On Quaternions ( - 1874)

"Instead of seeking to attain consistency and uniformity of system, as some modern writers have attempted, by banishing this thought of time from the higher Algebra, I seek to attain the same object, by systematically introducing it into the lower or earlier parts of the science." (William R Hamilton, "Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time", Transactions of the Royal Irish Academy, 1837)

"There is still something in the system [of quaternions] which gravels me. I have not yet any clear views as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties. [...] If with your alchemy you can make three pounds of gold, why should you stop there?" (John T Graves, [letter to William R Hamilton] 1843)

"And feeling that it must be possible to introduce Time into Algebra, in some such sense as Space is introduced into Geometry, I had at least an unpublished fancy, of which I have sometimes spoken with my friends, that by banishing this thought of time (or motion) from the higher Algebra to the utmost of my power, I might perhaps be enabled to return to it with a better chance of success." (William R Hamilton, [letter on quaternions John T. Graves] 1843)

"There seems to me to be something analogous to polarized intensity in the pure imaginary part; and to unpolarized energy (indifferent to direction) in the real part of a quaternion: and thus we have some slight glimpse of a future Calculus of Polarities. This is certainly very vague […]" (Sir William R Hamilton, "On Quaternions; or on a new System of Imaginaries in Algebra", 1844)

"The algebraically real part may receive [...] all values contained on the one scale of progression of number from negative to positive infinity; we shall call it therefore the scalar part, or simply the scalar of the quaternion, and shall form its symbol by prefixing, to the symbol of the quaternion, the characteristic Scal., or simply S., where no confusion seems likely to arise from using this last abbreviation. On the other hand, the algebraically imaginary part, being geometrically constructed by a straight line, or radius vector, which has, in general, for each determined quaternion, a determined length and determined direction in space, may be called the vector part, or simply the vector of the quaternion; andmay be denoted by prefixing the characteristic Vect., or V." (William R Hamilton, 1846)