c. 1300, pureli, "wholly, fully, completely; actually, really, truly," from pure + -ly (2). Sense of "without physical admixture" is from c. 1500.
Entries linking to purely
pure adj.
mid-13c., of gold, "unalloyed;" c. 1300 "unmixed, unadulterated; homogeneous," also "total, complete, absolute; bare, mere," also "sexually pure, virgin, chaste" (late 12c. as a surname, and Old English had purlamb "lamb without a blemish"), from Old French pur "pure, simple, absolute, unalloyed," figuratively "simple, sheer, mere" (12c.), from Latin purus "clean, clear; unmixed; unadorned; chaste, undefiled."
This is conjectured to be from PIE root *peue- "to purify, cleanse" (source also of Latin putus "clear, pure;" Sanskrit pavate "purifies, cleanses," putah "pure;" Middle Irish ur "fresh, new;" Old High German fowen "to sift").
It replaced Old English hlutor. The meaning "free from moral corruption" is recorded from mid-14c. In reference to bloodlines, attested from late 15c. In music, "mathematically perfect," by 1872.
-ly 2
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.