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Principle of Continuity: Sixteenth–Nineteenth Centuries

In: Excursions in the History of Mathematics

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  • Israel Kleiner

    (York University, Department of Mathematics and Statistics)

Abstract

The Principle of Continuity was a very broad law, used widely and importantly – though often not explicitly formulated – throughout the seventeenth, eighteenth, and nineteenth centuries. In general terms, the Principle of Continuity says that what holds in a given case continues to hold in what appear to be like cases. Specifically, it maintains that (1) What is true for positive numbers is true for negative numbers. (2) What is true for real numbers is true for complex numbers. (3) What is true up to the limit is true at the limit. (4) What is true for finite quantities is true for infinitely small and infinitely large quantities. (5) What is true for polynomials is true for power series. (6) What is true for a given figure is true for a figure obtained from it by continuous motion. (7) What is true for ordinary integers is true for (say) Gaussian integers.

Suggested Citation

  • Israel Kleiner, 2012. "Principle of Continuity: Sixteenth–Nineteenth Centuries," Springer Books, in: Excursions in the History of Mathematics, chapter 0, pages 197-214, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8268-2_9
    DOI: 10.1007/978-0-8176-8268-2_9
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