an unpublished letter from henry oldenburg to johann heinrich rahn

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Downloaded from rsnr.royalsocietypublishing.org on December 6, 2012 Letter from Henry Oldenburg to Johann Heinrich Rahn 263 This part is translated by Mr Old, and by me almost transcribed…’ (Rigaud, op. cit. (note 18), ii, p. 525). ‘Mr Old’ here must evidently be Oldenburg, though his work on this project has not been noticed by modern writers on him. The plan (which never came to fruition) was to publish this translation from Ferguson together with a translation (by Nicolaus Mercator) of Kinckhuysen’s Algebra, ofte stel-konst: see C. J. Scriba, ‘Mercator’s Kinckhuysen-Translation in the Bodleian Library at Oxford’, Br. J. Hist. Sci. 2, 45–58 (1964) (referring also to ‘Mr Old’: p. 50). 29 Martyn Wilkens, Officina algebrae, waerinne door een miraculosische inventie seer konstelijck gewrocht worden d’aequatien (Groningen, 1636). This work (of which no copy is known in Britain; there is a copy in Amsterdam University Library, pressmark 721.F.3) was mentioned in the review of Ferguson’s book in Philosophical Transactions (op. cit., note 28) as follows: ‘divers good Treatises of Algebra have been lately publish’t in Low Dutch. This Author [sc. Ferguson] cites Questions out of the 3d Century of Questions in the Officina Algebrae of Marten Wilkens, which we have not seen’ (p. 998). Wilkens was a mathematician from Emden who worked as a schoolmaster in Groningen and died some time before 1669. 30 Probably a reissue of Anthoni Smyters, Algebra, ofte reghel cos … het 4de deel (Rotterdam, 1612). 31 Frans van der Huyps, Algebra: ofte een noodige, korte en klare onder-wijsinge inde beginzelen en gronden van de setl-konst … verfattende: ’t eerste stel-konstigh boeck Diophanti Alexandrini (Amsterdam, 1661). The review of Ferguson’s book in Philosophical Transactions (op. cit., note 28) referred to a 1654 edition of this book (p. 999). 32 Erasmus Bartholinus, Dioristice, seu aequationum determinationes duabus methodis propositae (Copenhagen, 1663); this work is in two parts, each separately paginated, entitled ‘Dioristices methodus prima’ and ‘Dioristices methodus secunda’. Oldenburg refers to the final sentence of the second part (p. 55): ‘Quibus volupe est uberiori horum praeceptorum declaratione edoceri, exspectare poterunt Systema nostrum Matheseos Universalis, ubi, quae ad Analysin speciosam spectant omnia reperient prolixius praeceptis & exemplis proposita’ (‘For those who would like to learn from a fuller exposition of these precepts, they can await my Systema matheseos universalis, in which they will find everything that is relevant to algebra set out at greater length in precepts and examples’). This passage was quoted in Collins’s draft (StAUL, MS 31009, fo. 31 r ). 33 Collins’s draft referred to this project: ‘divers yeares being since elapsed and himselfe busy about reprinting Tychos observations we do not heare any thing more of the performance of his promises’ (StAUL, MS 31009, fo. 31 r ). Tycho Brahe’s manuscripts had been bought from Ludwig Kepler in 1662 by King Frederik III of Denmark, who commissioned Bartholinus to oversee their publication. On 22 February 1672 Oldenburg wrote to Bartholinus, enquiring ‘how far that more accurate edition of Tycho Brahe has proceeded’ (OC viii, p. 550); Bartholinus replied on 23 April that ‘we are trying to get my edition of the observations of Tycho Brahe printed at Paris’ (ibid., ix, p. 35); some pages were printed there, but the project was then abandoned (see ibid., iv, p. 575, and ix, p. 135). 34 René-François de Sluse [Slusius], Mesolabum seu duae mediae proportionales inter extremas datas per circulum et ellipsum vel hyperbolam infinitis modis exhibitae (Liège, 1659; 2nd edn, enlarged, with the addition of Pars altera de analysi, et miscellanea, Liège, 1668). 35 Carlo Rinaldini, Ars analytica mathematum, in tres partes distributa (four parts) (Florence, Padua, 1665–84). The parts were published as follows: part 1 (Florence, 1665); part 2 (Padua, 1669); part 3 (Padua, 1684); part 4, ‘paralipomena’ (Padua, 1682). Oldenburg refers to the Giornale veneto de’ letterati, no. 3, pp. 21–24, which gives an account of Rinaldini’s work, describing it as ‘Stampato in Padoa, 1671’. 36 Diophantus, Arithmeticorum libri sex, ed. and tr. C. G. Bachet de Méziriac, with notes by P. Fermat (ed. S. Fermat) (Toulouse, 1670): this work includes extracts from Fermat’s letters, edited by the Jesuit mathematician Jacques de Billy. 37 Jacques de Billy, Diophanti redivivi: in qua, non casu, ut putatum est, sed certissima methodo & analysis subtiliore, innumera enodantur problemata, quae triangulum rectangulum spectant (two parts) (Lyon, 1670). 38 Rahn, op. cit. (note 9).
