In this paper, we are interested in the canonical method for the estimation or measure of magnitudes in Leibniz. This method, which is based on the procedure of alternating subtractions known as anthyphairesis, enjoys a privileged role within Leibniz's conception of mathematics to the point that, in the 1690s, Leibniz defines mathesis universalis (general mathematics) as both the science of quantity in general and the science of the estimation of quantity. We first provide an historical contextu…
Read moreIn this paper, we are interested in the canonical method for the estimation or measure of magnitudes in Leibniz. This method, which is based on the procedure of alternating subtractions known as anthyphairesis, enjoys a privileged role within Leibniz's conception of mathematics to the point that, in the 1690s, Leibniz defines mathesis universalis (general mathematics) as both the science of quantity in general and the science of the estimation of quantity. We first provide an historical contextualization for the procedure of anthyphairesis with special emphasis on the definition of the equality of ratios of magnitudes by anthyphairesis; then, we reconstruct Leibniz's original contribution to the topics by individuating the conditions that he believed to be necessary to enable the exact measurement of quantities, to wit, the homogeneity condition, the extensivity condition, and the exactness condition.
