The performance of a diagrammatic method based on geometric and algebraic considerations is here illustrated. This method based on the particular symmetry of a thermodynamic diagram allows to obtain the most important thermodynamic expressions of a simple system. In fact, these thermodynamic expressions can be developed with the application of various geometric patterns to the proposed diagram. The particular symmetry of the thermodynamic diagram allows to develop a matrix formulation of the different geometric patterns. This matrix formalism requires that the thermodynamic parameters of the diagram be recast into a vectorial form.