In mathematics, the quaternions are a nummer seestem that extends the complex nummers. Thay wur first describit bi Erse mathematician William Rowan Hamilton in 1843 an applee'd tae mechanics in three-dimensional space. A featur o quaternions is that multiplication o twa quaternions is noncommutative. Hamilton defined a quaternion as the quotient o twa directit lines in a three-dimensional space or equivalently as the quotient o twa vectors.
- On Quaternions; or on a new System of Imaginaries in Algebra (letter to John T. Graves, dated October 17, 1843). 1843.
- Boris Abramovich Rozenfelʹd (1988). The history of non-euclidean geometry: evolution of the concept of a geometric space. Springer. p. 385.
- Hamilton. Hodges and Smith. 1853. p. 60.
- Hardy 1881 pg. 32. Ginn, Heath, & co. 1881.