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GREGORY第六算子

已有 442 次阅读 2019-12-1 19:36 |个人分类:异类微积分|系统分类:论文交流|文章来源:转载

GREGORY’S SIXTH OPERATION

TIZIANA BASCELLI, PIOTR BL ASZCZYK, VLADIMIR KANOVEI, KARIN U. KATZ, MIKHAIL G. KATZ, SEMEN S. KUTATELADZE, TAHL NOWIK, DAVID M. SCHAPS, AND DAVID SHERRY

【摘要】结合Marx Wartofsky的一篇论文,我们试图表明,数学史学需要对被审视的数学部分的本体论进行分析。在Ian Hacking之后,我们指出,在数学的历史上,偶然事件的数量比我们通常认为的要大。作为一个案例研究,我们分析了历史学家如何解释James Gregory在证明π的无理性的文章中的“终极术语”这一表达。Gregory在这里提到级数的last或ultimate terms。更广泛地说,我们分析了以下问题:从无穷小分析的早期历史来看,哪种现代框架更适合解释文本中的过程?以及相关的问题:在研究无穷级数和求积问题时,哪种逻辑理论接近于早期现代数学家可能使用过的?我们认为,一个从通常的古典分析的观点来看“不严格”实践的一个例子,实际上在现代无穷小理论中找到了接近的程序性表述。我们分析了导致Gregory的老师degli Angeli的宗教秩序,及Gregory在威尼斯的著作,在17世纪60年代末被镇压的社会和宗教的综合原因。

关键词:收敛;格雷戈里第六操作;无穷数;连续性法则;超越的齐次律


【Abstract】In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of π. Here Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? as well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s.

Keywords: convergence; Gregory’s sixth operation; infinite number; law of continuity; transcendental law of homogeneity

http://dx.doi.org/10.1007/s10699-016-9512-9dx.doi.org


Gregory's sixth operationarxiv.orgMatches for: MR=3772065mathscinet.ams.org





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