Excessively rare and mathematically important handwritten letter by Rene Descartes, alluding to the 'Theorem of Circles' and his condemnation at Utrecht
Excessively rare and mathematically significant ALS in French, signed “Descartes,” one page, 8.5 x 12.25, October 21, 1643. Handwritten letter to his friend Alphonse de Pollot, alluding to one of his mathematical theories, the Theorem of Circles (a premise to what is known today as Descartes’ Theorem), and sending thanks for his support in the Quarrel of Utrecht. Descartes vilifies his Protestant enemy at Utrecht, Gisbertus Voetius, and notes that he had recently proposed the 'Problem of Apollonius'—a famous mathematical problem involving the construction of a circle within a plane—to Princess Elisabeth of Bohemia, but fears it may be too difficult for her to solve.
Descartes opens the letter by offering thanks for Pollot's support in the Quarrel of Utrecht (translated): “I have no words to express the resentment that I have of the obligations that I have to you, but I assure you that it is extreme, and that I will keep them all my life.” After staying there sporadically, Descartes settled permanently in Holland in the spring of 1629. It was in these Batavian lands that the philosopher published his most famous texts: Méditations métaphysiques (1641), Principes de la Philosophie (1644 ) and the famous Discours de la Méthode, published in Leyden in 1637. Descartes' philosophy, opposed to the scholastic principles, did not fail to annoy the Protestant authorities, the first of which was Gisbertus Voetius, who launched a cabal against Descartes and his friend Henricus Regius, professor at the University of Utrecht. Accusing Descartes of atheism, Voetius instigated the publication of a brutal pamphlet, ‘Admiranda methodus,’ written by his pupil Martin Schook, in which Descartes is described as ‘a lying mouth’ and ‘a bastard of Christianity.’ This 'Quarrel of Utrecht' grew so tense that the philosopher called on the ambassador of France to defend him.
Descartes was condemned by the University of Utrecht on March 17, 1642, prohibiting the discussion of his works and making him subject to criminal charges, thereby forcing him to flee to The Hague. Thanks to his influential friends, Descartes was never put on trial, though he felt his reputation had been damaged. According to this letter's postscript, the matter had been settled for eight days: "I have been informed from Utrecht that there is no more fear for me, and that the name of His Highness, in Mr. de Ryusmond's letters, has calmed the whole storm. It was the chief joy I felt, to see that name revered, if not as it should, at least enough to prevent injustice in a town prone to mutiny and where the rebellious spirit of Voetius dominates." It would take 363 years for Descartes to be officially vindicated by the University of Utrecht—on March 23rd, 2005, the prestigious university finally lifted its condemnation of the teaching of the works of Descartes.
Additionally, Descartes makes mention of his famous correspondence with Princess Elisabeth of Bohemia, a well-educated royal who became his student in philosophy and morals. Here, he writes of sending her a geometrical problem of three circles, also known as Apollonius’ problem. In part (translated): "I regret having proposed the question of the three circles to the Princess of Bohemia, since it is so difficult, that it seems to me that even an angel who had no other instruction in algebra than that which St[ampioen] had given her couldn’t solve it without a miracle.” In solving the problem, René Descartes gave a formula relating the radii of the solution circles and the given circles, now known as Descartes' theorem. In spite of Descartes’ fears of its great difficulty, Princess Elisabeth also pioneered an alternate algebraic solution to Apollonius' problem. Descartes so admired the intellect of Elisabeth that in 1644, he dedicated his Principia philosophiae to the princess.
Addressed on the integral leaf in Descartes' hand to "Monsieur Alphonse de Pollot, Gentilhomme de la Chambre de son Altesse à la Haye." Housed in a custom-made slipcase. The letter is in fine condition, with intersecting folds and several small holes affecting the blank margin and address panel. Accompanied by full transcript in French, and an official French brochure published by the Imprimerie Nationale Exécutive du Louvre containing the decrees of the National Convention of October 2nd and 4th, 1793, granting "René Descartes the honors due to great men, & order to transfer to the Panthéon François his body, & his statue made by the famous Pajou."
This important letter is referenced in ‘Princess Elizabeth of Bohemia and Descartes’ letters’ by Erik-Jan Bos, published in Historia Mathematica in 2010. Bos writes: ‘On 21 October 1643 Descartes wrote to his friend Alphonse Pollot that he had recently proposed a mathematical problem to Elizabeth, but now feared it was too difficult. The problem in question was the problem of three circles, also known as Apollonius’ problem: given three circles in a plane, find a fourth circle that touches each of them. Descartes furthermore assumed that the required circle is located in the space between the three circles. Barely a month later, on 17 November, Descartes sent Pollot a letter for Elizabeth that contained his solution to the problem. On 21 November, Elizabeth sent her own solution to Descartes with a covering letter. Although Elizabeth’s solution is lost, Henk Bos has reconstructed it from Descartes’ reply of 29 November…According to Bos, Elizabeth’s solution is especially interesting, because, in the light of her efforts to solve the problem, Descartes changed or at least adjusted his opinions on the best way to approach geometrical problems.’
- Marquis de Queux de Saint-Hilaire’s collection (the letter was published for the first time by Victor Egger in the Annales de la faculté des Lettres de Bordeaux).
- Auction in Paris, Drouot - December 1981.
- Private collection.
- Lettres inédites de Descartes. E. de Budé. Durand & Pedone-Lauriel (1868, pp. 12-16)
- Annales de la faculté des Lettres de Bordeaux. Victor Egger (1881, pp. 190-191)
- Adam et Tannery, Œuvres de René Descartes, IV : Correspondance, lettre nº CCCXX.
- Descartes : œuvres/lettres, Pléiade, Gallimard, 1999, Paris, p.1108
- Vie de Monsieur Descartes, Adrien Baillet, Éditions Table Ronde, Paris, 1992, II.
- Descartes, Correspondance, Tome IV, Librairie philosophique J. Vrin.
- “Princess Elizabeth of Bohemia and Descartes’ letters (1650-1665)” by Erik-Jan Bos, Historia Mathematica (Volume 37, Issue 3, August 2010).
- "What Someone May Have Whispered in Elisabeth’s Ear” by Vlad Alexandrescu, Oxford Studies in Modern Philosophy, 2012.