Academic Journal
The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718)
| Title: | The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718) |
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| Authors: | Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma. Rosa Massa-Esteve, Antonio Mellado-Romero |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GRHCT - Grup de Recerca d'Història de la Ciència i de la Tècnica |
| Source: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Publisher Information: | Springer Science and Business Media LLC, 2021. |
| Publication Year: | 2021 |
| Subject Terms: | History of mathematics, Symbolic language, Diophantus [Algebrization], Àrees temàtiques de la UPC::Matemàtiques i estadística, Jacques Ozanam, Arithmetic, Loci, Matemàtiques i estadística [Àrees temàtiques de la UPC], Matemàtica -- Història, 06 humanities and the arts, Algebrization: Diophantus, 01 natural sciences, Classificació AMS::01 History and biography::01A History of mathematics and mathematicians, Mathematicians-Biography, 01 History and biography::01A History of mathematics and mathematicians [Classificació AMS], 0601 history and archaeology, 0101 mathematics, Matemàtics--Biografia, Seventeenth century |
| Description: | The version of record is available online at: http://dx.doi.org/10.1007/s00407-021-00274-3 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. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1432-0657 0003-9519 |
| DOI: | 10.1007/s00407-021-00274-3 |
| DOI: | 10.13039/501100011033 |
| Access URL: | https://philpapers.org/rec/GMETSB https://link.springer.com/article/10.1007/s00407-021-00274-3 |
| Rights: | Springer TDM CC BY NC ND |
| Accession Number: | edsair.doi.dedup.....1fca770f7ac99cfd85ef76c4d747a0b7 |
| Database: | OpenAIRE |
| ISSN: | 14320657 00039519 |
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| DOI: | 10.1007/s00407-021-00274-3 |