I assume what is meant is when was the idea of a vector as an entity in its
own right was invented, rather than the idea of a vector as expressed in
terms of its components (or coordinates). If the latter is meant, then I
remember vividly realizing some years ago, while reading the *Principia
Mathematica* that Isaac Newton had a very clear idea of composing a force,
expressed quantitatively, from its two or three components. That is, he
had a clear idea of what we might call coordinatewise vector addition.
Then there is the question of when the word "vector" may have been
introduced, and by whom, as contrasted with the concept of a vector as a
single entity.
In any case, here is a quotation (p 179-180) from B L van der Waerden's *A
History of Algebra* (1985) which may or may not shed some light on the
subject:
"In analogy to the complex numbers a+bi, [William Rowan] Hamilton [in
1843] wrote his triplets as a+bi+cj. He visualized his basic units 1,i,j
as mutually perpendicular "directed segments" of unit length in space.
Later on Hamilton himself used the word *vector*, which I shall also use.
He sought to represent products such as
(a+bi+cj)(x+yi+zj)
as vectors in the same space. [etc.]"
van der Waerden gives as references 5 items found in vol. 3 of *Hamilton's
Mathematical Papers* (1963).
Gordon Fisher gfisher@shentel.net