Descartes versus Fermat

Descartes read new books on mathematics and physics, coming from France through Father Mersenne, Mr. de Zuytlichem, and some booksellers in Holland.

One of these was of Beaugrand, the king’s secretary, on geostatics.

But Descartes was not very favorable to Mr. de Beaugrand, of whose capacity he had never had a very advantageous opinion.

De Beaugrand had also contributed on his side to diminish the esteem that Descartes could have had for his heart and his mind, when he had let himself go to jealousy against Des Argues.

Seeing that this one was interested with Father Mersenne to serve Mr. Descartes in the pursuit of the privilege that was asked of the court of France for the printing of his works, “he believed he had to throw obstacles in its way, following the bad commitment in which he had put himself to take the opposite side of Mr. Des Argues.” As a result of these steps he continued to render bad services to Mr. Descartes: and not having been able to prevent his essays from being printed with the permission of the king in Holland, he no longer found any other resource to the passion he had to harm him than that of decrying his works even before he had been able to see them, and to stifle them at their birth if it had been possible. He had hardly been able to seize a copy of the optics, either by surprising the kindness of Father Mersenne to whom Mr. Descartes had the last proofs sent, or by abusing the fidelity of the printer of Leyde, who had sent him the sheets as they were pulled from the press as we have noted elsewhere, that he had shown his eagerness to find him censors rather than readers. Finally he seemed to have wanted to top off his ill will by inserting something against him in his book on geostatics which was currently being printed, on the hurried reading he had made of some parts of his optics before sending it to Mr. de Fermat.

It must be admitted that Mr. Descartes appeared a little too sensitive at first to the irregularity of this conduct for a philosopher of his rank: and the indifference that he testified to seeing the book on geostatics could be suspected of affectation. The prejudice he conceived against this work was found (fortunately for his reputation) to be true and solid: but it seems that chance and resentment had little less part in it than his discernment. Mr. de Beaugrand’s book had almost as many censors as it met with intelligent readers. One of the first who refuted it was Mr. de La Brosse, a doctor by profession: and it was necessary that the book be of a great weakness to fall under these first blows, which in the judgment of the skillful people of the profession, were neither too rude, nor too cleverly delivered.

Mr. de Fermat, who was a particular friend of Mr. de Beaugrand, looked at this disgrace with eyes that marked the tenderness and compassion of his heart.

He would undoubtedly have spared nothing to support his interests, if he had a reason “to defend his cause without harming his own reputation”: and he had explained himself about it to Father Mersenne from the month of October or November of the previous year in these terms. “You sent me two discourses,” says Mr. de Fermat to this father, “one of which is against Mr. de Beaugrand, and the other is of the composition of Mr. Des Argues. I had already seen the second which is pleasant and made with a good mind. As for the first (that of Mr. de La Brosse against Mr. de Beaugrand) it cannot be bad if we remove the words of acrimony. For the cause of Mr. de Beaugrand is completely deplored. I wrote to him the same reasons from your printed matter to him himself, as soon as he had sent me his book.” The judgment of Mr. Descartes perfectly agreed with that of Mr. de Fermat on this point. “I have received,” he says to the same father, **“only a few days ago the two little books in folio that you sent me, one of which which treats of perspective “and which is by Mr. Des Argues” is not to be disapproved of, besides the curiosity and the neatness of his language is to be esteemed.

But as for the other (that of Mr. de La Brosse) I find that he refutes very badly a thing that I believe is very easy to refute, and that his silence would have been better than what he did.”** He then learned with pleasure that he had agreed on this point with Mr. de Fermat, and he still lowered something of the esteem he could have had before for Mr. de Beaugrand. “It is necessary,” he says, “that the pretended demonstration of geostatics be very defective, seeing that Mr. de Fermat himself who is so a friend of the author, disapproves of it; and that I who have not seen it, have judged that it was badly refuted, for the sole reason that I could not imagine that it was so little thing that what I saw was being refuted.”

These ways of judging others soundly, although different in these two rare men, can be considered as traits of the superiority that geniuses of the first order have above common minds. Mr. de Fermat closes his eyes to the interests of his friend, and approves the refutation that is made of his book, with a few harshness excepted. Mr. Descartes forgets the bad services of a man who had sought all the ways to disoblige him, and cannot approve a weak refutation of a bad book, in the decrying “of which he seemed to have some interest.” This apparent difference comes only from an equal background of integrity in one and the other: and without thinking of imitating each other they equally take care to prevent the effects of their passion, and they reunite in their main judgment, which ended in considering geostatics as a bad work, and in not approving its refutation in the manners and the style of Mr. de La Brosse.

The instances that Father Mersenne and Mr. Des Argues made to Mr. Descartes however prevailed over the resolution he had taken not to see the book of Mr. de Beaugrand. He therefore had it sought in Leyde and in Amsterdam, but in vain, and it was necessary to have it come from Paris. He had defended himself until then from seeing it, not by a feeling of contempt, but by the experience he had elsewhere of the mediocrity of the author, and by a wonderful aversion he had “for taking up the faults of others.” It was following this disposition of mind that he often declared himself against satirical writings, and against too bitter refutations. It was also what had prevented him from approving the book of Mr. de La Brosse against Mr. de Beaugrand. Besides, he says, “that Mr. de La Brosse had stopped at taking up things that could be excused: after which he had finished his refutation without showing the continuation of the reasoning that he was refuting.” So that those who like Mr. Descartes had not seen the geostatics of Mr. de Beaugrand had every reason to judge that Mr. de La Brosse had been content to “scratch him, or pull out his hair,” without having inflicted deep wounds on him.

Finally, he received the book of geostatics around the beginning of the month of June, by means of his “limousin,” that is to say, a new valet de chambre that Father Mersenne had sent him to succeed the young Gillot who had become a man of importance by the liberalities of his master, and who had made himself skillful enough under him to teach mathematics to others. He had no sooner read the geostatics than he recognized the precipitation with which he had judged Mr. de La Brosse. Having found the book even worse than his prejudice had made him conceive, he understood with Mr. de Fermat how the refutation of this “book could be good, although in considering it separately he could not regard it as a good piece because of the acrimony of its terms, and the little connection he had found in its reasoning.”

As for the judgment he made of geostatics after having read it, he found himself obliged to send it to Father Mersenne, as much for the satisfaction of this father as for that of Mr. Des Argues, to whom he was no longer in a state to refuse anything. This is what he did a few days later in a letter he wrote about it to this father in these terms. **“Although the faults that are found in the writing of geostatics are so gross that they cannot surprise anyone, and that for this subject they deserve rather to be despised than contradicted: nevertheless, since you desire to know my opinion, I will put it here in a few words.

I found in all this beautiful book in folio only a single proposition, although the author counts thirteen. For as for the first three and the tenth, they are only things of geometry so easy and so common that one cannot understand the elements of Euclid without knowing them. The V, VI, VII, VIII, IX, and X are only sequels, or repetitions of the fourth; and they cannot be true, if it is not. For the VII, the XII, and the XIII it is true that they do not depend thus on this fourth: but because the author uses them to try to prove them, and even that he only uses it alone for that, and that besides they are no more than the others of any importance, they should not be counted. So that there remains only the fourth all alone to consider: and it has already been so well refuted by Mr. de La Brosse that it is not necessary to add anything to it. For of five or six faults that he notes there, the smallest is sufficient to show that the reasoning of this author is not worth anything at all. I was very wrong last year in seeing this refutation of Mr. de La Brosse, without having seen the book that he refuted, not to approve of it. But the only reason that prevented me from it, was that I could not imagine that the things he took up were so absurd as he represented them: and I persuaded myself that he only exaggerated some omissions, or faults “committed by inadvertence, without touching the main reasons of the author.” But I see now that these main reasons, which I supposed had to be in his beautiful book, are not found there. And although I have seen many quadratures of the circle, of perpetual movements, and other similar pretended demonstrations which were false, I can nevertheless say with truth that I have never seen so many errors joined together in a single proposition.

In the paralogisms of the others one is accustomed to not meeting anything at first that does not seem true, so that one has trouble noting among many truths some small mixture of falsehood, which is the cause that the conclusion is not true. But here it is the opposite. One has trouble noting any truth on which this author has based his reasoning: and I cannot guess anything else that gave him occasion to imagine what he proposes, except that he equivocated on the word of “center” and that having heard the center of a balance named as well as the center of the earth, he imagined that what was true with regard to one, had to be also with regard to the other, from which he fell into a very great number of gross faults… in general, one can say that all that this book of geostatics contains is so little, that I am surprised that honest people have ever deigned to take the trouble to read it: and I would be ashamed of that which I took to mark you my opinion of it, if I had not done it at your request. I know that on your side you only asked me for it with the intention of making me say my opinion of the matter that the author treats there, without caring much about the way he treated it.

