an unpublished letter from henry oldenburg to johann heinrich rahn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 257 item de regulis Motus, [vi] Percussionis, et Hydrostatica; 62 Jacobi Gregorii Exercita[ti]ones Geometriae; 63 Nicolai Mercatoris Logarithmotechnia. 64 sub praelo nunc sudant Jeremiae Horroxii Astronomica a D[octo]re Wallisio digesta. 65 Cum candide adeo Instrumentorum Opticorum a Te paratorum communica[ti]onem offeras, liberalitatem tuam amplexamus, et quae proficisci a nobis rec[og]noscimenti loco poterunt, summa lubentia repollicemus. Qua ratione Hookius noster Micrographiae suae figuras adeo ampliatas conspicere potuerit, ipse in Libri illius praeloquio enarrat; 66 q[uo] d quis Anglici sermonis p[er]itus facili negotio interpretari Tibi poterit. Fas mihi – 67 fuerit epistolam hanc protrahere, cuj[us] nimine jam prolixitati veniam peto. Vale, Vir Eximie, et doctrinae atq[ue] Virtutis Tuae Cultori studiosiss[im]o faue. Dabam Londini 10 Junij 1671 68 Translation Henry Oldenburg, Secretary of the Royal Society, sends greetings to the most distinguished and most learned Mr Johann Heinrich Rahn, Secretary-Counsellor of Zurich. Distinguished Sir, Since it falls to me, more than to anyone else here in England, to conduct philosophical correspondence, I thought it altogether necessary to add my humble labour to that of my friend the most eminent Mr Haak when he was replying to your most recent letter. To begin with, let me indeed say what a pleasure it is for us to learn that there are also distinguished men in Switzerland (among whom you occupy, by right, the first place) whose minds and hands are dedicated to the cultivation of physics and mathematics. The task at which the British Royal Society labours is assuredly a difficult one, namely, tracing the inner parts of Nature, investigating the power of Art, and applying both to the use and advantage of human life. This is, indeed, not a task for one nation alone; in order to achieve so great a purpose, the learned and sharp-witted men of all countries must combine their wits and their efforts. Once again, we judge you, most learned Sir, worthy of great praise, for having also decided to make your contribution here, and to send us an account of your studies. It gives us great pleasure to learn that you have reduced the problems of Diophantus to algebra; we eagerly look forward to the publication of that work in Latin. No doubt you have become aware of the work that has been done on algebra in recent years in all countries. For example, Kinckhuysen printed an introduction to algebra in Dutch in 1661; he has also published two other books, entitled De grondt der Metkonst or Analytical Conicks (1660) and Geometrische Problemata met haën Analytical Calculus (1663). 27 Jacob Ferguson published a Labyrinthus algebriae; 28 and Martyn Wilkens, Officina algebriae. 29 To those can be added Smyters’s Algebra, 30 and Frans van der Huyps’s Algebra. 31 A few years ago Erasmus Bartholinus’s Dioristice sive Methodus aequationum prima et secunda was published in Denmark; at the end of that treatise, a general system of algebra was promised by the author32 —who, since then, has been occupied with publishing an accurate edition of Tycho’s observations. 33 De Sluse, at Liège, has been made famous by that splendid book entitled Mesolabum, with its second part, De analysi, et miscellanea (1661). 34 Rinaldini’s Geometra promotus has been published in Italy; I have not yet made up my mind about it, though learned men praise it highly. [Marginal note: See the description in the Giornale veneto of this book, entitled Analytica mathematum, by Carlo Rinaldini, 3 folio volumes (Padua, 1671).] 35 At Toulouse, in France, an edition of Diophantus was recently published with notes by Fermat, and with Fermat’s ‘Inventum novum analyticae doctrinae’, put together by the Jesuit de Billy from various of Fermat’s letters; 36 in it there are solutions to several numerical problems which others had given up trying to solve. This de Billy has published two volumes of Diophantus redivivus. 37 Here in England, roughly four years ago, your own Introduction to Algebra was published in English, together with much additional material by Dr Pell. 38 There was also published at that time a lecture on the use of curves for solving equations, at the end of Dr Barrow’s Lectiones geometricae, 39 as also M. Dary’s Miscellanies, on the measurement of curves. 40 What we especially desire is that someone will find and publish an easy method for obtaining the roots of the highest equations by means of logarithms: knowing that Mr Pell has done useful work on that
