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

Published online by Cambridge University Press:  19 July 2021

Niccolò Guicciardini
Affiliation:
Università degli Studi di Milano
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Summary

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 have to change just a few symbols. Such “domesticating” renderings, however, generate a remarkable shift in meaning, making those very equations – when so reformulated – not acceptable for their early-modern authors. They would have considered our equations, as we write them, wrong and 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.

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Anachronisms in the History of Mathematics
Essays on the Historical Interpretation of Mathematical Texts
, pp. 196 - 222
Publisher: Cambridge University Press
Print publication year: 2021

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