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Mathematical procedure equivalent to differential calculus
amongst modern scholars about the exact meaning of Fermat's adequality. Fermat's adequality was analyzed in a number of scholarly studies. In 1896, Paul
Adequality
French mathematician and lawyer (1601–1665)
developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method
Pierre_de_Fermat
Largest and smallest value taken by a function at a given point
Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory
Maximum_and_minimum
Extremely small quantity in calculus; thing so small that there is no way to measure it
Leibniz's law of continuity. The standard part function implements Fermat's adequality. The notion of infinitely small quantities was discussed by the Eleatic
Infinitesimal
Swiss mathematician (1707–1783)
Links to related articles v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The
Leonhard_Euler
In mathematics, straight line touching a plane curve without crossing it
of adequality to calculate tangents and other problems in analysis and used this to calculate tangents to the parabola. The technique of adequality is
Tangent
3rd-century Greek mathematician
term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent
Diophantus
Branch of mathematics
claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. The combination
Calculus
Function from the limited hyperreal to the real numbers
such, it is a mathematical implementation of the historical concept of adequality introduced by Pierre de Fermat, as well as Leibniz's transcendental law
Standard_part_function
Light rays follow quickest paths
principles in physics). It was the more notable because it used the method of adequality, which may be understood in retrospect as finding the point where the
Fermat's_principle
Generalization of the real numbers
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Surreal_number
linearum curvarum distributed in 1636, Fermat introduced the concept of adequality, which represented equality up to an infinitesimal error term. This method
History_of_calculus
Real numbers adjoined with a nil-squaring element
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Dual_number
Maclaurin series, Taylor series Fourier series Euler–Maclaurin formula Adequality Infinitesimal Archimedes' use of infinitesimals Gottfried Leibniz Isaac
List_of_calculus_topics
tangent line. This was discovered about the same time as Fermat's method of adequality. While Fermat's method had more in common with the infinitesimal techniques
Method_of_normals
Branch of mathematics
geometry, which is the precursor to modern calculus. Fermat's method of adequality allowed him to determine the maxima and minima of functions and the tangents
Mathematical_analysis
1734 book by George Berkeley
infinitesimals, but it is also used when discussing differentials, and adequality. The full text of The Analyst can be read on Wikisource, as well as on
The_Analyst
Modern application of infinitesimals
)(x_{k+1}-x_{k})=M(b-a)+\epsilon (b-a)} from which the result follows. Adequality Archimedes' use of infinitesimals Criticism of nonstandard analysis Differential
Nonstandard_calculus
German polymath (1646–1716)
Madison Mason Paine Romanticism → Category v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The
Gottfried_Wilhelm_Leibniz
About maxima and minima of functions
similar to the modern interior extremum theorem using an approach he called adequality. After Marin Mersenne passed the treatises onto René Descartes, Descartes
Interior_extremum_theorem
Formula for refraction angles
in a denser medium. Fermat's derivation also utilized his invention of adequality, a mathematical procedure equivalent to differential calculus, for finding
Snell's_law
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Hyperreal_number
Mathematical notion of infinitesimal difference
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Differential_(mathematics)
American mathematician
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Abraham_Robinson
Mathematical symbol used to denote integrals and antiderivatives
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Integral_symbol
System of numbers with non-finite quantities
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Levi-Civita_field
Calculus using a logically rigorous notion of infinitesimal numbers
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Nonstandard_analysis
French mathematician (1789–1857)
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Augustin-Louis_Cauchy
Mathematical statement of uniqueness, except for an equivalent structure
Look up up to in Wiktionary, the free dictionary. Abuse of notation Adequality Essentially unique List of mathematical jargon Quotient group Quotient
Up_to
Mathematical treatise by Archimedes
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
The Method of Mechanical Theorems
The_Method_of_Mechanical_Theorems
