Five Unknown Items from the Correspondence of Marin Mersenne

Notes

• Mersenne , M. Correspondance C. de Waard et al., 17 vols (Paris, 1933–88) [hereafter: MC]. The principal editors were Cornelis de Waard, Bernard Rochot, and Armand Beaulieu; other contributing scholars included René Pintard, Robert Lenoble, Jean Jacquot, Jean Bernhardt, and Alan Gabbey.
   Google Scholar
• Malcolm , N. 2001 . ‘Six Unknown Letters from Mersenne to Vegelin’ . The Seventeenth Century , 16 95–122.
   Google Scholar
• 1919 . Le Docteur Lazare Meyssonnier, conseiller et médecin du Roi, professeur de chirurgie à Lyon, 1611–1673 2 – 3 . Grenoble The date 1602, given in most reference works, is incorrect; the true date is established in the most detailed biographical study of Meyssonnier, G. Vellein, pp. (Vellein's pamphlet was printed in only 75 copies; it is not held by the Bibliothèque Nationale, nor by any library in Britain, but there is a copy in the Bibliothèque Municipale, Mâcon, pressmark 11068, fonds ancien.)
   Google Scholar
• Ibid. 7 – 10 . L. Meyssonnier, Oenologie ou discours du vin et de ses excellentes propriétés pour l'entremise de la santé et guérison des plus grandes maladies (Lyon, 1636).
   Google Scholar
• Vellein . Le Docteur Meyssonnier 10 – 12 .
   Google Scholar
• 2000 . Logic and the Art of Memory 94 London For comments on Meyssonnier's connection with the Lullian tradition of the ‘art of memory’ see P. Rossi, tr. S. Clucas, p.
   Google Scholar
• MC VIII, 330–3; here 331. The term ‘cahiers’ could also mean ‘gatherings’ (folded printed sheets); but Meyssonier's letter shows that he was still seeking a publisher at this stage.
   Google Scholar
• Atti della Accademia Nazionale dei Lincei R. de Mattei, ‘Un medico-filosofo francese estimatore ed amico del Campanella: Lazare Meyssonnier’, ser. 8, Memorie: classe di scienze morali, storiche e filologiche, 16 (1971–2), fase. 6 (351–79); here 378 (following Vellein).
   Google Scholar
• Meyssonnier . 1985 . Pentagonum 42 Paris ('R. P. M. Mersennus, Ordinis Minimorum, in Physicis, Mathematicis, quemadmodum & Theologicis Arcanis selectissimis, & reconditissimis Doctor Maximus, scriptor purissimus, vir humanissimus, Lutetiae à nobis visus, anno superiore M.DC.XXXVIII'). This comment arises when Meyssonnier says that he will not say anything more about the force of the imagination ('vis imaginations’), because he is awaiting the treatise on that subject promised by Mersenne. For Mersenne's promise (never fulfilled) of a work on ‘la force de l'imagination’, see his Les Questions théologiques, physiques, morales, et mathématiques [1634], qu. 17, printed in M. Mersenne, Questions inouyes; Questions théologiques; Les Méchaniques de Galilée; Les Préludes de l'Harmonie universelle, ed. A. Pessel, p. 280
   Google Scholar
• Meyssonnier . Pentagonum 81 ('Harmonica R. P. M. Merseni, Viri clarissimi, doctissimi, &C excellentissimi’).
   Google Scholar
• 33 – 4 . MC, VIII, 333 ('où je traitte des causes des qualités qui sont en vostre livre de Causis sonorum); M. Mersenne, Harmonicorum libri (Paris, 1636), book 2, prop. 42, pp.
   Google Scholar
• Meyssonnier . Pentagonum 16 The Jardin des Plantes, which began functioning in 1635 but did not open to the public until 1640, was a centre for the study of chemistry as well as medicinal botany (see R. Howard, La Bibliothèque et le laboratoire de Guy de La Brosse au Jardin des Plantes à Paris (Geneva, 1983)).
