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1560s, "valuation," from Latin aestimatus, verbal noun from aestimare (see esteem). Earlier in sense "power of the mind" (mid-15c.). Meaning "approximate judgment" is from 1580s. As a builder's statement of projected costs, from 1796.
1530s, "appraise the worth of," from Latin aestimatus, past participle of aestimare "to value, appraise" (see esteem). Meaning "form an approximate notion" is from 1660s. Related: Estimated; estimates; estimating.