Heuristic principle enunciated by Gottfried Wilhelm Leibniz
of the standard part function over the hyperreals. Law of continuity Adequality Leibniz Mathematische Schriften, (1863), edited by C. I. Gerhardt, volume
Transcendental law of homogeneity
Transcendental_law_of_homogeneity
Calculus textbook by Guillaume de l'Hôpital (1696)
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Analyse des infiniment petits pour l'intelligence des lignes courbes
Analyse_des_infiniment_petits_pour_l'intelligence_des_lignes_courbes
Mathematical notation used for calculus
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Leibniz's_notation
System of mathematical set theory
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Internal_set_theory
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Criticism of nonstandard analysis
Criticism_of_nonstandard_analysis
inimitable, preimage, subimago aequus aequ-, -iqu- even, level adequacy, adequality, adequate, disequilibrium, equable, equal, equality, equanimity, equant
List of Latin words with English derivatives
List_of_Latin_words_with_English_derivatives
Geometrical concept relating area and volume
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Cavalieri's_principle
1976 mathematics textbook by H. Jerome Keisler
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Elementary Calculus: An Infinitesimal Approach
Elementary_Calculus:_An_Infinitesimal_Approach
of mathematics, list of publications in mathematics. 1729 (anecdote) Adequality Archimedes Palimpsest Archimedes' use of infinitesimals Arithmetization
List of mathematics history topics
List_of_mathematics_history_topics
Hyperreal number that is equal to its own integer part
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Hyperinteger
Type of internal set in nonstandard analysis
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Hyperfinite_set
Mathematical term
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Microcontinuity
Textbook by Augustin-Louis Cauchy (1821)
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Cours_d'analyse
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Constructive nonstandard analysis
Constructive_nonstandard_analysis
Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory
Glossary_of_calculus
Ordered field that does not satisfy the Archimedean property
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Non-Archimedean_ordered_field
Proof technique in nonstandard analysis
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Overspill
; Schaps, David; Shnider, Steve (2013), "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond", Perspectives on Science, 21 (3):
Steve_Shnider
Sequence of points that get progressively closer to each other
{\displaystyle u_{H}} and u K {\displaystyle u_{K}} are infinitely close, or adequal, that is, s t ( u H − u K ) = 0 {\displaystyle \mathrm {st} (u_{H}-u_{K})=0}
Cauchy_sequence
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Increment_theorem
Mathematical model for describing material deformation under stress
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Infinitesimal_strain_theory
Principle that whatever succeeds for the finite also succeeds for the infinite
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Law_of_continuity
Type of set in mathematical logic
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Internal_set
French mathematician (1581–1638)
Diophantus' term παρισὀτης as adaequalitat, which became Fermat's technique of adequality, a pioneering method of infinitesimal calculus. Bachet was the earliest
Claude Gaspar Bachet de Méziriac
Claude_Gaspar_Bachet_de_Méziriac
Named set of points in nonstandard analysis
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Monad_(nonstandard_analysis)
Formalization in mathematical topos theory
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Synthetic differential geometry
Synthetic_differential_geometry
developments that led to infinitesimal calculus, including his technique of adequality. Louis Bertrand Castel, mathematician and physician. Jean-Antoine Chaptal
List_of_Occitans
Concept in model theory
v t e Infinitesimals History Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems
Transfer_principle
ADEQUALITY
ADEQUALITY
ADEQUALITY
ADEQUALITY
Boy/Male
Assamese, Indian, Kannada, Tamil
Intelligence; Thought
Biblical
peace; perfection; retribution
Boy/Male
Hindu, Indian, Punjabi, Sikh
The Light of God
Boy/Male
Hindu, Indian, Marathi
King of a Country
Surname or Lastname
English
English : from Anglo-Norman French waleis ‘Welsh’ (from a Germanic cognate of Old English wealh ‘foreign’), hence an ethnic name for a Welsh speaker. Compare Scottish Wallace.
Surname or Lastname
English
English : variant spelling of Hillier 1.
Surname or Lastname
English
English : variant spelling of Service.
Boy/Male
British, English
Gift from God
Boy/Male
Sikh
Famous victory
Girl/Female
English
From the linden tree island.
ADEQUALITY
ADEQUALITY
ADEQUALITY
ADEQUALITY
ADEQUALITY