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.
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            Take ye the sum of all the congregation. --Num. i.
                                                  2.
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   Note: Sum is now commonly applied to an aggregate of numbers,
         and number to an aggregate of persons or things.
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   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.
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            With a great sum obtained I this freedom. --Acts
                                                  xxii. 28.
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   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.
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   4. Height; completion; utmost degree.
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            Thus have I told thee all my state, and brought
            My story to the sum of earthly bliss. --Milton.
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   5. (Arith.) A problem to be solved, or an example to be
      wrought out. --Macaulay.
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            A sum in arithmetic wherein a flaw discovered at a
            particular point is ipso facto fatal to the whole.
                                                  --Gladstone.
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            A large sheet of paper . . . covered with long sums.
                                                  --Dickens.
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   {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.
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