How did the Fourth Lateran Council define transubstantiation?

The Fourth Lateran Council, convened by Pope Innocent III in 1215, officially sanctioned the term "transubstantiation" as the correct expression of Eucharistic doctrine.12

While the council did not provide an exhaustive philosophical treatise, its definition established that the substance of the bread and wine changes into the body and blood of Christ, while the empirical appearances remain unchanged. By formalizing this terminology, the council provided a foundation for later Scholastic theologians—such as St. Thomas Aquinas—to further interpret the Eucharist using Aristotelian concepts of "substance" and "accidents". This decree was part of the council's broader efforts to define church doctrine and address challenges from groups like the Cathari and Waldenses.321