Article ID: CBB393358626

Newton on constructions in geometry (2023)


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 In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic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.

Citation URI

This citation is part of the Isis database.

Similar Citations

Article Domski, Mary; (2013)
Kant and Newton on the a priori Necessity of Geometry (/p/isis/citation/CBB001320266/) unapi

Article Galuzzi, Massimo; (2010)
Newton's Attempt to Construct a Unitary View of Mathematics (/p/isis/citation/CBB001022150/) unapi

Article Anabel áuregui-Hernández; (2023)
On Arnauld’s geometry of straight lines (/p/isis/citation/CBB863240324/) unapi

Chapter McGuire, J. E.; (1983)
Space, geometrical objects, and infinity: Newton and Descartes on extension (/p/isis/citation/CBB000028528/) unapi

Chapter Raman, Shankar; (2012)
Constructing Selves, Making Publics: Geometry and Poetry in Descartes and Sidney (/p/isis/citation/CBB001201597/) unapi

Chapter Dunlop, Katherine; (2012)
What Geometry Postulates: Newton and Barrow on the Relationship of Mathematics to Nature (/p/isis/citation/CBB001500341/) unapi

Chapter Harper, William; (2012)
Newton, Huygens and Euler: Empirical Support for Laws of Motion (/p/isis/citation/CBB001500344/) unapi

Book David S. Richeson; (2019)
Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (/p/isis/citation/CBB243851906/) unapi

Book Janiak, Andrew; Schliesser, Erick; (2012)
Interpreting Newton: Critical Essays (/p/isis/citation/CBB001500334/) unapi

Chapter Andrew Janiak; (2015)
Mathematics and Infinity in Descartes and Newton (/p/isis/citation/CBB974951037/) unapi

Book Blackmore, John T.; Itagaki, Ryoichi; Tanaka, Setsuko; (2011)
Great Realists from Galileo to Planck (/p/isis/citation/CBB001500285/) unapi

Article Wade, Nicholas J.; (2005)
Vision and the Dimensions of Nerve Fibers (/p/isis/citation/CBB000600124/) unapi

Book Janiak, Andrew; (2008)
Newton as Philosopher (/p/isis/citation/CBB000850371/) unapi

Chapter Newman, William R.; (2009)
Geochemical Concepts in Isaac Newton's Early Alchemy (/p/isis/citation/CBB001021035/) unapi

Article Jen Nguyen; (2023)
Contextualizing Newton and Clarke’s “Argument from Quantity” (/p/isis/citation/CBB676111263/) unapi

Article Friesen, John; (2003)
Archibald Pitcairne, David Gregory and the Scottish Origins of English Tory Newtonianism, 1688--1715 (/p/isis/citation/CBB000340660/) unapi

Book Ducheyne, Steffen; (2012)
The Main Business of Natural Philosophy: Isaac Newton's Natural-Philosophical Methodology (/p/isis/citation/CBB001221237/) unapi

Article Kerszberg, Pierre; (2013)
Deduction Versus Discourse: Newton and the Cosmic Phenomena (/p/isis/citation/CBB001320867/) unapi

Thesis Gerald Charles Lawrence; (1968)
The Assimilation of Newtonian Mechanics, 1687-1736 (/p/isis/citation/CBB617132624/) unapi

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

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment