Did you say "linear"? ----------------------------
Over the course of the 19th century, the word "algebra" took on a new dimension. Of Arabic origin and derived from the title of a work by the Persian scholar al-Khwarizmi, since Viète and Peletier du Mans the term had referred to all the computational techniques involving the new kinds of numbers represented first by negative integers and then by complex numbers. Mathematical structures such as groups, rings and fields were originally conceived as extensions of the notion of number and therefore fall quite naturally under the umbrella of algebra. More generally, anything based on computation (operations such as addition or multiplication… including vector spaces!) is classified within the same field.
Yet the geometric origins remain apparent in the names given to these various concepts, as the use of the word "space" clearly shows. Similarly, "linear" contains the word "line". Derived from Latin, linearis describes something relating to a straight line. It entered French during the Renaissance with the same meaning; ever since, concepts closely connected with straight lines (vector lines, in our case)—in other words, those described by a first-degree equation—have been termed linear.
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A "vector"? Why that word… ----------------------------------