an unpublished letter from henry oldenburg to johann heinrich rahn

An unpublished letter from Henry Oldenburg to Johann 

Heinrich Rahn 

N. Malcolm 

Notes Rec. R. Soc. Lond. 2004 58, 

249-266 

doi: 10.1098/rsnr.2004.0065 

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Notes Rec. R. Soc. Lond. 58 (3), 249–266 (2004) doi 10.1098/rsnr.2004.0065 

AN UNPUBLISHED LETTER FROM HENRY OLDENBURG TO JOHANN 

HEINRICH RAHN 

by 

NOEL MALCOLM 

All Souls College, Oxford OX1 4AL, UK 

SUMMARY 

The Swiss mathematician Johann Heinrich Rahn studied under John Pell in Zurich in the 

1650s. Prompted by Pell (who worked on a revised version of Rahn’s treatise on algebra, 

which was published in London in 1668), Theodore Haak made contact with Rahn in 1671, 

and received a letter from him describing his recent work on optics. This letter was passed 

on to Henry Oldenburg, who, with the assistance of John Collins, composed a lengthy reply, 

surveying recent scientific and mathematical publications. Significantly, however, 

Oldenburg did not consult Pell, even though this correspondence arose in the first place 

from Pell’s friendship with Rahn; the reason for this omission was that Oldenburg and 

Collins hoped that Rahn could supply details of Pell’s mathematical methods that Pell himself 

was refusing to divulge. Oldenburg’s letter is published here for the first time. 

Keywords: early Fellows; Henry Oldenberg; Johann Heinrich Rahn; John Pell 

INTRODUCTION 

The correspondence of Henry Oldenburg (figure 1), conducted for the most part in his 

capacity as Secretary of The Royal Society, is a monument to his industry, curiosity, and 

tireless energy. In addition to dealing with an incoming tide of enquiries and requests, he 

was also active in making fresh contacts and seeking out information from new sources. 

There is evidence of this, in abundance, in the 13-volume modern edition of his correspondence. 

1 One small piece of further evidence can now be added: a letter, omitted from 

that edition, that was sent by Oldenburg to the Swiss mathematician Johann Heinrich 

Rahn on 10 June 1671. This letter is preserved in a scribal copy in the Zentralbibliothek, 

Zurich, in a set of transcripts of letters to Rahn and his father. 2 It does not seem to have 

generated any subsequent exchange of letters between Rahn and Oldenburg; in that sense 

it may be regarded both as a rather solitary item and, in effect, as a failure. Nevertheless, 

the origins of this letter were far from solitary; understanding its full story involves tracing 

relations between Oldenburg and no fewer than three other Fellows of The Royal 

Society—Theodore Haak, John Pell and John Collins. And the letter also possesses, in 

addition to its intrinsic interest, some value as a case-study, illustrating the nature of some 

of the problems Oldenburg confronted when his role as a correspondent brought his personal 

obligations and his professional duties into conflict. 

249 © 2004 The Royal Society



250 Noel Malcolm 

JOHANN HEINRICH RAHN 

Johann Heinrich Rahn (1622–76) was a member of a prominent Zurich family: his father 

served as a city councillor for more than 50 years, and was Bürgermeister (Mayor) of 

Zurich from 1655 until his death in 1669. Rahn probably acquired his special interest in 

mathematics from his uncle Johann Georg Werdmüller, who was the engineer in charge 

of the city’s fortifications. He himself was appointed a ‘Schützenmeister’, which meant 

that he supervised shooting practice, and a ‘Zeugherr’, responsible for military supplies 

and artillery. 3 His mathematical interests were stimulated in 1654 by the arrival in Zurich 

of John Pell, the former Professor of Mathematics at Amsterdam and Breda (and future 

FRS), who served as Cromwell’s envoy to the Protestant cantons of Switzerland from 

May 1654 to June 1658. The first sign of his connection with Pell is a letter he sent, dated 

4 November 1654, enclosing a short mathematical demonstration and thanking Pell for 

the gift of a copy of one of Pell’s publications, his compilation of texts refuting the 