   Google Scholar
• Meyssonnier . Pentagonum 17 – 9 . 36, 42, 75; cf. also his De abditis epidemion causis paraenetica velitatio (Lyon, 1641), p. ('nobis amicitiae & honoris causae semper nominandus R. Campanella’); his Nova, et arcana doctrina febrium (Lyon, 1641), p. 65; and MC, IX, 362. On the friendship with Campanella see de Mattei, ‘Un medico-filosofo francese’, esp. pp. 376- (where, however, the assumption is made that Meyssonnier did not visit Paris before 1641). It is surely also significant that the surintendant des finances Claude de Bullion was the dedicatee of both Campanella's Metaphysica in 1638 (see T. Campanella, Lettere, ed. V Spampanato (Bari, 1927), pp. 394–8) and Meyssonnier's Pentagonum in 1639. On Campanella's final years (1634–9) in France, see M.-P. Lerner, Campanella en France au XVIIe siècle (Naples, 1995).
   Google Scholar
• 1641 . Exercitatio in Hippocratis aphorismum de calculo ad N. V. Claudium Salmasium 208 Leiden J. van Beverwijck [I. Beverovicius],. p., Meyssonnier to van Beverwijck, 5 January 1640 ('dum Lutetiae, vocatus ad curam Aulici cujusdam fistulâ desperatâ laborantis, anno superiore degerem’).
   Google Scholar
• Ibid. 210 – 6 . for previous letters from Mersenne to van Beverwijck see pp. 203-, 206–8. For subsequent correspondence between van Beverwijck and Meyssonnier see pp. 213–14, 216–37.
   Google Scholar
• Trevisani , F. “ ‘Un corrispondente di Cartesio: alcune note su Lazare Meyssonnier (1611/12–1673), medico e astrologo lionese e sulla sua ” . In Belle Magie 37 – 44 . See (1669)’, History and Philosophy of the Life Sciences, 1 (1979), 285–308, esp. 285–98; and F. A. Meschini, Neurofisiologia cartesiana (Florence, 1998), pp.—(with a more complete tabulation of the correspondence: p. 38, n. 33).
   Google Scholar
• 1665 . DD. virorum epistolae et responsa, tum medica, tum philosophica 104 Rotterdam J. van Beverwijck [J. Beverovicius], ed., p. ('res aulicae’; ‘saepius viro reverendo M. Mersenno nostro occurro’). While he was there, Meyssonnier may also have made the acquaintance of Gassendi: a letter from the Genoese physician Girolamo Bardi to Gassendi of 23 January 1642 begins, ‘I had already been told in confidence by the distinguished Meyssonnier that you were staying in Paris’ ('Inaudiveram iam à Cl. Meyssonnerio te Lutetiae commorari’: P. Gassendi, Opera omnia, 6 vols (Lyon, 1658), VI, 444).
   Google Scholar
• DD. virorum epistolae 110 – 18 . van Beverwijck, pp.—(here p. 110). An extract from this letter is printed in MC, X, 765, where it is mistakenly described as a letter from van Beverwijck to Meyssonnier. In a letter datable to between September and early November 1641, Mersenne wrote to Vegelin: ‘Nous auons icy vn Medecin de Lyon, qui fait merueille pour guérir des fieures quartans’ (Malcolm, ‘Six Unknown Letters’, p. 105); very possibly this referred to Meyssonnier.
   Google Scholar
• Vellein . Le Docteur Lazare Meyssonnier; 33 – 7 . See this is corrected and supplemented on some points by de Mattei, ‘Un medico-filosofo francese’, and by E. Labrousse, L'Entrée de Saturne au Lion: l’éclipsé du soleil du 12 août 1654 (The Hague, 1974), pp. For comments on his character see N. Chorier, D. Petri Boessati…vita amicisque litteratis libri duo (Grenoble, 1680), pp. 223–8. One further piece of evidence of Meyssonnier's intellectual interests, not noticed by previous writers, may be added here: his letter to Athanasius Kircher of 26 May 1661, praising Kircher's works (Ponteficia Università Gregoriana, Rome, MS 555, fol. 271; this has been incorrectly catalogued as a letter from ‘Mensonnier’).
   Google Scholar
• See n. 7, above.
   Google Scholar
• Meyssonnier . Nova, et arcana doctrina 76 13 (Descartes), 95 (Harvey); Pentagonum, p. ('experimentorum testimonio’). The term ‘experimenta’ could be translated as ‘experiments’; but Meyssonnier otherwise shows no interest in interventive experimentation.
