Book ID: CBB887755156

Modes de l’analyse et formes de la géométrie (2021)

unapi

For a long time geometry, the science of continuous quantities, was opposed to arithmetic, the science of discrete quantities. Analysis and algebra functioned as communication tools. Analysis was a way of reasoning about what is not given, algebra a technique applied, thanks to a common language, to both geometry and arithmetic. They have been transformed by a long process, some important steps of which are studied in this book. The first chapter deals with the conceptual origins and evolution of analysis up to Descartes. The second discusses the constructive foundations of Euclidean geometry, which uses diagrams for spatial relations. The third studies the Cartesian reform of this geometry, opening the way to new applications of algebra to the theory of curves. The fourth discusses Lagrange's attempt to make analysis - called "algebraic" - the ultimate basis of mathematics. The fifth explores the extensions of this attempt to mechanics, called "analytic".

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Authors & Contributors
Wang, Xiaofei
Halák, Jan
Frank, Martin
Welsh, Whitney Elizabeth
Verburgt, Lukas M.
Terdimou, Maria
Concepts
Mathematics
Geometry
Algebra
Philosophy of mathematics
Arithmetic
Mechanics
Time Periods
18th century
19th century
17th century
16th century
Renaissance
Early modern
Places
Italy
England
Turin (Italy)
Scotland
Netherlands
Greece
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