Boscovich's geometrical principle of continuity, and the ``mysteries of the infinity''
type: Item
instance of: scholarly article
title: Boscovich's geometrical principle of continuity, and the ``mysteries of the infinity''
zbMATH Open document ID: 1395.01017
author: A. Del Centina
author: Alessandra Fiocca
published in: Historia Mathematica
publication date: 2018-06-01T00:00:00Z
full work available at URL: http://hdl.handle.net/11392/2383920
review text: Some principles in mathematics are used unknowingly for centuries until someone will discover them. This is the case for the geometrical principle of continuity, and this paper presents its formulation by Boscovich (1711--1787) and compares his treatment with that both by his forerunners and successors. The first one who used the principle was Kepler while considering conic sections cut by a plane rotating around a straight line. He was followed by Briggs, Desargues, Pascal and particularly Leibniz who recognized the principle and gave a name to it. Boscovich made the principle an explicit object of study with the aim to place it on secure grounds. After thorough analysis and underlining elements of novelty in his approach the authors nevertheless came to the conclusion that ``Boscovich looked at this principle more from the point of view of a philosopher, and scientist of nature, than from the point of view of a mathematician (\(\dots\)) and we shall not emphasize Boscovich's position as a forerunner of modern theories''.
reviewed by: Roman Duda
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 01A45
Mathematics Subject Classification ID: 01A55
zbMATH DE Number: 6879929
zbMATH Keywords: principle of geometrical continuity
zbMATH Keywords: conic sections
MaRDI profile type: Publication
OpenAlex ID: W2791209378
cites work: On Kepler's system of conics in \textit{Astronomiae pars optica}
cites work: Poncelet's porism: a long story of renewed discoveries. I
cites work: Perspective in Leibniz's invention of \textit{characteristica geometrica}: the problem of Desargues' influence
cites work: Q4340901
cites work: Q3745822
cites work: Q3225057
cites work: Optics. Paralipomena to Witelo \& optical part of astronomy. Transl. from the 1604 German original and with an introduction by William H. Donahue. With a preface by Dana Densmore and Donahue
cites work: Q4401917
cites work: Q4013712
cites work: Q4846441
cites work: The argument of generality in Carnot, Poncelet and Chasles
cites work: Q5272672
cites work: Q5817365
cites work: Q4510158
cites work: Conflicts between generalization, rigor and intuition. Number concepts underlying the development of analysis in 17th--19th century France and Germany
cites work: Q5805936
cites work: L'œuvre de Pascal en géométrie projective
DOI: 10.1016/J.HM.2018.02.002
description: scientific article; zbMATH DE number 6879929