   Google Scholar
• Meyssonnier . De abditis epidemion causis 10 – 11 . ('miasma pestiferum’), 13–20. Meyssonnier explained in the Preface (sig. a3v) that this work was written before the Pentagonum; it was presumably the work referred to in his letter to Mersenne of 25 February 1639 ('un autre que j'ay escript aussi en latin des causes de la peste’), which the editors of MC (VIII, 332) were not able to identify.
   Google Scholar
• Meyssonnier . 2000 . Pentagonum Pisa sig. ¶ ¶ ¶2r. This letter is omitted in Campanella, Lettere, ed. Spampanato, and in T. Campanella, Lettere, 1595–1638, non comprese nell'edizione di Vicenzo Spampanato, ed. G. Ernst.
   Google Scholar
• Lerner . Tommaso Campanella en France 17 – 31 . See pp.—, 63–4.
   Google Scholar
• Meyssonnier . Pentagonum 48, 67, 76, 88.
   Google Scholar
• MC, IX, 94, 29 January 1640 ('il y mesle tant d'astrologie, de chiromancie et autres telles niaiseries, que je n'en puis avoir bonne opinion’).
   Google Scholar
• Mersenne . Questions inouyes 279 ('chaque astre n'a point d'autre force sur nous que celle qu'il exerce avec sa lumiere, et sa chaleur’).
   Google Scholar
• BL, pressmark 722.i.20, collated with Bodl., pressmark 4° M 10 (2) Med. In the Bodleian copy, sig. ¶ ¶ ¶2 has been misbound (in the final gathering).
   Google Scholar
• 1974 . Athanasius Kircher S.J.: Master of a Hundred Arts, 1602–1680 Wiesbaden For biographical details see C. Reilly,.
   Google Scholar
• Athanasius Kircher: The Last Man who Knew Everything 13 – 15 . See MC, III, 432, 459, 504; XII, 29; and the comments in P. Findlen, ‘Introduction’ to E Findlen, ed., (New York, 2004), pp. (The clock used a sunflower, which turned to face the sun during the day: see the illustration reproduced in M. Baldwin, ‘Kircher's Magnetic Investigations’, in D. Stolzenberg, ed., The Great Art of Knowing: The Baroque Encyclopaedia of Athanasius Kircher (Stanford, Calif., 2001), pp. 27–36, at p. 31.)
   Google Scholar
• Opera omnia See MC, III, 426, and Gassendi, VI, 413–14.
   Google Scholar
• Kircher , A. 1641 . Magnes sive de arte magnetica opus tripartitum 79 – 97 . Rome On Kircher's work in this field see W Hine, ‘Athanasius Kircher and Magnetism’, in J. Fletcher, ed., Athanasius Kircher und seine Beziehungen zum gelehrten Europa seiner Zeit (Wiesbaden, 1988), pp.—, and Baldwin, ‘Kircher's Magnetic Investigations’. Mersenne's letter to Theodore Haak of 31 December 1639 shows that he had heard of Kircher's work from a third party (MC, VIII, 722); the fact that Mersenne's printed text was addressed to Naudé makes him the obvious candidate. For evidence of Naudé's closeness to Kircher at this time see Kircher's letter to Gassendi of 2 June (also discussing his work on magnetism): Gassendi, Opera omnia, VI, 436–7. On Mersenne's dealings with Kircher see also the study by W Hine, ‘The Mersenne-Kircher Correspondence on Magnetism’, in J. F. Sweets, ed., Proceedings of the Tenth Annual Meeting of the Western Society for French History, 14–16 October 1982 (Lawrence, Kansas, 1983), pp. 106–17 (which, however, is based only on the published correspondence).
   Google Scholar
• ibid. For the text see BL, MS Add. 4279, fols 145–6, printed in MC, VIII, 754–62. The first clear reference to this text is in Mersenne's letter to Johann Heinrich Bisterfeld of 15 October 1639 (533); Mersenne also sent a copy to Haak on 1 November (ibid., 584). The editors of MC suggest that the otherwise unidentified item sent by Mersenne to Grotius on 14 August was another copy of the same printed text (ibid., 483), but this seems less likely: that item was called a ‘livret’ (small book), whereas the phrases used to Bisterfeld and Haak were ‘foliolum’ and ‘fueillet’ (sheet). (John Pell called it a ‘charta’ (piece of paper): ibid., 631.) The ‘livret’ was more probably Mersenne's French translation of Edward Herbert's De veritate, of which Mersenne was distributing copies in early August 1639: see MC, VIII, 476–8.
