## Fermat

Fer·mat 1601-65; Fr. mathematician

- The dispute on the latter point between
**Fermat**and Descartes was continued, even after the philosopher's death, as late as 1662. - In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de)
**Fermat**(1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661). **Fermat**and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described.- Between Roberval and Descartes there existed a feeling of ill - will, owing to the jealousy aroused in the mind of the former by the criticism which Descartes offered to some of the methods employed by him and by Pierre de
**Fermat**; and this led him to criticize and oppose the analytical methods which Descartes introduced into geometry about this time. - No number of the form 4n+3, or 4n - I, can be the sum of two squares), and goes on to a d, practically, the condition stated by
**Fermat**, "and the double of it [n] increased by one, when divided by the greatest square which measures it, must not be divisible by a prime number of the form 4n - 1," except for the omission of the words "when divided.

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