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The notion of variable quantities ω in Bolzano’s early works

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F20%3A00535527" target="_blank" >RIV/67985955:_____/20:00535527 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1016/j.hm.2019.07.002" target="_blank" >https://doi.org/10.1016/j.hm.2019.07.002</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.hm.2019.07.002" target="_blank" >10.1016/j.hm.2019.07.002</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The notion of variable quantities ω in Bolzano’s early works

  • Original language description

    Amid the debate over infinitesimals, Bolzano introduced the alternative notion of variable quantities ω in his 1816 work on the binomial theorem. It has often been assumed that his 1817 definition of continuity using them is practically the modern one. This paper explores Bolzano’s early mathematical works and diaries to gain insight into the subtleties in his definition of ω and some of his mathematical procedures. We show that those quantities are not clearly ‘proto-Weierstrassian’ and argue that Bolzano was in the process of refinement and increasing abstraction of the idea of quantity that eventually led to the development of a theory of real numbers.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    60301 - Philosophy, History and Philosophy of science and technology

Result continuities

  • Project

    <a href="/en/project/GJ19-03125Y" target="_blank" >GJ19-03125Y: Mathematics in the Czech lands: from the Jesuit teaching to Bernard Bolzano</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2020

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    HISTORIA MATHEMATICA

  • ISSN

    1090-249X

  • e-ISSN

  • Volume of the periodical

  • Issue of the periodical within the volume

    50

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    25

  • Pages from-to

    25-49

  • UT code for WoS article

    000517656500003

  • EID of the result in the Scopus database

    2-s2.0-85072232956