   Google Scholar
• Mersenne , M. 1623 . Quaestiones celeberrimae in Genesim 889 – 901 . Paris cols 545–53; La Vérité des sciences contre les sceptiques ou pyrrhoniens [1625], ed. D. Descotes (Paris, 2003), pp. Questions théologiques, qu. 27, in Questions inouyes, pp. 311–13. See also W Hine, ‘Mersenne and Magnetism’, in J. F. Sweets, ed., Proceedings of the Twelfth Annual Meeting of the Western Society for French History, 24–27 October 1984 (Lawrence, Kansas, 1985), pp. 58–66
   Google Scholar
• MC, VIII, 761 ('quem de vi Magnetica meditari scribis’). Mersenne also promised to send Kircher his own observation of the degree of declination in Paris.
   Google Scholar
• Ibid. , 760 ('In eodem terrae puncto, sive eâdem regione, Magnetes omnes eodem modo déclinant’).
   Google Scholar
• Ibid. 247 – 67 . 631–2 (H. Gellibrand, A Discourse Maihematicall on the Variation of the Magneticall Needle (London, 1635)). On the work by English researchers in the 1630s see A. R. T. Jonkers, North by Northwest: Seafaring, Science, and the Earth's Magnetic Field, 2 vols (Göttingen, 2000), 1,330–5. See also the discussion of these issues in S. Pumfrey, ‘”These 2 hundred years not the like published as Gellibrand has done de Magnete”: the Hartlib Circle and Magnetic Philosophy’, in M. Greengrass, M. Leslie, and T. Raylor, eds, Samuel Hartlib and Universal Reformation: Studies in Intellectual Communication (Cambridge, 1994), pp.—(though Pumfrey gives a rather exaggerated account of the critical reactions of Mersenne and Pell to each other's work).
   Google Scholar
• Houghton Library, Harvard University, fMS Lat 306.1; this letter is the third in the group.
   Google Scholar
• Kircher . Magnes 453 – 4 . ('ex relatione Mersenni’). Mersenne's informant in Dordrecht was probably van Beverwijck. (Cornelis de Waard suggests that the measurement had been made by Mersenne himself on his visit to Dordrecht in 1630: MC, II, p. 525. But it seems unlikely that, knowing that declination varied over time, he would have sent an observation that was ten years out of date.)
   Google Scholar
• Ibid. 473 MC, IX, 31–8.
   Google Scholar
• Gorman , M. J. “ ‘The Angel and the Compass: Athanasius Kircher's Magnetic Geography’, in P. Findlen, ed. ” . In Athanasius Kircher: The Last Man who Knew Everything 239 – 59 . (New York, 2004), pp. here p. 257, n. 7.
   Google Scholar
• Kircher . Magnes 397 ('tractatu[m], videlicet, quo totius Geographiae restaurandae rationes, 8c modos exhiberem’); Gorman, ‘The Angel and the Compass’, p. 242
   Google Scholar
• Kircher . Magnes 397 – 8 . ('Verum cu[m] tantae molis opus ad vmbilicu[m] sine altioris auctoritatis fulcimento nos perducere posse speraremus, meritò negotium adeò gloriosum cum dolore omnium literarum amantium iniquam Remoram passum est. O vtinam nouus aliquis Atlas cum Hercule exoriretur, cuius industria Sc sumptibus Geographicum hoc opus restaurari possit?’). In classical mythology, after Hercules had agreed to carry the Earth for Atlas while the latter performed a labour on his behalf, he tricked Atlas into taking the burden from him again.
   Google Scholar
• Kircher , A. 1646 . Ars magna lucis et umbrae 553 Rome By this time, Mersenne had met Kircher, during his visit to Rome in the winter of 1644/5 (MC, XIII, pp. 242, 273, 320); so he may have had an opportunity to inspect Kircher's work in progress on this topic.