Downloaded from rsnr.royalsocietypublishing.org on December 6, 2012 264 Noel Malcolm 39 Isaac Barrow, Lectiones geometricae: in quibus (praesertim) generalia curvarum linearum symptomata declarantur (London, 1670). Lecture 13 (pp. 131–147) gives 13 ‘series’ of equations for different types of curve. (The copyist’s semicolon here is an error; Collins’s draft refers to ‘[>a] lecture about curves proper for solving of Aequations at the end of D r Barrowes Geometricall lectures’ (StAUL, MS 31009, fo. 31 r ).) 40 Michael Dary, Dary’s Miscellanies: Being, for the Most Part, a Brief Collection of Mathematical Theorems, from Divers Authors (London, 1669). 41 See Rahn’s letter to Haak, above. 42 Carlo Antonio Manzini, L’occhiale all’occhio, dioptrica practica (Bologna, 1660). 43 Francesco Eschinardi, Dialogus opticus, in quo aliquibus quaesitis compendiose respondetur [with] Centuria problematum opticorum … seu dialogi optici pars altera [and] Centuriae opticae pars altera, seu dialogi optici pars tertia (Rome, 1666). 44 Gilles François de Gottignies was a Jesuit scientist and mathematician who had studied under Grégoire de Saint-Vincent in Antwerp and had become Professor of Mathematics at the Collegio Romano. In a letter to Oldenburg from Venice written on 20 January 1671, John Dodington had written that ‘Padre Gottignes hath allmost finished a very Curious Booke concerning the admirable effects In dioptrica’ (OC vii, p. 405). In his letter to Collins of November or December 1670 (copied in Collins’s letter to Gregory of 15 December 1670: Turnbull, op. cit. (note 12), p. 140), the French Jesuit Jean Bertet had written that a work by de Gottignies on telescopes was on sale in Rome. Oldenburg asked Dodington to send ‘Gottignies Dioptricks’ (together with ‘Fabri in Archimedem’: see below, note 61) on 10 February 1671 (OC vii, p. 447); Dodington wrote on 4 April that he would send both works when he obtained them (ibid., vii, p. 551). But nearly a year later, on 4 March 1672, Oldenburg wrote to de Sluse (on the basis of a draft supplied by Collins) that ‘We still do not know what has happened in Italy to … Gottignies’s dioptrics, languishing, it is said, in a printer’s shop in Rome’ (ibid., viii, p. 576; cf. p. 546 for the draft). The work appears never to have been published. 45 Honoré Fabri, Synopsis optica, in qua illa omnia quae ad opticam, dioptricam, catoptricam pertinent … breviter quidem, accurate tamen demonstrantur (Lyon, 1667). The lens-design (invented by the prominent optical instrument-maker Eustachio Divini) is presented in Prop. 46 (pp. 131–138). 46 Père Cherubin d’Orléans, La Dioptrique oculaire, ou la theorique, la positive, et la mechanique, de l’oculaire dioptrique en toutes ses especes (Paris, 1671). 47 In Collins’s draft this information is given as follows: ‘In France the large and beautifull Dioptricks of Pere Cherubin is lately come out, of which Mons r Reignault a learned Math: of Lyons gives this character: ‘Je admire la belle Impression de la dioptrique du P. Cherubin sa dottrine est fort bonne. Ie ne auois pas une si grand Idee q’ Jenay, ce Liure est excellent le public luy en est grandement oblige’ [‘I admire the fine edition of Father Cherubin’s Dioptrique; the contents of his teachings are extremely good. I did not have such a high opinion of it before as I do now; the book is excellent, and the public is very much obliged to him for it’] (StAUL, MS 31009, fo. 31 v ). In an earlier letter to Gregory (6 May 1671), Collins quoted this comment by Raynaud and said that it was made in ‘a private Letter’ to Collins’s Jesuit correspondent, Jean Bertet (Turnbull, op. cit. (note 12), p. 186). François de Regnauld, seigneur du Buisson (1626–89), was a distinguished amateur mathematician, and a pupil and friend of Honoré Fabri, resident in Lyon: see J. Pernetti, Recherches pour servir à l’histoire de Lyon, ou les lyonnais dignes de mémoire, 2 volumes (Lyon, 1757), ii, pp. 122–124. 48 Isaac Barrow, Lectiones XVIII, Cantabrigiae in scholis publicis habitae; in quibus opticorum phaenomen�n genuinae rationes investigantur, ac exponuntur (London, 1669). 49 Erasmus Bartholinus, Experimenta crystalli Islandici disdiaclastici quibus mira & insolita refractio detegitur (Copenhagen, 1669). 50 Johann Heinrich Ott, Cogitationes physico-mechanicae de natura visionis (Heidelberg, 1670); this was the text of a lecture presented at Heidelberg University in December 1669. The author, who was from Schaffhausen and is known to have studied medicine in Basel, Montpellier and
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an unpublished letter from henry oldenburg to johann heinrich rahn

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