What is "infinitesimal increment"

Increment \In"cre*ment\, n. [L. incrementum: cf. F. incr['e]ment. See Increase.]

1. The act or process of increasing; growth in bulk, guantity, number, value, or amount; augmentation; enlargement.

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

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

2. Matter added; increase; produce; production; -- opposed to decrement. ``Large increment.''
   --J. Philips.

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.

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

   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.

   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.