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.