COMPLEMENT (Lat. complementum, from complere, to fill up), that which fills up or completes anything, e.g. the number of men necessary to man a ship. In geometry, the complement of an angle is the difference between the angle and a right angle; the complements of a parallelogram are formed by drawing parallel to adjacent sides of a parallelogram two lines intersecting on a diagonal; four parallelograms are thus formed, and the two not about the diagonal of the original parallelogram are the complements of the parallelogram. In analysis, a complementary function is a partial solution to a differential equation (q.v.); complementary operators are reciprocal or inverse operators, i.e. two operations A and B are complementary when both operating on the same figure or function leave it unchanged. A "complementary colour" is one which produces white when mixed with another (see Colour). In Spanish the word cumplimento was used in a particular sense of the fulfilment of the duties of polite behaviour and courtesy, and it came through the French and Italian forms into use in English, with a change in spelling to "compliment," with the sense of an act of politeness, especially of a polite expression of praise, or of social regard and greetings. The word "comply," meaning to act in accordance with wishes, orders or conditions, is also derived from the same origin, but in sense is connected with "ply" or "pliant," from Lat. plicare, to bend, with the idea of subserviently yielding to the wishes of another.
Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)