The objective of this paper is to propose a novel approach to automatically reason formulae of laws and their solutions. Our approach takes an intermediate position between the deductive approaches such aa dimension-baaed and symmetrybased reasoning and the empirical approaches such as BACON. It does not require a priori insights into the objective system but data through measurement, and hence it can be applied to various domains like BACON and is not limited to physics. In spite of its data-driven feature, the solutions of the formulae obtained by our approach are ensured to be sound similasly to the dimension-baaed approach. The basic idea is the combined use of deductive "scale.based reason. ing" and data-driven reasoning. Especially, the scale-based reasoning is the main part in this study. The features of our approach are demonstrated by deriving the basic formulae of the ideal gas law and Black’s specific heat law. The scalebased reasoning may provide a basis to develop qualitative models of ambiguous domains such aa biology, psychology, economics and social science. This will also contribute to the research area of knowledge discovery.