Infinitesimal increment

Increment In"cre*ment, n. [L. incrementum: cf. F. incr['e]ment. See {Increase}.] [1913 Webster] 1. The act or process of increasing; growth in bulk, guantity, number, value, or amount; augmentation; enlargement. [1913 Webster]

The seminary that furnisheth matter for the formation and increment of animal and vegetable bodies. --Woodward. [1913 Webster]

A nation, to be great, ought to be compressed in its increment by nations more civilized than itself. --Coleridge. [1913 Webster]

2. Matter added; increase; produce; production; -- opposed to {decrement}. ``Large increment.'' --J. Philips. [1913 Webster]

3. (Math.) The increase of a variable quantity or fraction from its present value to its next ascending value; the finite quantity, generally variable, by which a variable quantity is increased. [1913 Webster]

4. (Rhet.) An amplification without strict climax, as in the following passage: [1913 Webster]

Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report, . . . think on these things. --Phil. iv. 8. [1913 Webster]

{Infinitesimal increment} (Math.), an infinitesimally small variation considered in Differential Calculus. See {Calculus}.

{Method of increments} (Math.), a calculus founded on the properties of the successive values of variable quantities and their differences or increments. It differs from the method of fluxions in treating these differences as finite, instead of infinitely small, and is equivalent to the calculus of finite differences. [1913 Webster]