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Principle of Continuity: Sixteenth–Nineteenth Centuries

  • Israel Kleiner
Chapter

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.

Keywords

Nineteenth Century Euclidean Geometry Negative Number Projective Geometry Diophantine Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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