1680s, Englishing of Modern Latin fibrilla "a little fiber, a filament," especially in botany, diminutive of Latin fibra "a fiber, filament" (see fiber). Latin fibra and fibrilla were used in 17c. physiology in English alongside nativized fibre and fibril. From 1931 as "thread-like molecular formation."
word-formation element meaning "pertaining to, of the nature of," from Latin -arem, -aris "of the kind of, belonging to," a secondary form (by dissimilation) of -alis, used after syllables with an -l- (such as insularis for *insulalis, stellaris for *stellalis).
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Harper, D. (n.d.). Etymology of fibrillar. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/fibrillar