Principle of Continuity: Sixteenth–Nineteenth Centuries

Israel Kleiner ()
Additional contact information
Israel Kleiner: York University, Department of Mathematics and Statistics

Chapter Chapter 9 in Excursions in the History of Mathematics, 2012, pp 197-214 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8268-2_9

Ordering information: This item can be ordered from
http://www.springer.com/9780817682682

DOI: 10.1007/978-0-8176-8268-2_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().