Article ID: CBB032484097

Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia (2020)

unapi

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB032484097/

Similar Citations

Article Dunlop, Katherine; (2012)
The Mathematical Form of Measurement and the Argument for Proposition I in Newton's Principia (/isis/citation/CBB001211480/)

Article Kunkel, Paul; (2007)
The Tangency Problem of Apollonius: Three Looks (/isis/citation/CBB000831564/)

Article Scholz, Erhard; (2006)
Introducing Groups into Quantum Theory (1926--1930) (/isis/citation/CBB000771356/)

Article Kochiras, Hylarie; (2013)
Causal Language and the Structure of Force in Newton's System of the World (/isis/citation/CBB001320795/)

Article Pourciau, Bruce; (2003)
Newton's Argument for Proposition 1 of the Principia (/isis/citation/CBB000340514/)

Book Antonino Drago; (2017)
Dalla storia della fisica alla scoperta dei fondamenti della scienza (/isis/citation/CBB248791186/)

Article Brackenridge, J. Bruce; (2003)
Newton's Easy Quadratures Omitted for the Sake of Brevity (/isis/citation/CBB000340515/)

Book Leshem, Ayval; (2003)
Newton on Mathematics and Spiritual Purity (/isis/citation/CBB000320214/)

Book Lützen, Jesper; (2005)
Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics (/isis/citation/CBB000650671/)

Article Erlichson, Herman; (2003)
Passage to the Limit in Proposition I, Book I of Newton's Principia (/isis/citation/CBB000410829/)

Article Vincenzo De Risi; (2022)
Euclid Upturned: Borelli on the Foundations of Geometry (/isis/citation/CBB039446137/)

Article Resenfeld, Boris; (2002)
Some Remarks on New Editions of Apollonius' Conics (/isis/citation/CBB000740639/)

Book Apollonius of Perga, ; Rashed, Roshdi; Bellosta, Hélène; (2010)
La section des droites selon de rapports (/isis/citation/CBB001220540/)

Article Fried, Michael; (2003)
The Use of Analogy in Book VII of Apollonius' Conica (/isis/citation/CBB000740736/)

Article Paolo Freguglia; (2022)
Marinus Ghetaldus’s Supplementum Apollonij Galli. An Analysis (/isis/citation/CBB325369886/)

Thesis McKinney, Colin Bryan Powell; (2010)
Conjugate Diameters: Apollonius of Perga and Eutocius of Ascalon (/isis/citation/CBB001560832/)

Authors & Contributors
Fried, Michael N.
Scholz, Erhard
Rosenfeld, Boris A.
Rashed, Roshdi
Pourciau, Bruce H.
Montacutelli, Stefania
Concepts
Geometry
Mathematics
Physics
Mathematical physics
Conic sections
Mechanism; mechanical philosophy
Time Periods
17th century
Ancient
18th century
Early modern
Modern
20th century, early
Places
Greece
Italy
Great Britain
Rome (Italy)
Institutions
Accademia del Cimento, Florence
Comments

Be the first to comment!

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

Log in or register to comment