   Google Scholar
• Kircher , A. Magnes, sive de arte magnetica 294 – 1 . 3rd edn. (Rome, 1654), p.; see also Gorman, ‘The Angel and the Compass’, pp. 250-
   Google Scholar
• In this and the subsequent transcriptions from manuscript, expanded contractions are placed in square brackets; uncertain readings are placed in square brackets, with an italicized question mark; deleted material is presented in square brackets and described as such; interlineated material is presented in square brackets with the symbol ‘>’; and underlined material is presented in italics.
   Google Scholar
• Mersenne's four-page printed text: see above, n. 33.
   Google Scholar
• Kircher . Magnes (see above, at n. 32).
   Google Scholar
• Magnetic ‘declination’ was variation from true North; magnetic ‘inclination’ was variation from the horizontal (which changed in accordance with latitude).
   Google Scholar
• This refers to Mersenne's suggestion that Kircher use the Jesuit order for such information-gathering: see above, n. 35.
   Google Scholar
• See above, at nn. 41–5.
   Google Scholar
• This ‘non’ is lacking in the MS, but is required by the sense.
   Google Scholar
• Progymnastica Musicae pars Veterum restituta et ad. hodiernam praxin redacta The musicologist Giovanni Battista Doni (c. 1594–1647) was one of Mersenne's long-s ing correspondents. Cf. also MC, IX, 146–7, Doni to Mersenne, 29 February 1640: ‘ces jours passés j'ay parachevé les deux livres d'un traicté latin intitulé que j'ay quelque envie de faire imprimer par delà les monts. Je croy que je commenceray bientost à faire imprimer icy mon second livre des Annotations sur le Compendio avec ses 13 ou 14 traictez ou discours…’ The latter work was published as Annotazioni sopra il compendio de’ generi, e de’ modi della musica…con due trattati…et sette discorsi (Rome, 1640); the Latin treatise was eventually published in G. B. Doni, Lyra barberina, ed. A. F. Gori, 2 vols (Florence, 1763), I, 205–64.
   Google Scholar
• Revue biblique , 66 The Oratorian priest and oriental scholar Jean Morin (1591–1659) had travelled to Rome in the summer of 1639 (taking with him a letter from Mersenne to Doni: see MC, VIII, 437), and stayed there until the end of February 1640 (see MC, IX, 146). Morin's special field of interest was the relationship between the Hebrew Bible, the Samaritan Pentateuch, and the Septuagint (see P. Auvray, ‘Jean Morin (1591–1659)’, (1959), 397–414). Kircher's phrase was derived from the proverbial saying, ‘Spartam nactus es, hanc orna’ (see D. Erasmus, Adagiorum opus (Lyon, 1550), cols 562–6), which was used to mean ‘cultivate your own field of expertise’.
   Google Scholar
• 2005 . John Pell (1611–1685) and his Correspondence with Sir Charles Cavendish: The Mental World of an Early Modern Mathematician Oxford For biographical details see N. Malcolm and J. Stedall,.
   Google Scholar
• Ibid. 66 – 73 . This text became known as An Idea of Mathematics or (in the Latin version) Idea mathesem.
   Google Scholar
• Rivet's letter does not survive; Mersenne's reply to it is in MC, VIII, 238–46 (commenting on the ‘discours du Sr Pell’: 240).
   Google Scholar
• 96 – 8 . See MC, VIII, 689, and Malcolm, ‘Six Unknown Letters’, pp.
   Google Scholar
• 90 – 2 . See MC, VIII, and IX, passim, and the letters to Haak printed in the appendix to vol. XI. On Cavendish's patronage of Pell see Malcolm and Siedali, John Pell, pp.
   Google Scholar
• See MC, X, 610–11; Malcolm, ‘Six Unknown Letters’, pp. 104, 116 (n. 64).
   Google Scholar
• John Pell, passim. For all the foregoing details, see Malcolm and Stedall
   Google Scholar
• 1986 . Annals of Science , 43 The existence of this letter was first noticed by Jan van Maanen, who printed a short extract from it in his ‘The Refutation of Longomontanus’ Quadrature by John Pell’, 315–52; here 335, n. 33.
   Google Scholar
• John Pell 429 – 30 . Sir Charles Cavendish: see his letter to Pell of 7 October 1645 (BL, MS Add. 4278, fols 215–16, printed in Malcolm and Stedall pp.—).
