Sentence:  The theory of <WSD>transcendental</WSD> numbers was originated by Liouville in his famous memoir† of 1844 in which he obtained, for the first time, a class, "très-étendue", as it was described in the title of the paper, of numbers that satisfy no algebraic equation with integer coefficients. 
Meaning of the word marked with <WSD> tags:  Not algebraic (i.e., not the root of any polynomial that has positive degree and rational coefficients).