Variables, limits, and infinitesimals in Portugal in the late 18th century

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• 作者：Domingues ; Joã ; o Caramalho
• 关键词：01A50 ; Mathematics in Portugal ; Variables ; Limits ; Infinitesimals
• 刊名：Historia Mathematica
• 出版年：2004
• 期刊代码：68_03150860
• 类别：mt
• 出版时间：February, 2004
• 卷：31
• 期：1
• 页码：15-33
• 文件大小：173 K

摘要

Two of the most important Portuguese mathematicians of the late 18th century, José Anastácio da Cunha and Francisco Garção Stockler, showed interest in the question of the principles of the calculus and wrote on that subject. In spite of both being admirers of Newton and d'Alembert, only Stockler based the calculus on the concept of limit; Cunha used his own definition of infinitesimal. Here, I present the fundamental concepts on which Cunha and Stockler based their versions of the calculus and I argue that the main difference between them lies in different notions of variable.