Adequality (original) (raw)
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam (a Latin treatise circulated in France c. 1636) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus. According to André Weil, Fermat "introduces the technical term adaequalitas, adaequare, etc., which he says he has borrowed from Diophantus. As Diophantus V.11 shows, it means an approximate equality, and this is indeed how Fermat explains the word in one of his later writings." (Weil 1973). Diophantus coined the word παρισότης (parisotēs) to refer to an approximate equality. Claude Gaspard Bachet de Méziriac translated Diophantus's Greek word into Latin as adaequalitas. Paul Tannery's French trans
| Property | Value |
|---|---|
| dbo:abstract | Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam (a Latin treatise circulated in France c. 1636) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus. According to André Weil, Fermat "introduces the technical term adaequalitas, adaequare, etc., which he says he has borrowed from Diophantus. As Diophantus V.11 shows, it means an approximate equality, and this is indeed how Fermat explains the word in one of his later writings." (Weil 1973). Diophantus coined the word παρισότης (parisotēs) to refer to an approximate equality. Claude Gaspard Bachet de Méziriac translated Diophantus's Greek word into Latin as adaequalitas. Paul Tannery's French translation of Fermat’s Latin treatises on maxima and minima used the words adéquation and adégaler. (en) L’adégalité, dans l'histoire du calcul infinitésimal, est une technique développée par Pierre de Fermat, dont il dit qu'il l'a empruntée à Diophante. L'adégalité a été interprétée par certains chercheurs comme signifiant « l'égalité approximative ». John Stillwell illustre la technique dans le cadre de différentiation de comme suit. Si nous désignons l'adégalité par , alors il est juste de dire que et donc que pour la parabole est adégal à . Cependant, n'est pas un nombre ; en fait, est le seul nombre auquel est adégal. C'est le « vrai » sens dans lequel représente la pente de la courbe. Une procédure similaire en analyse non standard consiste à déterminer la partie standard (ou ombre) d’un réel donné. (fr) |
| dbo:wikiPageExternalLink | https://scholarship.claremont.edu/pitzer_fac_pub/118 |
| dbo:wikiPageID | 30609033 (xsd:integer) |
| dbo:wikiPageLength | 16756 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1070146365 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Calculus dbr:A_K_Peters,_Ltd. dbr:Enrico_Giusti dbr:Method_of_normals dbr:Descartes dbr:Archive_for_History_of_Exact_Sciences dbr:John_Stillwell dbr:Maxima_and_minima dbr:Claude_Gaspard_Bachet_de_Méziriac dbr:André_Weil dbr:Paul_Tannery dbr:Tangent dbr:Michael_Sean_Mahoney dbc:History_of_calculus dbr:Fermat's_principle dbr:Non-standard_analysis dbr:Center_of_mass dbr:Hyperreal_number dbr:Area dbc:Mathematical_terminology dbr:Latin dbr:Diophantus dbr:Marin_Mersenne dbr:Pierre_de_Fermat dbr:Real_number dbr:Kirsti_Andersen dbr:Infinitesimal_calculus dbr:Transcendental_law_of_homogeneity dbr:Standard_part_function dbr:Snell's_law dbr:Victor_J._Katz dbr:Least_action |
| dbp:date | September 2016 (en) |
| dbp:reason | too much unnecessary information displayed with poor formatting (en) |
| dbp:wikiPageUsesTemplate | dbt:Citation dbt:Citation_needed dbt:Cleanup dbt:Reflist dbt:Sfn dbt:Infinitesimals |
| dct:subject | dbc:History_of_calculus dbc:Mathematical_terminology |
| rdfs:comment | Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam (a Latin treatise circulated in France c. 1636) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus. According to André Weil, Fermat "introduces the technical term adaequalitas, adaequare, etc., which he says he has borrowed from Diophantus. As Diophantus V.11 shows, it means an approximate equality, and this is indeed how Fermat explains the word in one of his later writings." (Weil 1973). Diophantus coined the word παρισότης (parisotēs) to refer to an approximate equality. Claude Gaspard Bachet de Méziriac translated Diophantus's Greek word into Latin as adaequalitas. Paul Tannery's French trans (en) L’adégalité, dans l'histoire du calcul infinitésimal, est une technique développée par Pierre de Fermat, dont il dit qu'il l'a empruntée à Diophante. L'adégalité a été interprétée par certains chercheurs comme signifiant « l'égalité approximative ». John Stillwell illustre la technique dans le cadre de différentiation de comme suit. Si nous désignons l'adégalité par , alors il est juste de dire que (fr) |
| rdfs:label | Adequality (en) Adégalité (fr) |
| owl:sameAs | freebase:Adequality wikidata:Adequality dbpedia-fr:Adequality https://global.dbpedia.org/id/2dMur |
| prov:wasDerivedFrom | wikipedia-en:Adequality?oldid=1070146365&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Adequality |
| is dbo:knownFor of | dbr:Pierre_de_Fermat |
| is dbo:wikiPageRedirects of | dbr:Adequal |
| is dbo:wikiPageWikiLink of | dbr:Calculus dbr:List_of_calculus_topics dbr:Method_of_normals dbr:List_of_Occitans dbr:The_Analyst dbr:List_of_mathematics_history_topics dbr:Mathematical_analysis dbr:Maxima_and_minima dbr:Christiaan_Huygens dbr:Claude_Gaspar_Bachet_de_Méziriac dbr:Glossary_of_calculus dbr:Tangent dbr:Fermat's_principle dbr:Cauchy_sequence dbr:History_of_calculus dbr:Diophantus dbr:Pierre_de_Fermat dbr:Fermat's_theorem_(stationary_points) dbr:Infinitesimal dbr:Transcendental_law_of_homogeneity dbr:Standard_part_function dbr:Snell's_law dbr:Up_to dbr:List_of_things_named_after_Pierre_de_Fermat dbr:Nonstandard_calculus dbr:Adequal |
| is dbp:knownFor of | dbr:Pierre_de_Fermat |
| is foaf:primaryTopic of | wikipedia-en:Adequality |