extrapolate (v.)

1610s, "to alter or enlarge (a writing) by inserting new material," from Latin interpolatus, past participle of interpolare "alter, freshen up, polish;" of writing, "falsify," from inter "among, between" (see inter-) + polare, which is related to polire "to smoothe, polish," from PIE root *pel- (5) "to thrust, strike, drive," the connecting notion being "to full cloth" [Watkins].

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.

"an approximate calculation made by inferring unknown values from trends in the known data," 1867, noun of action from extrapolate by analogy of interpolation. The original sense was "an inserting of intermediate terms in a mathematical series." The transferred sense of "drawing of a conclusion about the future based on present tendencies" is from 1889.

word-forming element meaning "outside; beyond the scope of; in addition to what is usual or expected," in classical Latin recorded only in extraordinarius, but more used in Medieval Latin and modern formations; it represents Latin extra (adv.) "on the outside, without, except," the old fem. ablative singular of exterus "outward, outside," comparative of ex "out of" (see ex-).