The document discusses the reduction of categorical syllogisms, which is the process of expressing syllogisms that are validly expressed in figures other than the first figure into equivalent syllogisms in the first figure. It explains the key consonants - S, P, M, and C - that indicate the logical operations needed to perform this reduction, such as simple conversion, accidental conversion, mutation, or taking the contradictory of a proposition. Examples are provided to illustrate how syllogisms from figures 2 through 4 can be reduced to equivalent syllogisms in the first figure through these operations.