Descartes: A Biography

c CUNYB/Clarke     December, :

Retreat and Defence (–) 

desired. Your other writings which preceded it reminded me of the Bradamente of

our poets, who was unwilling to accept anyone as a servant unless they had previously

been tested against them in a duel....I assure you that I have great respect for your

merit, and when I look at the most recent way in which you find tangents to curved

lines, I have nothing else to reply except that it is very good. If you had explained it in

this way at the beginning, I would not have contradicted it at all. (ii.)

This apparent reconciliation was unfortunately short-lived. One month

later (August), Descartes writes to Mersenne about Fermat’s

continued objections. He says he is slow to displease him, given the com-

pliments that had been exchanged. However, ‘the enthusiasm with which

he continues to claim victory for his method and to persuade people that I

did not understand it...forces me to express some truths here that seem

to me will not be to his advantage’ (ii.). But byOctober, he writes

sympathetically to Fermat to inform him ‘frankly that I have never met

anyone who showed me that he knew as much as you do in Geometry’

(ii.), and that the residual items of dispute were comparable to ‘small

imperfections in diamonds, in contrast with great blemishes in ordinary

stones’ (ii.).

During this dispute with critics in France who were often vaguely iden-

tified, Descartes seems to have reserved his harshest comments for Pierre

Petit (–). Petit had circulated objections to theDiscourseand the

Dioptricsbeginning in March. Descartes thought he was a charlatan,

that there were as many ‘impertinences and mistakes as there are lines in

his writing,’ and that if he lived in a country where the Inquisition was

active, he would have reason ‘to fear the flames’ (ii.). By April,he

was punning on his name (Mr. Little) by describing him as a little bark-

ing dog. ‘I think you pay too much attention to Mr. Petit by contradicting

him. One should allow little dogs to bark without bothering to resist them’

(ii.).His estimation of the mathematical talents of Roberval and Fer-

mat was almost as negative. He thought Roberval was as vain ‘as a woman

who puts a ribbon in her hair in order to appear more beautiful’ (ii.).

He asked Mersenne not to bother him any further with Fermat’s letters. ‘I

am completely disgusted with his discussion, and I find nothing reasonable

in anything he says’ (ii.–). By August of, Descartes writes in

confidence to Huygens – there was no risk here, as with Mersenne, that his

comments would be reported back to their targets – to tell him that he had

done no significant work during the whole summer. There were ‘certain

people who dabbled in geometry’ and who, without understanding