   Google Scholar
• 1644 . Rotundi in piano, seu circuii, absoluta mensura 324 – 5 . Amsterdam Longomontanus's quadrature of the circle was published in his; Pell's refutation was printed on one small leaf of paper, the only known copy of which (BL, MS Add. 4280, fol. 205) is given in photo-reproduction in van Maanen, ‘The Refutation’, pp.
   Google Scholar
• 1644 . Cogitata physico-mathematica 69 Paris The author of this quadrature was the sieur Cornu, a surveyor and amateur mathematician from Pont-sur-Yonne (near Sens), who had corresponded sporadically with Mersenne since 1635 (see MC, IV, 59 (n.); V, 177–84; XV, 345–6). Mersenne referred to this quadrature, without stating the inventor's name, in his, ‘Phaenomena hydraulica’, p.; he attributed it to Cornu in a manuscript note (see MC, VI, 298). He also referred to it in a letter to Torricelli on 24 June 1644 (MC, XIII, 164); in another letter to Torricelli, dated 10 October 1645, he wrote that ‘I have just seen the man who has here found the quadrature [of the circle], the duplication of the cube, and the triplication [sic for ‘trisection’] of the angle. When these three sheets are published, I shall immediately send them to you’ ('Jam jam vidi hominem qui hîc quadraturam, duplicationem cubi et triplicationem anguli reperiit. Ubi haec edentur tria folia, confestim ad te mittam’: ibid., XIII, 496). These printed sheets, if they subsequently appeared, have not been identified.
   Google Scholar
• 1647 . Controversiae de vera circuii mensura…pars prima 47 – 9 . Amsterdam This demonstration of Pell's theorem by the mathematician Gilles Personne de Roberval (1602–75) was published in J. Pell, pp.
   Google Scholar
• n 468 A positive integer is called a perfect number if it is equal to the sum of all of its positive divisors, excluding n itself. The first such number is 6 (= 1+2+3); the next is 28 (= 1+2+4+7 + 14). The mathematician Pietro Bongo (d. 1601) included a brief discussion of perfect numbers in his book on the significance—moral, theological, etc.—of different numbers: P. ‘Bongus’, Mysticae numerorum significations liber, 2 vols (Bergamo, 1583–4). (Each chapter of the book is devoted to a number; this discussion is in the chapter for number 28.) In the original edition of his book, he gave a table in which perfect numbers were ordered according to the number of digits they contained, up to 24 digits (II, 68). There was one perfect number for each of these categories, with the exception of numbers of 5, 11, 17, and 23 digits, for which no perfect number was available; thus he claimed to provide 20 perfect numbers in total. In a later edition of his book, retitled Numerorum mysteria (Bergamo, 1591, and several subsequent editions), the table was extended to numbers of 28 digits, with the same null categories (Paris, 1618 edition, p.); thus the total claimed there was in fact 24, and not, as Mersenne remembered, 28. In his Preface to Cogitata physicomathematica Mersenne had committed the same error; there he wrote that 20 of Bongo's numbers were imperfect, so that he gave only 8 perfect numbers ('quippe 20 sunt imperfecti, adeo vt solos octo perfectos habeat’: sig. a4v), and he added that 3 others were known, bringing the total to 11. Charles Henry has suggested that this discussion of perfect numbers in Mersenne's Preface was a summary of passages in letters from Fermât and Frenicle de Bessy: ‘Recherches sur les manuscrits de Pierre de Fermât suivies de fragments inédits de Bachet et de Malebranche’, Bulletino di bibliografia e di storia delle scienze matematiche e fisiche, 12 (1879), 477–568, 619–740; here 524.
   Google Scholar
• Literally . “ ‘we shall offer grass’; to offer grass (a piece of turf) was a symbolic gesture expressing an acknowledgement of defeat (see Pliny ” . In Historia naturalis 22.4.8).
   Google Scholar
• The mathematician Pierre de Fermât (1601–65) was conseiller of the Parlement of Toulouse, and commissaire aux requêtes du Palais.
