Here cI . . . . . c~ are vectors (control points) in some s-dimensional linear space, say W. The control polygon is then determined by the composite vector c r R "~ and we can think of c geometrically as a polygonal line. Various algorithms for the manipulation and computation of such curves take the form of successive geometric alterations of the control polygon. In particular, in the case of ...

In our software system Descartes we have implemented a wide range of interactive map-based tools intended to support exploratory analysis of spatial data and decision-making in a geographic context. The tools can be accessed through the Web and, hence, could potentially serve a broad user community. However, the novelty of the tools makes them difficult to understand and use. The users need ins...

(1) Institut National de la Santé et de la Recherche M Laboratoire du Développement Normal et Patho Immunitaire, Paris, France. (2) Université Paris Descartes, Faculté de Médecine Descartes, Institut Fédératif de Recherche Neck (IFR94), Paris, France. (3) Assistance Publique-Hôpitaux de Paris, Hôpital Nec Unité d’Immunologie et Hématologie Pédiatrique, Pa (4) Assistance Publique-Hôpitaux de Par...

1. The Antecedent of Any Mechanical Conception. The Moving Point. The mental pictures of natural phenomena are of very different kinds. Among the simplest and most basic of these mental pictures we may include the kinematical model of the motion of a geometrical point. Such a picture is an abstraction, i.e., an ideal construction, which may be obtained conveniently through axiomatic treatment o...

Claude Clerselier leitor da dúvida de René Descartes 
 Resumo: foi amigo, correspondente, tradutor e editor Descartes, quem publicou os três volumes correspondência (Cartas do senhor Descartes), O homem mundo. Sua atividade sempre animada por um duplo desígnio : divulgar a filosofia construindo veiculando, entretanto, imagem mais ortodoxa possível filósofo. Essa Cleserlier « vulgarizador »...

Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where f1, . . . , fk ∈ L[x1, . . . , xn] and no more than μ distinct exponent vectors occur in the monomial term expansions of the fi. We prove that F has no more than 1 + ( Cn(μ− n)3 log(μ− n) )n geometrically isolated roots in Ln, where C is an explicit and effectively computable constant depending only on L. This gi...

Stephen Gaukroger’s new biography of Descartes is a major accomplishment. Gaukroger offers the reader an overview of Descartes’ life and works, with healthy doses of intellectual background thrown in for good measure. It should have a major impact on Cartesian studies, both within the history of philosophy and within the history of science. As Gaukroger’s full title makes clear, this is suppose...

A slightly different question is how many positive zeros a polynomial has. Here the basic result is known as “Descartes’ rule of signs”. It says that the number of positive zeros is no more than the number of sign changes in the sequence of coefficients. Descartes included it in his treatise La Géométrie, which appeared in 1637. It can be proved by a method based on factorization, but, again, j...