# Almost Equal: the Method of Adequality from Diophantus to Fermat and Beyond

@article{Katz2012AlmostET, title={Almost Equal: the Method of Adequality from Diophantus to Fermat and Beyond}, author={Mikhail G. Katz and David M. Schaps and Steven Shnider}, journal={Perspectives on Science}, year={2012}, volume={21}, pages={283-324} }

We analyze some of the main approaches in the literature to the method of ‘adequality’ with which Fermat approached the problems of the calculus, as well as its source in the παρισότης of Diophantus, and propose a novel reading thereof. Adequality is a crucial step in Fermat's method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat's collected…

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## References

SHOWING 1-10 OF 110 REFERENCES

### Fermat's methods of maxima and minima and of tangents. A reconstruction

- History
- 1968

I t is well known tha t I~'ERMAT 1 was the first to use the characteristic behaviour of an algebraic expression near its ext rema as a criterion for the determinat ion of these extrema. 2 When it…

### Fermats «adæquare» – und kein Ende?

- Philosophy
- 2011

In his papers on the determination of maxima and minima and on the calculation of tangents Pierre Fermat uses two different Latin verbs, æquare and adæquare, which do not differ semantically but are…

### The Mathematical Career of Pierre de Fermat, 1601-1665

- Mathematics
- 1973

Preface (1994) ix Introduction xi Acknowledgments xvii I. The Personal Touch 1 1. Mathematics in 1620 2. Fermat's Life and Career in Parlement 3. Motivation to Mathematics II. Nullum Non Problema…

### Proofs and Retributions, Or: Why Sarah Can’t Take Limits

- Mathematics
- 2015

The small, the tiny, and the infinitesimal (to quote Paramedic) have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that…

### Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus

- Mathematics
- 2012

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the…

### THE ROLE OF PARADOXES IN THE EVOLUTION OF MATHEMATICS

- Philosophy
- 1994

A paradox has been described as a truth standing on its head to attract attention. Undoubtedly, paradoxes captivate. They also cajole, provoke, amuse, exasperate, and seduce. More importantly, they…

### Non-Standard Analysis

- Mathematics
- 1977

1. As early as 1934 it was pointed out by Thoralf Skolem (see [17]) that there exist proper extensions of the natural number system which have, in some sense, ‘the same properties’ as the natural…

### The Mathematical Career of Pierre de Fermat

- MathematicsThe Mathematical Gazette
- 1974

Fisher begins by sketching his achievements and denigrating those of Karl Pearson, who died 20 years before the first edition appeared. He then reviews the work of Bayes and Laplace in scientific…

### Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond

- Philosophy
- 2013

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s…