Cavalieri’s Indivisibles

Andersen, Kirsti; Giusti, Enrico; Jullien, Vincent

doi:10.1007/978-3-319-00131-9_3

Cited by 5 publications

(5 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…92 This counter-example is given by Cavalieri himself. He claims that it was sent to him by an anonymous writer (see Andersen (1985), p. 309) 93 See Aristotle's Physics, VI, 9, 239b5-240a20; as well as Simplicius' Commentary on Aristotle's Physics, 140.29. See also Aristotle's claim on the possibility of dispensing with the infinite in mathematics (Physics,III,11,.…”

Section: Plato Vs 'Mathematical Atomism'mentioning

confidence: 99%

The Mathematical Anti-atomism of Plato’s Timaeus

Brisson¹,

Ofman²

2022

Ancient Philosophy

View full text Add to dashboard Cite

In Plato’s eponymous dialogue, Timaeus, the main character presents the universe as an (almost) perfect sphere filled by tiny, invisible particles having the form of four regular polyhedrons. At first glance, such a construction may seem close to an atomistic theory. However, one does not find any text in Antiquity that links Timaeus’ cosmology to the atomists, while Aristotle opposes clearly Plato to the latter. Nevertheless, Plato is commonly presented in contemporary literature as some sort of atomist, sometimes as supporting a form of so-called ‘mathematical atomism’. However, the term ‘atomism’ is rarely defined when applied to Plato. Since it covers many different theories, it seems that this term has almost as different meanings as different authors. The purpose of this article is to consider whether it is correct to connect Timaeus’ cosmology to some kind of ‘atomism’, however this term may be understood. Its purpose is double: to obtain a better understanding of the cosmology of the Timaeus, and to consider the different modern ‘atomistic’ interpretations of this cosmology. In short, we would like to show that such a claim, in any form whatsoever, is misleading, an impediment to the understanding of the dialogue, and more generally of Plato’s philosophy.

show abstract

Section: Plato Vs 'Mathematical Atomism'mentioning

confidence: 99%

The Mathematical Anti-atomism of Plato’s Timaeus

Brisson¹,

Ofman²

2022

Ancient Philosophy

View full text Add to dashboard Cite

show abstract

“…En este sentido, podría elaborarse una clasificación entre los tipos de cuadraturas propuestas en este siglo. Recientemente, Jesper Lützen ha llevado a cabo una clasificación de esta naturaleza, que es bastante compleja, estableciendo tres criterios de distinción: 25 (1) el tipo de solución, esto es, si se trata de una construcción efectivamente geométrica o si, dejando de lado la cuestión de la constructibilidad geométrica de un cuadrado que sea igual al círculo o de la circunferencia extendida en línea recta, se propone una solución algebraica o aritmética, lo que es el caso de la mayoría de las propuestas del siglo XVII; (2) si el tipo de cuadratura que se ofrece nos da un resultado que es aproximado o exacto; (3) si se provee la determinación del área o circunferencia de la totalidad del círculo en términos de su radio (en este caso, tendríamos una cuadratura definida), o si se busca determinar el área o el largo del arco de cualquier sector del círculo (es decir, una cuadratura indefinida). Más aún, podrían llevarse a cabo nuevas subdivisiones teniendo en cuenta estos criterios, lo que nos muestra un panorama bastante complejo.…”

Section: La Clasificación De Las Cuadraturas Según Leibnizunclassified

“…Société Hollandaise des Sciences),Amsterdam, Swets & Zeitlinger N.V., 1910, vol. 12; Gregory, James, Vera circuli et hyperbolae quadratura, Padua, Paolo Frambotto, 1667 25. Lützen, Jesper, "17th century arguments for the impossibility of the indefinite and the definite circle quadrature", Revue d'Histoire desMathématiques, 20, 2014, pp.…”

mentioning

confidence: 99%

La visión de Leibniz sobre el producto infinito de Wallis

Quintana¹

2020

Topicos

View full text Add to dashboard Cite

En este trabajo examinaré de qué manera Leibniz consideró el producto infinito de Wallis para la cuadratura del círculo. En particular, mostraré que Leibniz concibió que el resultado de Wallis no es equivalente al suyo, pues de la infinitización del producto del matemático británico, según la lectura del de Leipzig, se sigue un absurdo. De esta manera, se justificaría la concepción de Leibniz de que su propuesta de una cuadratura aritmética exacta del círculo no tiene precedentes.

show abstract

“…The definition of an integral has been around since the 17th century and even earlier when mathematicians such as Cavalieri and Fermat began experimenting with integrals of polynomials (see [1]). The definite integral has the precise meaning of the area underneath a graph y = f (x).…”

Section: Introductionmentioning

confidence: 99%

Redefining the integral

Orr¹

2018

Preprint

View full text Add to dashboard Cite

In this paper, we discuss a similar functional to that of a standard integral. The main difference is in its definition: instead of taking a sum, we are taking a product. It turns out this new "star-integral" may be written in terms of the standard integral but it has many different (and similar) interesting properties compared to the regular integral. Further, we define a "star-derivative" and discuss its relationship to the "star-integral".

show abstract

Cavalieri’s Indivisibles

Cited by 5 publications

References 1 publication

The Mathematical Anti-atomism of Plato’s Timaeus

The Mathematical Anti-atomism of Plato’s Timaeus

La visión de Leibniz sobre el producto infinito de Wallis

Redefining the integral

Contact Info

Product

Resources

About