"But in dealing with given quantics, we may without loss of generality consider the covariant as a function of the like form with the quantic,..."
Arthur Cayley, An Introductory Memoir upon Quantics, Philosophical Transactions of the Royal Society of London, Vol. 144, (1854), pp. 245-258.
The equivalent phrase "Without losing generality" appears earlier in W. T. Thomson, On the lines of curvature of surfaces of the second order, Cambridge Mathematical Journal, Vol. IV. May, 1845.