 From an algebra of logic point of view, the 1854 treatment at times seems less elegant than that in the 1847 book, but it gives a much richer insight into how Boole thinks about the foundations for his algebra of logic. The final chapter on logic, Chapter XV, was an attempt to give a uniform proof of the Aristotelian conversions and syllogisms. (It is curious that prior to Chapter XV Boole did not present any examples of arguments involving particular propositions.) The details of Chapter XV are quite involved, mainly because of the increase in size of expressions when the Elimination and Development Theorems are applied. Boole simply left most of the work to the reader. Later commentators would gloss over this chapter, and no one seems to have worked through its details.