Gómez-García, Francisco (Author)
Herrero-Piñeyro, Pedro J. (Author)
Linero-Bas, Antonio (Author)
M. Rosa Massa-Esteve (Author)
Mellado-Romero, Antonio (Author)
The introduction of a new analytical method, due fundamentally to François Viète and René Descartes and the later dissemination of their works, resulted in a profound change in the way of thinking and doing mathematics. This change, known as process of algebrization, occurred during the seventeenth and early eighteenth centuries and led to a great transformation in mathematics. Among many other consequences, this process gave rise to the treatment of the results in the classic treatises with the new analytical method, which allowed new visions of such treatises and the obtaining of new results. Among those treatises is the Arithmetic of Diophantus of Alexandria (approx. 200–284) which was written, using the new algebraic language, by the French mathematician Jacques Ozanam (1640–1718), who in addition to profusely increasing the original problems of Diophantus, solved them in a general way, thus obtaining many geometric consequences. The work is handwritten, it has never been published, it has been lost for almost 300 years, and the known references show its importance. We will show that Ozanam’s manuscript was quoted as an important work on several occasions by others mathematicians of the time, among whom G. W. Leibniz stands out. Once the manuscript has been located, our aim in this article is to show and analyze this work of Ozanam, its content, its notation and its structure and how, through the new algebraic method, he not only solved and expanded the questions proposed by Diophantus, but also introduced a connection between the algebraic solutions and what he called geometric determinations by obtaining loci from the solutions.
...More
Article
Rashed, Roshdi;
(1999)
Pierre Fermat et les débuts modernes de l'analyse diophantiene
(/isis/citation/CBB000330311/)
Article
Echelbarger, Charles;
(2013)
Hume on the Objects of Mathematics
(/isis/citation/CBB001201145/)
Article
Philip Beeley;
(2019)
Practical Mathematicians and Mathematical Practice in Later Seventeenth-Century London
(/isis/citation/CBB006065321/)
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
Thomaidis, Yannis;
(2005)
A Framework for Defining the Generality of Diophantos' Methods in “Arithmetica”
(/isis/citation/CBB000740272/)
Article
MacKenzie, Scott R.;
(2014)
Sexual Arithmetic: Appetite and Consumption in The Way of the World
(/isis/citation/CBB001201791/)
Article
Knobloch, Eberhard;
(2013)
Analiticidad, equipolencia y teoría de curvas en Leibniz
(/isis/citation/CBB001214081/)
Book
Davide Gullotto;
(2023)
La Repubblica dei Matematici. Storia dell’analisi matematica nell’età di Euler e Leibniz
(/isis/citation/CBB269641386/)
Article
Christianidisa, Jean;
Oaks, Jeffrey;
(2013)
Practicing Algebra in Late Antiquity: The Problem-Solving of Diophantus of Alexandria
(/isis/citation/CBB001211810/)
Article
Yuste, Piedad;
(2008)
Ecuaciones cuadráticas y procedimientos algorítmicos. Diofanto y las matemáticas en Mesopotamia
(/isis/citation/CBB000933627/)
Article
Christianidis, Jean;
(2007)
The Way of Diophantus: Some Clarifications on Diophantus' Method of Solution
(/isis/citation/CBB000772444/)
Article
Thomaidis, Yannis;
(2011)
Some Remarks on the Meaning of Equality in Diophantos's Arithmetica
(/isis/citation/CBB001022169/)
Article
Acerbi, Fabio;
(2009)
The Meaning of [Greek transliteration begin]plasmatikon[Greek transliteration end] in Diophantus' Arithmetica
(/isis/citation/CBB000932071/)
Book
Lloyd Strickland;
Harry R. Lewis;
(2022)
Leibniz on Binary: The Invention of Computer Arithmetic
(/isis/citation/CBB215936036/)
Article
Federico Raffo Quintana;
(2018)
Leibniz on the Requisites of an Exact Arithmetical Quadrature
(/isis/citation/CBB986988543/)
Article
Luo, Jianjin;
(2003)
On the Development of the Formulae for Sums of Integers
(/isis/citation/CBB000774899/)
Book
Wardhaugh, Benjamin;
(2012)
The History of the History of Mathematics: Case Studies for the Seventeenth, Eighteenth, and Nineteenth Centuries
(/isis/citation/CBB001251196/)
Article
Goldstein, Joel A.;
(2000)
A Matter of Great Magnitude: The Conflict over Arithmetization in 16th-, 17th-, and 18th-Century English Editions of Euclid's Elements Books I Through VI (1561-1795)
(/isis/citation/CBB000110930/)
Book
Grabiner, Judith V.;
(2010)
A Historian Looks Back: The Calculus as Algebra and Selected Writings
(/isis/citation/CBB001033182/)
Article
Maria Rosaria Enea;
Giovanni Ferraro;
(2020)
Analytic and Arithmetic Methods in Liouville's Identities
(/isis/citation/CBB311764284/)
Be the first to comment!