Although Carnot's contributions to thermodynamics have been universally recognized, it is usually with the reservation that there were serious gaps in his proof. Careful study of his memoir shows that Carnot implicitly defined heat so as to make it equivalent to entropy. With this interpretation it may be shown that his logic was flawless, that he believed in the kinetic nature of heat, and that his theorems are based on the first and second laws of thermodynamics.