Downloaded from rsnr.royalsocietypublishing.org on December 6, 2012 258 Noel Malcolm subject, but that, nevertheless, he has not yet published it, I thought I should mention it to you, in order to find out your thoughts about it. So far as optics are concerned, we are delighted that you have completed a treatise on optics, dioptrics, and catoptrics, together with an appendix on practical dioptrics, in which you show the way (and perhaps the measure), and the necessary tools, for grinding and polishing [lenses]. 41 We hope that copies of it will soon be delivered to us. No doubt you already know Manzini’s Dioptrica, 42 and the Novum problematum opticorum centuria by Eschinardi, 43 published in Italy; we have recently learned that another work has been published there, the Dioptrica by de Gottignies, a pupil of Grégoire de Saint-Vincent, together with a treatise on telescopes and microscopes. 44 There is also the Synopsis optica of Honoré Fabri, which discusses the ocular lens consisting of two half-lenses, touching at the centres of their convex sides, and each having the plane side facing outwards: this is like the one invented by the most distinguished Eustachio Divino, but Fabri claims that he was the first to demonstrate it. 45 In addition, there is the elegant Dioptrique of Father Cherubin, recently published in France, 46 to which Regnauld of Lyon pays the following tribute: he says that he admires the beauty of this publication, that he greatly prefers the author’s theory which is set out in it, and that he thinks the Republic of Letters will be indebted to him. 47 Here in London Barrow’s Lectiones dioptricae have been published, and are much admired. 48 In Denmark Erasmus Bartholinus published a dissertation De chrystallo islandico dis-diaclastico, in which he painstakingly explores many things, and learnedly explains them. 49 You cannot be unaware of the work which your countryman the most learned Johannes Ott recently published in Heidelberg, entitled Cogitationes physico-mechanicae de natura visionis. 50 Otherwise, the Italians have published Rossetti’s physico-mathematical treatise; 51 Benedetto Castelli’s works, collected in one volume; 52 Baliani’s posthumous minor works; 53 Borelli’s Motiones naturales in gravitate dependentes; 54 Montanari’s experiments on the rising of liquids in tubes, and on the glass bubbles which, when their extremities are broken, shatter into extremely small parts; 55 and Mengoli’s works on music. 56 In France they have published Blondel’s De resistentia corporum ellipticorum; 57 Milliet de Chales’s edition of Euclid; 58 Mouton’s De mensura diametri solis et lunae; 59 Antoine de la Loubère’s polemical Appendices, against Maignan; 60 and Honoré Fabri’s commentaries on Archimedes. 61 And, indeed, in England we have Dr Wallis’s De motu et libra; his De calculo centri gravitatis; his De regulis motis, vi percussionis, et hydrostatica; 62 James Gregory’s Exercitationes geometriae; 63 and Nicolaus Mercator’s Logarithmotechnia. 64 Jeremy Horrox’s work on astronomy, edited by Dr Wallis, is currently in the press. 65 Since you so candidly offer to send details of the optical instruments which you have prepared, we welcome your generosity, and with the greatest pleasure we promise in return to send you whatever things may serve to express our gratitude. The reason why our friend Hooke was able to observe on such a large scale the things he has illustrated in his Micrographia is explained by him in the preface to his book: anyone skilled in the English language will easily be able to translate it for you. 66 I should [not] prolong this letter—for the excessive prolixity of which I beg your pardon. Farewell, distinguished Sir, and look kindly on this most devoted admirer of your teachings and your virtue. London, 10 June 1671 RAHN’S LETTER TO PELL Oldenburg did not receive any reply from Rahn. An explanation—at least, an ostensible explanation—of this fact was supplied four years later, when Rahn at long last wrote directly to his old mathematics tutor, John Pell. The text of his letter (figure 2) is as follows. À studioso quodam, Algebram, non amplius meam sed multis nominibus tuam, mihi ex munificentia tua transmissam accepi, unde colligo, tot annorum decursu, memoriam mei, adhuc apud te
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an unpublished letter from henry oldenburg to johann heinrich rahn

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