Two Jesuits Against the Indivisibles

Descotes, Dominique

doi:10.1007/978-3-319-00131-9_11

Seventeenth-Century Indivisibles Revisited

2015

DOI: 10.1007/978-3-319-00131-9_11

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Two Jesuits Against the Indivisibles

Dominique Descotes

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Fermat’s Dilemma: Why Did He Keep Mum on Infinitesimals? And the European Theological Context

2017

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Abstract. The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be so treated and involve additional tools-leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat's manuscript but it is Breger who tampers with Fermat's procedure by moving all terms to the left-hand side so as to accord better with Breger's own interpretation emphasizing the double root idea. We provide modern proxies for Fermat's procedures in terms of relations of infinite proximity as well as the standard part function.

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Fermat’s Dilemma: Why Did He Keep Mum on Infinitesimals? And the European Theological Context

2017

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Giordano Bruno and Bonaventura Cavalieri's theories of indivisibles: a case of shared knowledge

Rossini

2018

Intellectual History Review

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At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometryespecially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. Relying on the methodology of "historical epistemology", this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of "shared knowledge". The paper shows that the ideaon which both Bruno and Cavalieri buildthat geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics.

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Two Jesuits Against the Indivisibles

Cited by 2 publications

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Fermat’s Dilemma: Why Did He Keep Mum on Infinitesimals? And the European Theological Context

Fermat’s Dilemma: Why Did He Keep Mum on Infinitesimals? And the European Theological Context

Giordano Bruno and Bonaventura Cavalieri's theories of indivisibles: a case of shared knowledge

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