Leonhard Euler primarily applied the term transcendental to quantities which could be variable or determined. Analyzing Euler's use and understanding of mathematical transcendence as applied to operations, functions, progressions, and determined quantities as well as the eighteenth century practice of definition allows the author to evaluate claims that Euler provided the first modern definition of a transcendental number. The author argues that Euler's informal and pragmatic use of mathematical transcendence highlights the general nature of eighteenth century mathematics and proposes an alternate perspective on the issue at hand: transcendental numbers inherited their transcendental classification from functions.
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Book
Bradley, Robert E.;
D'Antonio, Lawrence A.;
Sandifer, C. Edward;
(2007)
Euler at 300: An Appreciation
(/isis/citation/CBB000830141/)
Article
Giovanni Ferraro;
(2020)
Euler and the Structure of Mathematics
(/isis/citation/CBB453451930/)
Chapter
Pulte, Helmut;
(2001)
Order of Nature and Orders of Science: On the Material Philosophy of Nature and Its Changing Concepts of Science from Newton and Euler to Lagrange and Kant
(/isis/citation/CBB000101471/)
Article
Glasberg, Ronald;
(2003)
Mathematics and Spiritual Interpretation: A Bridge to Genuine Interdisciplinarity
(/isis/citation/CBB000411132/)
Book
Leonhard Euler;
Christian von Goldbach;
Franz Lemmermeyer;
Martin Mattmüller;
(2015)
Leonhardi Euleri opera omnia. Ser. 4, A Leonhardi Euleri commercium epistolicum = Correspondence of Leonhard Euler Vol. 4 Pars 1
(/isis/citation/CBB406214307/)
Book
Ronald S. Calinger;
(2015)
Leonhard Euler: Mathematical Genius in the Enlightenment
(/isis/citation/CBB749253216/)
Article
Roman Sznajder;
(2016)
On Known and Less Known Relations of Leonhard Euler with Poland / O znanych i mniej znanych relacjach Leonharda Eulera z Polską
(/isis/citation/CBB070750288/)
Book
Henry, Philippe;
(2007)
Leonhard Euler “incomparable géomètre”
(/isis/citation/CBB000953060/)
Article
Ferraro, Giovanni;
(2008)
The Integral as an Anti-Differential. An Aspect of Euler's Attempt to Transform the Calculus into an Algebraic Calculus
(/isis/citation/CBB000933315/)
Book
Nahin, Paul J.;
(2006)
Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
(/isis/citation/CBB000772751/)
Article
Mallion, Roger;
(2008)
A Contemporary Eulerian Walk over the Bridges of Kaliningrad
(/isis/citation/CBB000931915/)
Article
Zhang, Sheng;
(2007)
Euler and Euler Numbers
(/isis/citation/CBB000760554/)
Article
Verdun, Andreas;
(2013)
Leonhard Euler's Early Lunar Theories 1725--1752: Part 2: Developing the Methods, 1730--1744
(/isis/citation/CBB001211762/)
Article
Ermolaeva, Natalia;
(2008)
Les mathématiciens de Saint-Pétersbourg et les problèmes cartographiques
(/isis/citation/CBB001021143/)
Book
Richeson, David S.;
(2008)
Euler's Gem: The Polyhedron Formula and the Birth of Topology
(/isis/citation/CBB000950327/)
Article
Mayfield, Betty;
(2013)
Women and Mathematics in the Time of Euler
(/isis/citation/CBB001320026/)
Article
Coates, John;
(2008)
Euler's Work on Zeta and L-Functions and Their Special Values
(/isis/citation/CBB000931916/)
Article
Ferraro, Giovanni;
(2004)
Differentials and Differential Coefficients in the Eulerian Foundations of the Calculus
(/isis/citation/CBB000410838/)
Article
Bullynck, Maarten;
(2010)
Factor Tables 1657--1817, with Notes on the Birth of Number Theory
(/isis/citation/CBB001033636/)
Book
Brummelen, Glen Van;
Kinyon, Michael;
(2005)
Mathematics and the Historian's Craft: The Kenneth O. May Lectures
(/isis/citation/CBB001023435/)
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