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De Morgan's Formal Logic , which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic , contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that it is a lattice-theoretical formulation of Boolean algebra; (6) discuss some issues of historical priority; and (7) conclude with the puzzle of LCT's lack of influence.