The story
From sesqui- (“one and a half”) + linear; “conjugate linear” being considered metaphorically “half linear”, hence one and a half times linear, as opposed to bilinear (“linear in both variables”).
Etymology from Wiktionary, CC BY-SA 4.0.
sesquilinear
Today it means: (of a map of a complex vector space) Linear in one coordinate and conjugate linear in the other Full definition →