The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718)

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma. Rosa Massa-Esteve, Antonio Mellado-Romero
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引用次数: 1

Abstract

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.

Abstract Image

丢番图《算术》的六卷书增加了又减少了,变得似是而非:雅克·奥扎南(1640-1718)丢失的手稿
一种新的分析方法的引入,从根本上说是由于弗朗索瓦·维特和勒内·笛卡尔以及他们的作品后来的传播,导致了思维和数学方法的深刻变化。这种变化被称为代数化过程,发生在17世纪和18世纪初,导致了数学的巨大变革。在许多其他后果中,这一过程导致了用新的分析方法处理经典论文中的结果,这允许对这些论文进行新的观察并获得新的结果。在这些论文中,有法国数学家雅克·奥扎南(1640–1718)使用新的代数语言编写的《亚历山大的丢番图算术》(约200–284),他除了大量增加丢番图的原始问题外,还以通用的方式解决了这些问题,从而获得了许多几何结果。这幅作品是手写的,从未出版过,已经失传了近300年,已知的参考文献表明了它的重要性。我们将展示,奥扎南的手稿曾多次被当时的其他数学家引用为重要作品,其中G.W.莱布尼茨尤为突出。一旦找到手稿,我们在本文中的目的是展示和分析Ozanam的这部作品、它的内容、它的符号和它的结构,以及他如何通过新的代数方法,不仅解决和扩展了Diophantus提出的问题,而且还引入了代数解和他所谓的几何确定之间的联系,通过从解中获得轨迹。
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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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