Seki’s Theory of Elimination as Compared with the Others’

This is an enlarged version of the authors’ papers published in Journal of Northwest University (Natural Science Edition), 33 Nos.3 and 4 (2003). Added is Section 3, where proofs are given of the main properties of determinants and resultants as originally introduced by Seki Takakazu (1642?–1708), Etienne Bezout (1739–83), James J. Sylvester (1814–97) and Arthur Cayley (1821–95).