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.

Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736) / N. Guicciardini Corsi Salviati - In: Anachronisms in the History of Mathematics: Essays on the Historical Interpretation of Mathematical Texts / [a cura di] N. Guicciardini. - [s.l] : Cambridge University Press, 2021. - ISBN 9781108834964. - pp. 196-222

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

Niccolò Guicciardini Corsi Salviati
2021

Abstract

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.
History of mathematics; Historiography; Differential equations; Gottfried Wilhelm Leibniz; Johann Bernoulli
Settore MAT/04 - Matematiche Complementari
Dipartimenti di Eccellenza 2018-2022 - Dipartimento di FILOSOFIA
Book Part (author)
File in questo prodotto:
File Dimensione Formato  
Anachronism_6_Guicciardini air.pdf

non disponibili

1.14 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/857511
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact