Descartes's Secret Notebook

  62 brought the letters in question to Kepler and made his acquaintance: Shea, 105.

  62 aware of Kepler's work through his friend Beeckman: Adam and Tannery (1986), X:23.

  62 published it in Mysterium cosmographicum (1596): The treatise was written in July 1595, and so Kepler, who was born on December 27, 1571, was twenty-three years old at the time of his discovery. See Mehl, 17 n. 9, for details.

  CHAPTER 5: THE ATHENIANS ARE VEXED BY A PERSISTENT ANCIENT PLAGUE

  Page

  67 at two different locations separated by a known distance: This was one of the greatest scientific achievements in antiquity. Eratosthenes measured that sunlight made an angle of a fiftieth of a circle (about seven degrees) from the perpendicular in Alexandria, and cast no shadow (meaning the angle was zero) in Syene in Upper Egypt. The two cities are 500 miles apart (5,000 stadia). Hence he computed the circumference of the earth to be 50 × 500 = 25,000 miles (250,000 stadia). For more complete details see Pasachoff, Astronomy, 15.

  67 to help his countrymen rid themselves of the plague: Heath, A History of Greek Mathematics, 1:246-60.

  67 say, 1,000 cubic meters: I am using meters in this example not because the me-ter is an ancient measure (it is not), but rather because it is the only unit that allows me to use nice whole numbers such as 1,000, to make the mathematical example simple and illustrative while maintaining a reasonable size for a temple.

  CHAPTER 6: THE MEETING WITH FAULHABER AND THE BATTLE OF PRAGUE

  Page

  72 the mystic-mathematician Johann Faulhaber: Baillet (1691), 1:67.

  72 Descartes' earlier biographer, Daniel Lipstorp: Lipstorp, Spedmina philosophiae cartesianae, 78-79. The story is reprinted in Adam and Tannery (1986), X: 252-53. 73 his own book, the Geometrie, published in 1637: See Kenneth L. Manders, “Descartes and Faulhaber,” Bulletin Cartesien: Archives de Philosophic 58, cahier3 (1995), 1-12.

  73 Mehi concluded that Faulhaber and Descartes were close friends: Mehl, 193.

  74 why Descartes chose this particular pseudonym: Kurt Hawlitschek, “Die Deutschlandreise des Rene Descartes,” Berichte xur Wissenschaftsgechichte 25 (2002), 240.

  74 was born in Uhn and was trained as a weaver: Kurt Hawlitschek, Johann Faulhaber

  1580-1635: Fine Bltitezeit der mathematischen Wissenschaften in Uhn, 13. 76 the meeting between Descartes and Faulhaber: Baillet (1691), 1:68.

  76 “I want you to enter my study”: Baillet (1691), 1:68.

  76 “Cubic Cossic Pleasure Garden of All Sorts of Beautiful Algebraic Examples”: Lipstorp, Specimina philosophiae cartesianae, 79. I am indebted to Dr. Kurt Hawlitschek of Ulm for bringing this quotation to my attention.

  77 problems in Roth's book, and solved them as well: Baillet (1691), 1:69.

  78 the actual fighting since he was a volunteer: Baillet (1691), 1:73.

  80 as he had hoped to do two years earlier: Adam and Tannery (1986), X:22.

  CHAPTER 7: THE BROTHERHOOD

  Page

  83 Baillet tells us: Baillet (1692), 29.

  83 associated with the Rosicrucian order—Johann Faulhaber: Richard Watson.

  Cogito, Ergo Sum: The Life of Rene Descartes, 103, argues that Descartes had already met a Rosicrucian before his trip to Germany. According to Watson, Descartes' friend in Holland Cornelius van Hogeland was a Rosicrucian.

  86 “After six score years, I shall be found”: Baillet (1691), 1:89.

  86 The brothers made the following six rules: Baillet (1691), 1:90.

  87 “like news of a Second Coming”: Baillet (1691), 1:92.

  87 the flaming star is passed around: Anonymous, Chevalier de ? Aigle du Pelican ou Rosecroix, 5-7.

  88 Pythagorean theorem and early ideas about irrational numbers: Watson argues in Cogito, Ergo Sum, 103-4, that scholars who persist in claiming that the Rosicrucians never existed lack an understanding of the nature of secret societies and how they operate.

  89 arrested by the Jesuits shortly after the publication appeared: See Andrea, Adam

  Haslmayr, der erste Verkunder der Manifeste de Rosenkreuzer, 20.

  CHAPTER 8: SWORDS AT SEA AND A MEETING IN THE MARAIS

  Page

  93 the effects of the hostilities on the inhabitants of this region: Baillet (1691), I; 101.

  93 “could have beenfatalfor him”: Baillet (1691), 1:101.

  95 “conduct him to his destination as peacefully as possible”: Baillet (1692), 49.

  97 “lodged somewhere in the Marais of the Temple in Paris”: Visitors to the Marais today can see both the rue du Temple and the rue Vielle du Temple. 97 “in a manner imperceptible to the senses”: Baillet (1692), 55.

  99 in the form of mutual attacks: Information on Marin Mersenne comes mostly from Vittorio Boria, “Marin Mersenne: Educator of Scientists.”

  100 the worldwide correspondence he received and sent: Boria, 91.

  CHAPTER 9: DESCARTES AND THE ROSICRUCIANS

  Page

  102 by members of the Brotherhood of the Rosy Cross: Mehl, 31-36.

  102 used the term “Olympic” to mean intelligible or comprehensible: Mehl, 31.

  102 code words for philosophy, magic, and alchemy: Mehl, 32.

  102 described by Oswald Croll in his Basilica chymica: Descartes to Mersenne, February 9, 1639, in Adam and Tannery (1988), 11:498.

  103 eventually led to the decline of the order: Yates, The Rosicrucian Enlightenment, 15-29.

  103 three years before the publication of this text: Mehl, 37.

  105 as well as about their orbits in the sky: Mehl, 43-45.

  105 The Rosicrucians named their principle Est, Non est: Mehl, 104-6.

  106 selling his compass for use in engineering and for military purposes: Boyer and Merzbach, History of Mathematics, 320.

  106 A published description of Faulhaber's qualifications included the following: Testimonial about Johann Faulhaber by Johann Remmelin (1583-1632), published in Ulm in 1620, translated from the German by Kenneth L. Manders, in “Descartes and Faulhaber,” Bulletin Cartesien: Archives de Phdosophie 58, cahier 3 (1995), 2.

  107 Jacques Maritain says the following: Maritain, The Dream of Descartes, 18.

  108 Hawlitschek hypothesizes in his book: Hawlitschek, Johann Faulhaber 1580-1635: Eine Bliitezeit der mathematischen Wissenschaften in Vim.

  108 meet Faulhaber so they could discuss mathematics: Hawlitschek, “Die Deutsch-landreise des Rene Descartes,” Berichte zur Wissenschaftsgechichte 25 (2002), 235-38.

  108 which led him to invent his own, related devices: Mehl, 43.

  109 similarities in the content of the two manuscripts were discovered: Mehl, 194.

  109 “worthy of making their acquaintance”: Mehl, 212 n. 87.

  110 the first one appearing in mid-October: See Ivo Schneider, Johannes Faulhaber 1580-1635, 18-19, which includes the actual astronomical table prepared by Faulhaber. The story also appears in Shea, The Magic of Numbers, 104, although the date is given as September 1 (which would be true according to the Julian, rather than Gregorian, calendar).

  111 “cabalistic log-arithmo-geometro-mantica”: Mehl, 207. Ill in a very personal, insulting way: Mehl, 214.

  CHAPTER 10: ITALIAN CREATIONS

  Page

  114 “at leastl may become more capable”: Baillet (1692), 56.

  115 the victory and the battle never took place, and were pure fiction: Frederic C. Lane, Venice: A Maritime Republic, 57.

  116 as we would obtain today by solving the equation x+(l/7)x=19: Boyer and Merzbach, 15-16.

  117 giving the two roots, or solutions, of this equation:

  2a

  118 people had been trying for many centuries: Boyer and Merzbach, 283.

  118 and sometimes a professorship at a university: Jean Pierre Escofier, Galois Theory, 14.

  118 the coefficient of x3 is 1, and there is no x2 term: Escofier, 14.

  119 a poem in Italian in which he embedded his formula: Escofier, 14.

  120-21 work done a century earlier by
the Italians: The formulas developed by Tartaglia and Cardano and Ferrari are very complicated. Here is one of them, a general formula for the solution of the cubic equation x3 + qx — r=0. The solution is in which the cube roots are varied so that their product is always -q/3.

  121 revive the use of the equal sign we use today: Florian Cajori, A History of

  CHAPTER 11: A DUEL AT ORLEANS, AND THE SIEGE OF LA ROCHELLE

  Page

  123 a wife “of good birth and much merit”: Baillet (1691), 11:501.

  124 remained known only as “Father P.”: Baillet (1691), 11:501.

  125 Baillet tells us: Baillet (1692), 69.

  127 who wanted to observe the siege: Baillet (1691), 1:155.

  127 “well appreciated by Cardinal Richelieu”: Baillet (1691), 1:157.

  128 was there, meeting the British officers: Baillet (1691), 1:159.

  128 tried to eat the leather of belts and boots: Information about the siege obtained from documents kept at the Protestant Museum of La Rochelle.

  129 troops with their guns and ample ammunition: Today, La Rochelle is a popular tourist destination and a thriving resort town. The old part of the city, dating from the twelfth to sixteenth centuries, looks much as it did in centuries past, and the medieval walls of the harbor with their towers still stand today. But the people of La Rochelle, most of whom are Catholic, as is the case throughout France, clearly are not proud of their history. Finding any reminders of the great siege of 1628 is very difficult, and the tourist office in town can supply visitors with no brochures or any kind of information whatsoever about this part of the city's history.

  CHAPTER 12: THE MOVE TO HOLLAND AND THE GHOST OF GALILEO

  Page

  132 active population enjoyed the fruits of peace: Descartes, Oiscours de la Methode, edited by Etienne Gilson.

  132 had also contributed to his decision to leave France: Gustave Cohen, Ecrivains frangais en HoUande dans la premiere moitie du XVIIe siecle, 402-9.

  133 “by all rights declare it as your own”: Quoted in Jean-Marie Beyssade, Etudes sur Descartes, 33.

  134 “to make him ashamed, especially if I had his letter”: Descartes to Mersenne in 1629, quoted in Stephen Gaukroger, Descartes: An Intellectual Biography, 223.

  135 “had learned many things from you”: Quoted in Varaut, 109.

  135 “which you describe by the name mathematico-physics”: Quoted in Michel Fichant, Science et metaphysique dans Descartes et Leibniz, 19.

  136 “of ants and small worms”: Quoted in Beyssade, Etudes, 33.

  136 In October 1629, Descartes started to work on a book: For this date see Gilson's edition of Discours de la Methode, 103 n. 3.

  137 as he later described his resolution: Beyssade, Etudes, 36.

  137 that could enrage the powerful Inquisition: Beyssade. Etudes, 40.

  138 fifth part of his Discourse, Descartes wrote the following: Descartes, Discours de hMethode, Gallimard ed., Ill, author's translation.

  139 An excerpt follows: Descartes to Mersenne, April 15, 1630, in Adam and Tannery (1974), 1:145, author's translation.

  140 within his theory of the universe: Fichant, 22.

  140 deciphering whether a symbol was a number or an abstract sign: Fichant, 26.

  141 Hiding his physics by way of a “fable” was one more layer: J. P. Cavaille, Descartes: ha fable du monde, 1.

  143 The letter is datelined Deventer, end of February 1634: E Alquie (1997), 492-93.

  CHAPTER 13: A SECRET AFFAIR

  Page

  145 a pretty servant named Helene Jans: Some scholars believe that Jans was the name of her father.

  146 “ten years now that God has removed me from that dangerous engagement”: Varaut, 139.

  146 “prescribes for those who live in bachelorhood”: Baillet (1691), 11:89.

  146 perhaps to work as a maid for his hndlady: Gaukroger, Descartes (1995), p. 333.

  148 other mathematicians of the day: Varaut, 141.

  CHAPTER 14: DESCARTES' PHILOSOPHY AND THE

  DISCOURSE ON THE METHOD

  Page

  151 impervious to the dangers of skepticism: E Copleston, A History of Philosophy, IV:66-67.

  152 never accepting the authority of any previous philosophy: E Copleston, 67.

  152 The Discourse was Descartes' first published book: E de Buzon, preface, in Descartes, Discours de h Methode, Gallimard ed., 7.

  153 one that has no center and whose dimensions are infinite: E de Buzon in Descartes, Discours, Gallimard ed., 9.

  154 sanitized scientific writings, and published them: F. de Buzon in Descartes.

  Discours, Gallimard ed., 11. 154 when it was withdrawn from publication: F. de Buzon in Descartes, Discours,

  Gallimard ed., 11.

  154 “because of its certitude and its reasoning”: Descartes, Discours de h Methode, edited by Etienne Gilson, 52.

  155 “march forward with confidence in this life”: Descartes, Discours, edited by Etienne Gilson, 56.

  156 “rolling here and there in the world”: Descartes, Discours, edited by Etienne Gilson, 84.

  159 alluding to the association with the brotherhood: Mehl, 87. 159 “knowing more than they know”: Descartes, Discours, Gallimard ed., 82, author's translation.

  159 “one would consider the most curious”: Descartes, Discours, Gallimard ed., 78, author's translation.

  160 dealing with special knowledge: magic, astrology, and alchemy: F. de Buzon in Descartes, Discours, edited by Gallimard, 78 n. 2. See also Descartes, Discours, Etienne Gilson, 49 n. 2.

  160 the problem solved in his secret notebook: F. de Buzon in Descartes, Discours,

  Gallimard ed., 93 n. 1. 160 “sum of all the science of pure mathematics”: Fichant, 24.

  CHAPTER 15: DESCARTES UNDERSTANDS THE ANCIENT DELIAN MYSTERY

  Page

  164 on the second page of his Geometrie: Adam and Tannery (1982), VI:370.

  165 neither are any other higher-order roots: See the upcoming book by Simon Winchester, Fatal Equation (HarperCollins, 2009), for the story of the life of Galois.

  CHAPTER 16: PRINCESS ELIZABETH

  Page

  168 set his dogs on the impudent peasant: J.-M. Beyssade and M. Beyssade, eds., Descartes: Correspondence avec Elizabeth, 24.

  169 “mysteries of nature as well as geometry”: Baillet (1691), 11:233.

  171 “both disciplines are equally easy to understand”: Baillet (1691), 11:233.

  172 to take care of a fellow royal in distress: Gaukroger, Descartes, 385.

  173 wanted to devote her life to studying it: Baillet (1691), 11:231.

  CHAPTER 17: THE INTRIGUES OF UTRECHT

  Page

  175 “only because we clearly and distinctly perceive this”: Adam and Tannery

  (1983), VII:214. See also Gaukroger, Descartes, 343. 177 “belongs to the Society of the Brothers of the Rosy Cross”: Quoted in Mehl, 92.

  179 helping him promote his teachings in Holland: Varaut, 235.

  CHAPTER 18: THE CALL OF THE QUEEN

  Page

  181 “the most intimate secrets of his heart”: Baillet (1691), 11:242.

  182 “ever love me because I resemble you in any way”: Baillet (1691), 11:243.

  182 Descartes wrote the following curious passage: Descartes to Chanut, from

  Egmond, Holland, November 1, 1646, in Beyssade and Beyssade, 245-46. 186 “the letter Your Majesty has written me”: Beyssade and Beyssade, 284.

  186 Alexander the Great comes to mind: Varaut, 254.

  187 “place where I might do better”: Beyssade and Beyssade, 281.

  188 “from aperson another religion”: Varaut, 258.

  191 the last letter Descartes would write to her: Descartes to Elizabeth, from Stockholm, October 9, 1649, in Beyssade and Beyssade, 234-35.

  192 “M;y desire to return to my desert grows every day more and more”: Varaut, 269.

  CHAPTER 19: THE MYSTERIOUS DEATH OF DESCARTES

  Page


  194 “theologians of Utrecht and Leyden had dechred upon him”: Baillet (1691), 11:417.

  195 to offer his services to the ailing philosopher: Baillet (1691), 11:417.

  195 “as an adult in good health without bleeding”: Reported in Baillet (1692), 49.

  196 “I will die with more contentment if I do not see him”: Baillet (1691), 11:418.

  197 did not take well to his philosophy: Baillet (1691), 11:415.

  197 the chim that Descartes was poisoned: Varaut, 271-81.

  198 the man she called “M;y Illustrious Master”: Baillet (1692), 268.

  199 paying for the expenses of Descartes' funeral: Baillet (1691), 11:425.

  199 in the Church of Sainte-Genevieve-du-Mont in Paris: Baillet (1692), 270.

  199 in the ancient Church of Saint-Germain-des-Pres: These details are from Genevieve Rodis-Lewis, in John Cottingham, ed., The Cambridge Companion to Descartes, 57 n. 74.

  200 be buried with the rest of his bones: See Berzelius to Cuvier, April 6, 1821, in Adam and Tannery (1983), XII:618-19.

  200 the Musee de I'Homme (the Museum of Man) in Paris: The museum is at the Trocadero, across from the Eiffel Tower, in Paris. I tried to decipher the writings on the skull when I visited the museum in the summer of 2004-I could make out only the word “Stockholm” and a date that looks like 1660 or 1666.

  201 the deceased philosopher's valet, Henry Schluter: Adam and Tannery (1986), X:l, after Baillet.

  201 making a small fortune on these items a few years later: Adam and Tannery (1986), X:l, after Baillet.

  202 Chanut took all of these items under his “particular protection”: Adam and Tannery (1986), X:3, after Baillet.

  203 neither time nor patience for publication requests: Adam and Tannery (1974), I:xvii (based on Lipstorp).