Mathematics grows by conceptual change, including the incorporation of new mathematical objects, which entail new techniques of proof and new families of results. Usually, new techniques, results and conceptual changes are explained as resulting from "generalization" and "abstraction". Our research project aims to map the emergence of implicit novel mathematical notions of number, magnitude, and ratio in mathematical practice, as opposed to mathematical texts. In particular, we will study the role of practical geometry and the practices related to the art of measuring as sources for the crucial innovation of the arithmetical continuum. We will analyse also how mathematical instruments offered materializations of new implicit notions and justifications for new algorithms which only later on would find formal expression.