   Google Scholar
• Oeuvres 302 – 14 . Fermât had previously posed a similar problem in letters to the Parisian mathematicians Bernard Frenicle de Bessy and Pierre Brûlart (or ‘Bruslart’) de Saint-Martin. In his letter to Brûlart of 31 May 1643 he proposed the problem, ‘Trouver un triangle rectangle duquel le plus grand côté soit un quarré et la somme des deux ou trois autres [sic] soit quarrée’ (P. de Fermât, ed. P. Tannery and C. Henry, 4 vols (Paris, 1891–1912), II, 259). Writing to Mersenne in August 1643, he responded to the news that both Frenicle and Brûlart regarded this problem as insoluble, and insisted that not only was it soluble, but he had already found the solution (MC, XII, 271–2; cf. also his letter to Mersenne of 1 September 1643, ibid., 313–14). For a discussion of Fermat's work on these problems, which derived from book 6 of the Arithmetic of Diophantus, see M. S. Mahoney, The Mathematical Career of Pierre de Fermât, 1601–1665, 2nd edn. (Princeton, N.J., 1994), pp. Pell's rough notes on his initial attempt to tackle this problem are in BL, MS Add. 4278, fol. 222r.
   Google Scholar
• Geometria indivisibilium continuorum nova quadam ratione promota The mathematician Bonaventura Cavalieri (c.1598–1647) had published his in Bologna in 1635. Mersenne stayed briefly in Bologna, some time between 1 and 10 April 1645, and visited Cavalieri twice (see MC, XIII, 246, 422–3, 431; for Cavalieri's later account of their conversations, see ibid., 465–7).
   Google Scholar
• 1644 . Opera geometrica 427 Florence The mathematician Evangelista Torricelli (1608–47) had been appointed Galileo's successor (in 1642) as mathematician and philosopher to Grand Duke Ferdinando II of Tuscany, residing in Florence thereafter. The work referred to here is his. One week earlier, Sir Charles Cavendish had written to Pell from Paris that Mersenne ‘hath brought the greatest rarities he could finde in Italie…Tauricells worckes all, as I thinke, which are rare heere’ (BL, MS Add. 4278, fol. 213v, printed in Malcolm and Stedall, John Pell, p.).
   Google Scholar
• Oculus Enoch et Eliae sive radius sidereomysticus: pars prima 336 – 56 . The astronomer and Capuchin friar Anton-Maria Schyrle von Rheita (15971660) published his in Antwerp in 1645; it ended with a short section on the design of telescopes (pp.—), recommending hyperbolic lenses.
   Google Scholar
• 1989 . Planetary Astronomy from the Renaissance to the Rise of Astrophysics: Part A: Tycho Brahe to Newton 119 – 43 . Cambridge Michael Florent van Langren (e. 1600–1675), a member of a Flemish globe- and map-making family, ‘Royal Mathematician and Cosmographer’ to Philip had hit on the idea of using the changing appearance of the moon as a celestial clock in order to solve the problem of determining longitude. By 1643 he had prepared 30 detailed drawings of different phases of the moon. When he heard of similar selenographic projects by other scientists (Hevelius and Caramuel), he printed his first map as a broadsheet in March 1645 (see E. A. Whitaker, ‘Selenography in the Seventeenth Century’, in R. Taton and C. Wilson, eds, pp. here pp. 127–8). The visible features of the lunar surface were traditionally described as ‘seas’ and ‘islands’.
   Google Scholar
• A proverbial saying (from Horace): ‘Parturient montes, nascitur ridiculus mus’, ‘The mountains go into labour, and a ridiculous mouse is born’—used of one who promises much and produces little.
   Google Scholar
• 498 MC, XIII, 497–9, here p. ('Vestri Cyclometriae refutationem hisce adjunxi. De reliquis quae proposuisti, aliàs’).
   Google Scholar
• For the letter see MC, XIII, 497–9 (where the transcription mistakenly gives ‘petitionibus’ (498, 1. 18) for ‘peritioribus’). Pell's final draft of this letter, not noticed by the editors of MC, is in BL, MS Add. 4278, fol. 220r.
   Google Scholar
• This phrase appears in the MS with superscripts to indicate word-order, thus: 2rationis ‘humanae leges.
   Google Scholar
• The ‘chartula’ or little piece of paper was Pell's refutation of Longomontanus, printed on one small leaf (see above, n. 64). Pell's method involved calculating a series of tangents, starting with the tangent for 45° and halving the angle each time until he reached the tangent of half the angle subtended (at the centre) by one side of a 256-sided polygon. His penultimate tangent, 0.0245486, was for the equivalent angle of a 128-sided polygon.