But it is a subject that well deserves that I employ some of my best hours on it, whereas I only gave one of those that I wanted to lose to this one. That’s why I prefer to send it to you separately on the first trip.”**

In order not to fail his word, he worked incessantly on the “examination” that he had promised to these two friends of the “geostatic question” in itself; and he made a small treatise of it that he sent them around the 22nd, or 23rd day of the month of July. Father Mersenne was so content with it that he wrote back to him the first day of August, to tell him that in his sense he had surpassed himself in this writing, and that this small treatise contained all the mechanics, except the single force of “percussion.” Father Mersenne did not believe he had to remain in the terms of this compliment, and fifteen days later he told Mr. Descartes that Mr. Des Argues and the other scholars to whom he had shown this writing were of the opinion that it should be printed. Mr. Descartes replied to him around the beginning of September that the writing did not at all deserve to be published: but that if it was absolutely desired that it be, the thing was quite indifferent to him, provided that his name did not appear there, and that some terms of acrimony were removed, and some too harsh epithets that he had used against the geostatician, in the thought that they would fall, and that they would perish under the hand of Father Mersenne, with the letter he wrote to him about it in private. It is not that according to him these epithets did not suit Mr. de Beaugrand well enough by treating him with rigor: but he recognized that it was not convenient for him to write them; and that they had escaped from his pen “only in favor of the trick he had played” on Father Mersenne, Mr. Des Argues and him, for the privilege of his essays.

It would have been a beautiful trait of generosity in Mr. Descartes not to have let himself go to his resentments at the first blow. But having had this weakness, it was still glorious enough for him to get up from it so early. To repair it still in a way more worthy of him, he revoked by a letter of October 1 to Father Mersenne the permission he seemed to have given him to print his geostatic writing, under the pretext that he had not composed it with this view. He also alleged as a reason that this small treatise was not finished enough to walk alone. On the other hand, it would have been in his opinion to give him a very bad company to join it with his opinion of the book of Mr. de Beaugrand. Besides, he would have been ashamed that one would have taken the occasion to believe that he would have stopped seriously to say his opinion of this book. In addition, these two writings being joined together would have made “only a book worthy of being covered with blue paper.”

But so that his refusal did not entirely chagrin Father Mersenne, he added that if his geostatic writing contained something that was worth the trouble of being seen, he believed that it would be more appropriate to insert it in the collection of the objections that had been made to him until then and that were to be made to him in the sequel. In fact, this collection was to be only a bundle of all kinds of matters: and his intention was to have it printed volume by volume as he would see the matters grow, as much of the objections of others, as of his answers and of his other flying writings.

Some Cartesian mathematicians of our days have believed that this geostatic writing was melted in the cell of Father Mersenne, and that this father for having refused to communicate it to the envious of Mr. Descartes, seemed to have innocently contributed to the loss that the public would have made of it, in the supposition that the friends to whom he had had it read, would have given it back into his hands, without having taken a copy of it. But it appears that this writing is none other than that which we find printed in the first volume of the letters of Mr. Descartes concerning the question of knowing, “if a body weighs more or less being close to the center of the earth than being far from it.” One will have almost no reason to doubt it, if one notes that this writing is the effect of the promise he had made ten days before, that is to say, towards the middle of July to Mr. Des Argues and to Father Mersenne, to send them an examination or dissertation of the geostatic question by the first ordinary after that by which he sent them his opinion on the geostatics of Mr. de Beaugrand. Some Cartesians of our days have believed that this writing was truly “the statics” of Mr. Descartes, and they seem to have wanted to confuse the genus with its species: but Mr. Descartes gave them the example by using the same expression in some encounters, and even in other occasions of a still more general term to call this treatise his “small writing of mechanics.” We have seen that Mr. Descartes to take away from Father Mersenne the desire to have it printed had used the pretext that it was not finished. In fact, he fell asleep at the end, so that having gone to rest, he had the writing transcribed the next morning, and sent it to the post for Paris without rereading it, and without thinking that he had not finished.

Mr. Des Argues noticed it, and he said his thought about it to Father Mersenne, who wrote to Mr. Descartes the first day of September to inform him of it, and to let him know at the same time that some made difficulty in admitting the principle he had supposed in his examination of the geostatic question.

Mr. Descartes judged these two points too important to delay a long time in answering Father Mersenne. He therefore sent him from the 12th of September an ample explanation to serve as a demonstration to the principle he had supposed in his writing, persuaded that when he had saved this principle from criticism, he would protect all the deductions he had made from it.

As for the other point which concerned the defect that Mr. Des Argues had noted at the end of his writing, Mr. Descartes admitted the fact; and he recognized that not only had he not finished his writing, but that he had even mistaken himself in the last lines he had written of it, because the overwhelming where sleep had reduced him had made him lose the attention that was necessary to him. This is what made him ask Father Mersenne to thank Mr. Des Argues for his advice, and then to erase the last lines of his writing where the defect began.