late 14c., "a prohibition" (a sense now obsolete), also "absence, nonexistence; opposite," from Old French negatif and directly from Latin negativus (see negative (adj.)).
Meaning "a negative statement" is from 1560s. Sense of "that side of a question which denies what the opposite side affirms" is from 1570s. Meaning "the right or power of refusing assent" is from 1610s. Meaning "a negative quality" is from 1640s. In mathematics, "a negative number," from 1706. Photographic sense of "image in which the lights and shades are the opposite of those in nature" is recorded by 1853. As a response, "I refuse, disagree, no," from 1945, originally in radio communication.