“On a theory of the syzygetic relations of two rational integral functions, comprising an application ot the theory of Sturm’s functions, and that of the greatest algebraical common measure.” Offprint from Philosophical transactions, Vol. 143, Part III

London: Taylor and Francis, 1853. FIRST SEPARATE PRINTING. Original blue cloth, author and title in gilt on front cover and spine, yellow paste-downs. From the Haskell Norman library with his bookplate. First separate printing. “Sylvester is best known for his extensive work in the field of invariants, especially that performed in conjunction with Arthur Caley, but he also left important theorems in connection with Sturm’s functions, canonical forms, and determinants. In the present paper, he applied Sturm’s process of the greatest alegbraic common measure to two independent functions f(x) and φ(x), and investigated the nature of the roots of a quintic equation.”

DSB, XIII, pp. 216-221; Norman, 2045 (this copy).