History of Vector

   

The parallelogram law for the addition of vectors is so intuitive that its origin is unknown. It may have appeared in a now lost work of Aristotle (384 – 322 B.C.), and it is in the Mechanics of Heron (first century A.D.) of Alexandria.  It was also the first corollary in Isaac Newton’s (1642–1727) Principia Mathematica (1687). In the Principia, Newton dealt extensively with what are now considered vectorial entities (e.g., velocity, force), but never the concept of a vector. The systematic study and use of vectors were a 19^th and early 20^th century phenomenon.

Vectors were born in the first two decades of the 19^th century with the geometric representations of complex numbers.  Caspar Wessel (1745–1818), Jean Robert Argand (1768–1822), Carl Friedrich Gauss (1777–1855), and at least one or two others conceived of complex numbers as points in the two-dimensional plane, i.e., as two-dimensional vectors.  Mathematicians and scientists worked with and applied these new numbers in various ways; for example, Gauss made crucial use of complex numbers to prove the Fundamental Theorem of Algebra (1799).  In 1837, William Rowan Hamilton (1805–1865) showed that the complex numbers could be considered abstractly as ordered pairs (a, b) of real numbers. This idea was a part of the campaign of many mathematicians, including Hamilton himself, to search for a way to extend the two-dimensional "numbers" to three dimensions; but no one was able to accomplish this, while preserving the basic algebraic properties of real and complex numbers.