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.

FrançoisViète和RenéDescartes从根本上引入了一种新的分析方法，后来又传播了他们的作品，这导致了思维方式和数学方法的深刻变化。这种变化被称为代数化过程，发生在十七世纪和十八世纪初，并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对经典论文中的结果进行处理，从而使人们对此类论文有了新的认识并获得了新的结​​果。在那些论文中，算术法国数学家雅克·奥扎南（Jacques Ozanam）（1640–1718）使用新的代数语言撰写的《亚历山大·狄奥菲图斯》（约200–284）一书，他不仅大量增加了《狄奥菲图斯》的原始问题，而且在总体上解决了这些问题方式，从而获得许多几何结果。该作品是手写的，从未出版过，已经失传了近300年，而已知的参考文献也表明了它的重要性。我们将证明，当时其他数学家多次引用Ozanam的手稿是一件重要的著作，其中GW Leibniz就是其中的佼佼者。找到手稿后，本文的目的是展示和分析Ozanam的工作，其内容，符号和结构，以及如何通过新的代数方法，