Article ID: CBB393358626

Newton on constructions in geometry (2023)

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Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject. Samenvatting Newton was kritisch over Descartes constructivistische visie op de grondslagen van de meetkunde, georganiseerd rond bepaalde principes voor het tekenen van krommen. In ongepubliceerd werk schetste Newton een eigen constructivistisch programma, gebaseerd op zijn ‘organische’ methode voor het tekenen van krommen, die de emblematische constructiemethode van Descartes met draaiende liniaal en bewegende kromme als een speciaal geval onderbrengt, maar zonder de zwakte van de Cartesiaanse aanpak dat niet alle kegelsneden tekenbaar zijn. Dit Newtoniaanse programma is weinig bestudeerd en is doordachter en technisch inhoudelijker dan algemeen wordt erkend. Het botst ook met, en vervangt en verbetert, de wellicht beter bekende eerdere uitspraken van Newton over dit onderwerp.

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Authors & Contributors
Janiak, Andrew
Blackmore, John T.
Domski, Mary
Ducheyne, Steffen
Friesen, John
Galuzzi, Massimo
Journals
Almagest
Foundations of Science
Historia Mathematica
History of Science
HOPOS
Journal of the History of the Neurosciences
Publishers
Cambridge University Press
University of Oklahoma
Princeton University Press
Sentinel Open Press
Springer
Concepts
Geometry
Philosophy of science
Mathematics and its relationship to science
Methodology of science; scientific method
Mathematics
Natural philosophy
People
Newton, Isaac
Descartes, René
Leibniz, Gottfried Wilhelm von
Locke, John
Archimedes
Arnauld, Antoine
Time Periods
17th century
18th century
16th century
19th century
Ancient
Enlightenment
Places
England
France
Scotland
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