late Old English, "intentionally untrue, lying," of religion, "not of the true faith, not in accord with Christian doctrines," from Old French fals, faus "false, fake; incorrect, mistaken; treacherous, deceitful" (12c., Modern French faux), from Latin falsus "deceptive, feigned, deceitful, pretend," also "deceived, erroneous, mistaken," past participle of fallere "deceive, disappoint," which is of uncertain origin (see fail (v.)).
Adopted into other Germanic languages (cognates: German falsch, Dutch valsch, Old Frisian falsk, Danish falsk), though English is the only one in which the active sense of "deceitful" (a secondary sense in Latin) has predominated. From c. 1200 as "deceitful, disloyal, treacherous; not genuine;" from early 14c. as "contrary to fact or reason, erroneous, wrong." False alarm recorded from 1570s. False step (1700) translates French faux pas. To bear false witness is attested from mid-13c. False prophet "one who prophecies without divine commission or by evil spirits," is attested from late 13c.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
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Definitions of falsely from WordNet
in an insincerely false manner;
a seduction on my part would land us with the necessity to rise, bathe and dress, chat falsely about this and that, and emerge into the rest of the evening as though nothing had happened
in an incorrect manner;
to credit Lister with the first formulation of the basic principle of stratigraphy would be to bestow credit falsely