Panza, Marco (Author)
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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Article
Ferraro, Giovanni;
Panza, Marco;
(2012)
Lagrange's Theory of Analytical Functions and His Ideal of Purity of Method
(/isis/citation/CBB001220403/)
Article
Lambert, Kevin;
(2013)
A Natural History of Mathematics: George Peacock and the Making of English Algebra
(/isis/citation/CBB001320192/)
Article
Echelbarger, Charles;
(2013)
Hume on the Objects of Mathematics
(/isis/citation/CBB001201145/)
Article
Engelhard, Kristina;
Mittelstaedt, Peter;
(2008)
Kant's Theory of Arithmetic: A Constructive Approach?
(/isis/citation/CBB001230070/)
Article
Terdimou, Maria;
(2007)
Geometry Versus Algebra. Ancient Greek and Western Mathematics:Parallel or Intersecting Options by the Greek Scholars of the 18th Century?
(/isis/citation/CBB000931865/)
Article
Jan Halák;
(2022)
Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction
(/isis/citation/CBB074170500/)
Article
Martin Frank;
(2014)
Ettore Ausonio, predecessore di Giovanni Battista Benedetti come matematico al servizio del Duca di Savoia
(/isis/citation/CBB232360533/)
Article
Lukas M. Verburgt;
(2018)
Duncan F. Gregory and Robert Leslie Ellis: Second-Generation Reformers of British Mathematics
(/isis/citation/CBB954232268/)
Thesis
Welsh, Whitney Elizabeth;
(2011)
Unthinkable: Mathematics and the Rise of the West
(/isis/citation/CBB001560636/)
Article
Bockstaele, Paul;
(2009)
Between Viète and Descartes: Adriaan van Roomen and the Mathesis Universalis
(/isis/citation/CBB000932082/)
Article
David Rabouin;
(2016)
Mathesis universalis et algèbre générale dans les Regulae ad directionem ingenii de Descartes
(/isis/citation/CBB100086042/)
Article
Boucard, Jenny;
(2011)
Louis Poinsot et la théorie de l'ordre: un chaînon manquant entre Gauss et Galois?
(/isis/citation/CBB001034693/)
Article
Maronne, Sébastien;
(2010)
Pascal versus Descartes on Solution of Geometrical Problems and the Sluse-Pascal Correspondence
(/isis/citation/CBB001031516/)
Article
Xiaofei Wang;
(2022)
How Jean-Baptiste Delambre read ancient Greek arithmetic on the basis of the arithmetic of “complex numbers” at the turn of the 19th century
(/isis/citation/CBB809964800/)
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/)
Book
Stedall, Jacqueline A.;
(2011)
From Cardano's Great Art to Lagrange's Reflections: Filing a Gap in the History of Algebra
(/isis/citation/CBB001321014/)
Book
Leo Corry;
(2022)
British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750)
(/isis/citation/CBB193067062/)
Chapter
Antonino Drago;
(2009)
Lagrange's Arguing in Mecanique Analytique
(/isis/citation/CBB618628082/)
Article
Grabiner, Judith;
(2009)
Why Did Lagrange “Prove” the Parallel Postulate?
(/isis/citation/CBB001023437/)
Thesis
Ganea, Mihai;
(2006)
Foundations of Arithmetical Knowledge
(/isis/citation/CBB001561724/)
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