The History of a Lemma from Archimedes to Newton
In this work, we identify some traces of the history of <i>Archimedes’ straight line</i>, a lemma introduced by Archimedes within the solution of prop. II 4 of <i>On the Sphere and Cylinder</i>, in which it is asked to cut a sphere with a plane in order to obtain two spherica...
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| Formato: | Artigo |
| Idioma: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Acceso en liña: | https://www.mdpi.com/2227-7390/11/3/747 |
| _version_ | 1827759945289826304 |
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| author | Emilia Florio |
| author_facet | Emilia Florio |
| author_sort | Emilia Florio |
| collection | DOAJ |
| description | In this work, we identify some traces of the history of <i>Archimedes’ straight line</i>, a lemma introduced by Archimedes within the solution of prop. II 4 of <i>On the Sphere and Cylinder</i>, in which it is asked to cut a sphere with a plane in order to obtain two spherical segments such that their ratio is equal to a given ratio. In the course of solving this proposition with the method of analysis, assuming given what is required, as specified in this method, Archimedes traces the path along which one goes in search of the final point, from which what is required comes, expressed in a lemma which in history is referred to as <i>Archimedes’ straight line</i> or the <i>square problem</i>. The Syracusan mathematician promised to later give a solution to the lemma, but he did not keep his promise. The lemma was taken up again by Eutocius of Ascalon towards the end of the Hellenistic period, it had considerable resonance among some Arab mathematicians, who traced a specific line of research around it, finally finding attention in the Latin tradition up to Newton within the first part of the history of the path of the analytic method. |
| first_indexed | 2024-03-11T09:34:44Z |
| format | Article |
| id | doaj.art-c7acdee013754283917a196a5df69f1a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:34:44Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c7acdee013754283917a196a5df69f1a2023-11-16T17:24:00ZengMDPI AGMathematics2227-73902023-02-0111374710.3390/math11030747The History of a Lemma from Archimedes to NewtonEmilia Florio0Department of Mathematics and Computer Science, Università della Calabria, 87036 Rende, ItalyIn this work, we identify some traces of the history of <i>Archimedes’ straight line</i>, a lemma introduced by Archimedes within the solution of prop. II 4 of <i>On the Sphere and Cylinder</i>, in which it is asked to cut a sphere with a plane in order to obtain two spherical segments such that their ratio is equal to a given ratio. In the course of solving this proposition with the method of analysis, assuming given what is required, as specified in this method, Archimedes traces the path along which one goes in search of the final point, from which what is required comes, expressed in a lemma which in history is referred to as <i>Archimedes’ straight line</i> or the <i>square problem</i>. The Syracusan mathematician promised to later give a solution to the lemma, but he did not keep his promise. The lemma was taken up again by Eutocius of Ascalon towards the end of the Hellenistic period, it had considerable resonance among some Arab mathematicians, who traced a specific line of research around it, finally finding attention in the Latin tradition up to Newton within the first part of the history of the path of the analytic method.https://www.mdpi.com/2227-7390/11/3/747history of mathematicshistory of scienceArchimedesEutociusArchimedes’ straight linesquare problem |
| spellingShingle | Emilia Florio The History of a Lemma from Archimedes to Newton Mathematics history of mathematics history of science Archimedes Eutocius Archimedes’ straight line square problem |
| title | The History of a Lemma from Archimedes to Newton |
| title_full | The History of a Lemma from Archimedes to Newton |
| title_fullStr | The History of a Lemma from Archimedes to Newton |
| title_full_unstemmed | The History of a Lemma from Archimedes to Newton |
| title_short | The History of a Lemma from Archimedes to Newton |
| title_sort | history of a lemma from archimedes to newton |
| topic | history of mathematics history of science Archimedes Eutocius Archimedes’ straight line square problem |
| url | https://www.mdpi.com/2227-7390/11/3/747 |
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