We examine the analytical theories of heat developed by Laplace, Poisson and Carnot, and the thermodynamic theories based on the energy conservation and the principle of the increase of entropy formulated by Clausius. We present an analysis of the approaches developed by Maxwell, Gibbs, Planck, Duhem, Nernst, and De Donder as well as the irreversible thermodynamics of Prigogine, and the theory of liquid gas transition of van der Waals. We show that the thermodynamic potentials dominated the development of the theory of thermodynamics since Gibbs. They were introduced by Massieu under the name of characteristic functions and were demonstrated by Gibbs to have the suitable properties to characterize equilibrium of systems with variable composition, and to hold the convexity properties. We also show that the thermodynamic potentials were the relevant quantity in the Duhem approach to thermodynamics and to thermochemistry.

We examine the concept of probability from its emergence within the realm of the games of chance and the development of the theory of probability until the appearance of the treatise of Kolmogorov on this subject. The discipline related to that theory is framed as the science of aleatory events. Probability is understood as a primitive concept represented by a measure assigned to the space of events and obeying the fundamental postulates of the theory. The measurement of probability is the ratio of the number of the observed favorable outcomes and the total number of observed outcomes when these numbers are larger enough.

We examine the metaphysical theories of motion and matter developed by Democritus, Plato, and Aristotle, as well as other theories that appeared later on and were great influenced by Aristotle. We distinguish two subsequent developments. One is the impetus theory for the projectile motion and the other is the void theory for the rise of liquids by suction. We analyze the Galileo theory of motion, emphasizing the crucial step in its development which was the precise definition of velocity. We also analyze the events related to the experiments of Torricelli, which was understood as the production of void, and his explanation based on the weight of the atmospheric air.

We present an analysis of the first analytical physical theories developed after the introduction of calculus. The underlying framework of these theories is the differential and integral calculus in the form developed by Leibniz. We point out the fundamental laws, or principles, or postulates upon which they are founded, and show some results or laws that are derived from them. We point out the main concepts of the theories drawing attention to the primitive or primary concepts, which are those undefinable. The theories that we describe are those that emerged just after the introduction of calculus, from Varignon to Navier. The areas of these theories include mechanics, electricity, magnetism, light, propagation of sound and propagation of heat.