Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736)

The differential equations as written by Leibniz and by his immediate followers look very similar to the ones in use nowadays. They are familiar to our students of mathematics and physics. Yet, in order to make them fully compatible with the conventions adopted in our textbooks, we only need to change a few symbols. Such “domesticating” renderings, however, generate a remarkable shift in meaning, making those very equations — when thus reformulated — unacceptable for their early-modern authors. They would have considered our equations, as we write them, wrong and would have corrected them back, for they explicitly adopted tasks and criteria different from ours. In this chapter, focusing on a differential equation formulated by Johann Bernoulli in 1710, I evaluate the advantages and risks inherent in these anachronistic renderings.