   Google Scholar
• 338 This letter was first noticed by van Maanen, who printed an extract from it in ‘The Refutation’, p., n. 42, but mis-dated it to before 8 November, on the grounds that it was sent enclosed in a letter from William Petty to Pell which bore that date (a date which was in fact Old Style, i.e. 8/18 November). The letter is dated the Ides of November (i.e., the 13th) by Mersenne.
   Google Scholar
• This news of Longomontanus's death was false.
   Google Scholar
• See above, n. 66.
   Google Scholar
• In his letter to Mersenne of 18 October Pell had quoted this sentence from Mersenne's letter of 7 October and had written that he found two words in it illegible (reproducing the forms of the words which are transcribed above as ‘etiam’ and ‘[edat?]’). Mersenne rewrites the final phrase, having apparently not kept a copy of the letter.
   Google Scholar
• See above, n. 56.
   Google Scholar
• Exercitationum mathematicarum decas prima The mathematician Camillo Glorioso (or Gloriosi) (b. 1572), author of 2 vols (Naples, 1627–35), had in fact died in 1643. Pell had of course been unaware of this when he asked Mersenne in his letter of 18 October to solicit from him (and Torricelli) demonstrations of Pell's theorem.
   Google Scholar
• See above, n. 72.
   Google Scholar
• See above, n. 71.
   Google Scholar
• A Study of the 102 – 6 . On Roberval's work on the centres of gravity of plane figures (and solids), see E. Walker, Traité des indivisibles of Gilles Persone de Roberval (New York, 1932), pp.—, and L. Auger, Gilles Personne de Roberval (1602–1675): son activité intellectuelle dans les domaines mathématique, physique, mécanique et philosophique (Paris, 1962), pp. 32–8. ‘Semicircle’ here refers to the plane figure; ‘semicircumference’ refers just to the curved boundary—which can also be considered to have a centre of gravity, if thought of as a physical object similar to a curved piece of wire. Roberval's method, as applied to semicircles and semicircumferences, was set out in a short text dated 1645: Bibliothèque Nationale, Paris, MS f.1. 7226, fols 72–6. Mersenne also reported Roberval's discovery in a letter of November or December 1645 to Giovanni Battista Baliani (see MC, XIV, 29–30, where the editor mistakenly supposes that he was alluding to Baliani's own work).
   Google Scholar
• 122 444 See Cavendish's letter to Pell of 12 December 1645: ‘Mersennus remembers him to you & will according to your desire write by the next oportunitie to Tauricell & Caualiero’ (BL, MS Add. 4278, fol. 232r, printed in Malcolm and Stedall, John Pell, p.). Cavalieri's demonstration is in Pell, Controversiae…pars prima, p. 60
   Google Scholar
• See MC, Xiy 366.
   Google Scholar
• Controversiae…pars prima 55 Pell, p. This brief composite text is printed in MC, XIII, 463, where the editors mistakenly suppose that it is the text of a letter sent by Mersenne to Pell in July or August 1645. It consists of just two sentences; the first is from Letter 3 above (the first half of the sentence beginning ‘Porrò quadraturae…’: above, p. 82); the second is from Letter 5 above (the sentence beginning ‘Cùm autem noster…’ (slightly modified): above, p. 86).
   Google Scholar
• Bulletin cartésien , 30 For the history of the MS in the intervening years (stolen from the Académie des Sciences by Guglielmo Libri; sold by him to Lord Ashburnham; purchased after Ashburnham's death by Alfred Morrison; sold at Sotheby's to Maggs in April 1918) see E.-J. Bos and M. van Otegem, ‘Notes sur la correspondance de Descartes’, (http://www.cartesius.net/bulletin_XXX.html). Some of the differences noted here are also recorded by Bos and van Otegem from the transcription of the MS given in The Collection of Autograph Letters and Historical Documents formed by Alfred Morrison, 2nd series, 7 vols (London, 1893–97), III, 106.
   Google Scholar
• XV This refers to the measure or scale, drawn on a piece of paper two and a half feet long, which Descartes enclosed with this letter. On it he had marked precise divisions in the region of 2’ 3”—2’ 4”, to be used by Mersenne in measuring the height of mercury (in a Torricellian tube) under different meteorological conditions; he had also retained an identical measure, so that he could compare Mersenne's observations with his own (see MC, 571).
   Google Scholar