Sense evolved in Latin from "refurbish," to "alter appearance of," to "falsify (especially by adding new material)." Middle English had interpolen (early 15c.) in a similar sense. Related: Interpolated; interpolating.
"make an approximate calculation by inferring unknown values from trends in the known data," 1862 (in a Harvard observatory account of the comet of 1858), from extra- + ending from interpolate. Said in early references to be a characteristic word of Sir George Airy (1801-1892), English mathematician and astronomer. Related: Extrapolated; extrapolating.