Anachronisms in the History of Mathematics Book contents
- Frontmatter
- Contents
- Contributors
- Figures
- Preface
- 1 Introduction: The historical interpretation of mathematical texts and the problem of anachronism
- 2 From reading rules to reading algorithms: textual anachronisms in the history of mathematics and their effects on interpretation
- 3 Anachronism and anachorism in the study of mathematics in India
- 4 On the need to re-examine the relationship between the mathematical sciences and philosophy in Greek antiquity
- 5 Productive anachronism: on mathematical reconstruction as a historiographical method
- 6 Anachronism in the Renaissance historiography of mathematics
- 7 Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736)
- 8 Euler and analysis: case studies and historiographical perspectives
- 9 Measuring past geometers: a history of non-metric projective anachronism
- 10 Anachronism: Bonola and non-Euclidean geometry
- 11 Anachronism and incommensurability:words, concepts, contexts, and intentions
- Index
7 - Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736)
Published online by Cambridge University Press: 19 July 2021
- Frontmatter
- Contents
- Contributors
- Figures
- Preface
- 1 Introduction: The historical interpretation of mathematical texts and the problem of anachronism
- 2 From reading rules to reading algorithms: textual anachronisms in the history of mathematics and their effects on interpretation
- 3 Anachronism and anachorism in the study of mathematics in India
- 4 On the need to re-examine the relationship between the mathematical sciences and philosophy in Greek antiquity
- 5 Productive anachronism: on mathematical reconstruction as a historiographical method
- 6 Anachronism in the Renaissance historiography of mathematics
- 7 Deceptive familiarity: differential equations in Leibniz and the Leibnizian school (1689–1736)
- 8 Euler and analysis: case studies and historiographical perspectives
- 9 Measuring past geometers: a history of non-metric projective anachronism
- 10 Anachronism: Bonola and non-Euclidean geometry
- 11 Anachronism and incommensurability:words, concepts, contexts, and intentions
- Index
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.
Keywords
- Type
- Chapter
- Information
- Anachronisms in the History of MathematicsEssays on the Historical Interpretation of Mathematical Texts, pp. 196 - 222Publisher: Cambridge University PressPrint publication year: 2021