Abstract Thermodynamic can be described as the set of consistent thermodynamic equations, that constructs quantitative relations between experimental values of different types of physical properties of some coexisting together substances. Values of e.g. specific heat, heat of chemical reactions, vapor pressure and other similar must be adequate.

One of the method to produces the expected consistency is the hierarchic procedure of evaluation of experimental data. Started from pure element, we pass to the pure compounds, then to binary system, tertiary system and so on. But this procedure creates new problem. Among others there must be mentioned at least two: the growing errors of estimated values for more complex systems and difficulty with use simultaneously different type of experimental data. Application of so called coordination calculus, used in geodesy, into thermodynamic problems creates the effective tool to overcome the difficulties.

Based on thermodynamic principles we can creates some constrains in the form of non-linear equations and inequalities describing relations between data of known experiments. Of course, they can not be fulfilled directly by experimental values, but can be fulfilled by some corrected values. As the best values of such corrections we can chose values gives the minimum of squares. Such set of constrains and lest square condition create non-linear optimization problem, easy to solve.

Next step of calculation is the precision evaluation of such consistent data. It can be solve based on so called error propagation procedure. This theoretical elaboration was used to create procedure that led to consistent Au-Ag binary phase diagram.