De l’intraitable à l’indéterminé : entre calcul et géométrie, réflexions leibniziennes autour de ⁰⁄₀ (1700-1706)
In 1672, Leibniz introduced the expression “” in a mathematical text dealing with number series to express the sum of units. It probably is one of the first appearances of this expression in the history of mathematics. Nonetheless, Leibniz abandoned it shortly afterwards. The expression reappeared i...
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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2021-05-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/3028 |
| Summary: | In 1672, Leibniz introduced the expression “” in a mathematical text dealing with number series to express the sum of units. It probably is one of the first appearances of this expression in the history of mathematics. Nonetheless, Leibniz abandoned it shortly afterwards. The expression reappeared in the context of differential calculus at a time in which it was being hotly disputed at the Académie royale des sciences. One of the prominent issues raised by the introduction of the new calculus was whether the notion of differential should be distinguished in practice from that of absolute zero. This article examines the efforts made in the context of a new mathematical practice to make sense of the expression “”. We will show how the expression stopped representing an algebraic impossibility, the idea was introduced that “0” should no longer be thought of as an absolute zero. Henceforth the expression would indicate the existence of a singularity of a curve. The analysis of this attempt to make sense of an algebraic expression highlights how important the diagrammatic representation of the characters involved in calculus was for the early practitioners of differential calculus. |
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| ISSN: | 1281-2463 1775-4283 |