Etymology
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interpolation (n.)
1610s, "act of interpolating;" 1670s, "that which is interpolated," from French interpolation (17c.) or directly from Latin interpolationem (nominative interpolatio), noun of action from past participle stem of interpolare "to alter; falsify" (see interpolate).
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extrapolation (n.)

"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.

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interposition (n.)
late 14c., from Old French interposicion "interpolation, intercalation; suspension, break" (12c.), from Latin interpositionem (nominative interpositio) "an insertion," noun of action from past participle stem of interponere "to put between, place among; put forward," from inter "between" (see inter-) + ponere "to put, place" (past participle positus; see position (n.)).
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