In a way that approaches a value or line very closely but never quite reaches it, like how a curve can get infinitely close to a straight line without touching it.
From asymptote (Greek 'asymptotos' meaning 'not falling together'), combining 'a-' (not) and 'symptote' (falling together). The -ically suffix makes it an adverb form. The mathematical concept was formalized in the 17th century to describe curves in geometry.
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