In conventional thermodynamics, the two most important consequences of the second law of thermodynamics, namely, the existence of an absolute temperature scale and the existence of an entropy function are deduced from the Kelvin-Planck statement or its equivalent, the Clausius statement, with the aid of the Carnot engine and Carnot refrigerator. In the Caratheodory method, a new statement of the second law is made; the Carnot cycle is dispensed with and purely analytical methods are used to derive the absolute temperature and the entropy. It is shown in this paper how the analytic methods of Caratheodory may be used without replacing the traditional statements of the second law by a new axiom. Both the Caratheodory statement of the second law and the Caratheodory theorem on Pfaffian differential forms are unnecessary.