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#top Algebraic Sum

From The Collaborative International Dictionary of English v.0.48 [gcide]:

Sum \Sum\, noun [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.

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.

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.

{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.