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Algebraic

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraic curve

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraic sum

Sum Sum, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See Sub-, and cf. Supreme.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. ``The sum of forty pound.' --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. Algebraic sum, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. In sum, in short; in brief. [Obs.] ``In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.' --Rogers.

Sum Sum, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See Sub-, and cf. Supreme.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. ``The sum of forty pound.' --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. Algebraic sum, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. In sum, in short; in brief. [Obs.] ``In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.' --Rogers.

Algebraical

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraic Al`ge*bra"ic, Algebraical Al`ge*bra"ic*al, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Algebraic curve, a curve such that the equation which expresses the relation between the co["o]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve.

Algebraically

Algebraically Al`ge*bra"ic*al*ly, adv. By algebraic process.

Algebraically Al`ge*bra"ic*al*ly, adv. By algebraic process.

Algebraist

Algebraist Al"ge*bra`ist, n. One versed in algebra.

Algebraist Al"ge*bra`ist, n. One versed in algebra.

Algebraize

Algebraize Al"ge*bra*ize, v. t. To perform by algebra; to reduce to algebraic form.

Algebraize Al"ge*bra*ize, v. t. To perform by algebra; to reduce to algebraic form.

Graphic algebra

-graph -graph (-gr[.a]f) [From Gr. gra`fein to write. See Graphic.] A suffix signifying something written, a writing; also, a writer; as autograph, crystograph, telegraph, photograph. Graphic Graph"ic (gr[a^]f"[i^]k), Graphical Graph"ic*al (-[i^]*kal), a. [L. graphicus, Gr. grafiko`s, fr. gra`fein to write; cf. F. graphique. See Graft.] 1. Of or pertaining to the arts of painting and drawing. 2. Of or pertaining to the art of writing. 3. Written or engraved; formed of letters or lines. The finger of God hath left an inscription upon all his works, not graphical, or composed of letters. --Sir T. Browne. 4. Well delineated; clearly and vividly described. 5. Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer. Graphic algebra, a branch of algebra in which, the properties of equations are treated by the use of curves and straight lines. Graphic arts, a name given to those fine arts which pertain to the representation on a fiat surface of natural objects; as distinguished from music, etc., and also from sculpture. Graphic formula. (Chem.) See under Formula. Graphic granite. See under Granite. Graphic method, the method of scientific analysis or investigation, in which the relations or laws involved in tabular numbers are represented to the eye by means of curves or other figures; as the daily changes of weather by means of curves, the abscissas of which represent the hours of the day, and the ordinates the corresponding degrees of temperature. Graphical statics (Math.), a branch of statics, in which the magnitude, direction, and position of forces are represented by straight lines Graphic tellurium. See Sylvanite.>

-graph -graph (-gr[.a]f) [From Gr. gra`fein to write. See Graphic.] A suffix signifying something written, a writing; also, a writer; as autograph, crystograph, telegraph, photograph. Graphic Graph"ic (gr[a^]f"[i^]k), Graphical Graph"ic*al (-[i^]*kal), a. [L. graphicus, Gr. grafiko`s, fr. gra`fein to write; cf. F. graphique. See Graft.] 1. Of or pertaining to the arts of painting and drawing. 2. Of or pertaining to the art of writing. 3. Written or engraved; formed of letters or lines. The finger of God hath left an inscription upon all his works, not graphical, or composed of letters. --Sir T. Browne. 4. Well delineated; clearly and vividly described. 5. Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer. Graphic algebra, a branch of algebra in which, the properties of equations are treated by the use of curves and straight lines. Graphic arts, a name given to those fine arts which pertain to the representation on a fiat surface of natural objects; as distinguished from music, etc., and also from sculpture. Graphic formula. (Chem.) See under Formula. Graphic granite. See under Granite. Graphic method, the method of scientific analysis or investigation, in which the relations or laws involved in tabular numbers are represented to the eye by means of curves or other figures; as the daily changes of weather by means of curves, the abscissas of which represent the hours of the day, and the ordinates the corresponding degrees of temperature. Graphical statics (Math.), a branch of statics, in which the magnitude, direction, and position of forces are represented by straight lines Graphic tellurium. See Sylvanite.>

Multiple algebra

Multiple Mul"ti*ple, a. [Cf. F. multiple, and E. quadruple, and multiply.] Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts. Law of multiple proportion (Chem.), the generalization that when the same elements unite in more than one proportion, forming two or more different compounds, the higher proportions of the elements in such compounds are simple multiplies of the lowest proportion, or the proportions are connected by some simple common factor; thus, iron and oxygen unite in the proportions FeO, Fe2O3, Fe3O4, in which compounds, considering the oxygen, 3 and 4 are simple multiplies of 1. Called also the Law of Dalton, from its discoverer. Multiple algebra, a branch of advanced mathematics that treats of operations upon units compounded of two or more unlike units. Multiple conjugation (Biol.), a coalescence of many cells (as where an indefinite number of am[oe]boid cells flow together into a single mass) from which conjugation proper and even fertilization may have been evolved. Multiple fruits. (Bot.) See Collective fruit, under Collective. Multiple star (Astron.), several stars in close proximity, which appear to form a single system.

Multiple Mul"ti*ple, a. [Cf. F. multiple, and E. quadruple, and multiply.] Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts. Law of multiple proportion (Chem.), the generalization that when the same elements unite in more than one proportion, forming two or more different compounds, the higher proportions of the elements in such compounds are simple multiplies of the lowest proportion, or the proportions are connected by some simple common factor; thus, iron and oxygen unite in the proportions FeO, Fe2O3, Fe3O4, in which compounds, considering the oxygen, 3 and 4 are simple multiplies of 1. Called also the Law of Dalton, from its discoverer. Multiple algebra, a branch of advanced mathematics that treats of operations upon units compounded of two or more unlike units. Multiple conjugation (Biol.), a coalescence of many cells (as where an indefinite number of am[oe]boid cells flow together into a single mass) from which conjugation proper and even fertilization may have been evolved. Multiple fruits. (Bot.) See Collective fruit, under Collective. Multiple star (Astron.), several stars in close proximity, which appear to form a single system.

- basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally...

- In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false...

- In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive...

- Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

- a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital ****ociative algebra. As K-algebras, they generalize...

- In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset...

- In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic...

- In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

- In mathematics, the geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product...

- In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

- In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false...

- In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive...

- Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

- a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital ****ociative algebra. As K-algebras, they generalize...

- In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset...

- In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic...

- In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

- In mathematics, the geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product...

- In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

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