Undamaging comes from un- ('not') + damaging, from damage, from Old French damage, from Latin damnum ('loss, harm, injury'). The historical chain includes Old English un-, Old French damage, and Latin damnum. The quoted older senses, "not" and "loss, harm, injury", supply the semantic anchors for undamaging. The formation is best read as compound and borrowed: the word undamaging carries its older form-history into a compact English lexical shape. In present English it is used as a adj, "not causing damage or harm". Related English forms include damage and damaging. The result is a adj whose etymology preserves both the older form and the later English specialization.