multiplication by another ring element, i.e. (ax)y =a(xy), where a is a scalar and x and y are elements of the ring.

Banach, Lie algebra, etc.: see the first element.

1854  G. Boole Investig. Laws Thought ii. 37 Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone.

1870  B. Pierce Linear Associative Algebra 21 This is quite an important limitation, and the algebras which are subject to it will be called associative.

1914 Trans. Amer. Math. Soc. 15 162 In discussing primitive algebras we may without any real loss of generality assume that any element commutative with every other element of the algebra is a scalar, i.e., an element of the field F.

1956  R. H. Atkin Math. & Wave Mech. iii. 76 As in all algebras we find it convenient to introduce two identity operators.

1963  G. F. Simmons Introd. Topol. & Mod. Anal. xii. 303 A C*-algebra with the further property of being closed in the weak operator topology is called a W*-algebra. Algebras of this kind are also called rings of operators, or von Neumann algebras.

2010  J. J. Rotman Adv. Mod. Algebra (ed. 2) vi. 484 The tensor product of algebras is an ‘honest’ construction.

 3.  In extended use and fig Something, esp. a system or process, that resembles algebra in substituting one thing for another, or in using symbols, signs, etc., to represent ideas and concepts. Cf. grammar n. 6a.

1663  W. Clark Marciano ii. i. 13 Fly! Fly! avaunt with that base cowardly gibbrish; That Algebra of honour.

a1721  M Prior Dialogues of Dead: Locke & Montaigne (1907) 233 Egad Simile is the very Algebra of Discourse.

1831 Blackwood's Edinb. Mag. 29 509/1 Our modern costumiers take measure by algebra, and cut out by diagrams.

1929 Writer July 221/1 Every free-lance ought to know at least the commonest of these symbols in the algebra of publication.

1937  A. Huxley Let. 6 Dec. (1969) 428, A very remarkable man called Sheldon, a psychologist... [who] seems..to have evolved a genuine algebra in terms of which to discuss the problem [sc. of psychological types].

1990 Sci. Amer. Nov. 97/1 The novel algebra of their fields describes our world quite well, abuzz with diverse particles as it is.

2005 LA Weekly (Nexis) 25 Feb. 44, I wondered: Was there some emotional algebra to this music that, once understood, would unlock a new landscape of meaning?

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