Danish circle-squarer Longomontanus. 4 What further contacts they had over the next two 

years is not known, but at some time in early 1657 Rahn began to receive regular weekly 

tutorials from Pell. As John Aubrey would later write (summarizing what Pell had told 

him), ‘Rhonius [the latinized version of ‘Rahn’] was D r Pell’s scholar at Zurich, and 

came to him every friday night’; Pell himself would refer to Rahn as his ‘disciple’ and 

would retain ‘coppies of the most considerable papers that he wrought in my presence or 

that I gave him to transcribe’. 5 

In early 1658 Rahn was appointed ‘Landvogt’ (provincial governor) of Kyburg, a district 

at the northern edge of the canton of Zurich; writing to Pell from there on 3 March 

1658, he remarked that his heavy administrative workload prevented him from spending 

any time on mathematics, but said that he had the consolation of remembering ‘how 

many very delightful hours’ they had spent together. 6 Nevertheless, during the next year 

he somehow found time to compose the German-language textbook on algebra that 

would make him famous: Teutsche Algebra, oder algebraische Rechenkunst, zusamt 

ihrem Gebrauch (Zurich, 1659). This work was heavily indebted to Pell, and it was a debt 

that Rahn was happy to acknowledge (though, probably in deference to Pell’s own habitual 

modesty, without mentioning his name): Rahn explained in his preface that ‘in the 

solutions, and in the arithmetic too, I make use of a completely new method … which I 

first learned from an eminent and very learned person.’ This new method, he explained, 

consisted in ‘a triple margin’—Pell’s system of presenting the working-out of a problem 

in three columns. But that was not the only thing owed to Pell in this volume: Rahn also 

introduced the division sign (which Pell had invented), and in a section on squaring the 

circle he presented the theorem Pell had defended in his controversy with 

Longomontanus. 7 

When Rahn’s book was published, Pell was back in London, leading a somewhat 

obscure existence without any public or academic position. He was no longer in touch 

with Rahn, but in November 1660 he did receive a copy of Rahn’s book from his friend 

Theodore Haak (the German-born scholar and translator, a man of wide scientific interests, 

who would be elected FRS in the following year). 8 Other copies evidently found 

their way to England, for in the early 1660s two separate translations of it were under-



Letter from Henry Oldenburg to Johann Heinrich Rahn 251 

Figure 1. Portrait of Henry Oldenburg by Jan van Cleef, 1668. (Copyright © The Royal Society.) 

taken: one by Thomas Brancker, and the other commissioned by John Collins. These two 

projects were combined in 1665, and the translation was then submitted to Pell for revision 

and improvement; by the time this work was published as An Introduction to 

Algebra in 1668, Pell’s interventions had amounted to replacing roughly half of Rahn’s 

text with new material of his own. 9 It was during the preparation of that modified translation 

that Pell wrote to Haak (on 13 June 1666):




I wish you could … learne from Zurich, concerning Johan Heinrich Rahn, lately Landvogt der 

Graffschaft Kyburg, whether he be yet alive, whether he be now at Zurich, what titles or offices 

he hath now. You gave me his booke in November 1660. I suppose you know that it is turned into 

English, and that 15 sheets of it are printed. Some mention should be made of him, if we can get 

sufficient information concerning him. 10 

From the absence of such details about Rahn in the printed volume, it would appear 

that Haak’s attempts to carry out this task met with no success during the following two 

years. But in 1671 he did make contact with Rahn (who had in fact returned to Zurich in 

1664). On 17 May 1671 Rahn wrote what was evidently a reply to Haak’s enquiries, giving 

news of his own scientific work and asking for details of new mathematical publications 

in England. On receiving this letter, Haak seems to have passed it on to Oldenburg; 

his motives for doing so would probably have included both a desire to stimulate contacts 

between The Royal Society and foreign scientists, and the feeling that Oldenburg 

was particularly well placed to provide news of recent publications. Oldenburg, in turn, 

passed the letter to John Collins, who was playing an increasingly active role as his 

adviser on mathematical matters. All that survives of Rahn’s letter to Haak (to which 

Oldenburg’s letter to Rahn is in effect a reply) is the following extract made by Collins, 

which was later copied out (together with other associated items from Collins’s papers) 

by David Sinclair and sent to Collins’s correspondent in Scotland, James Gregory. 

RAHN’S LETTER TO HAAK 

Ex literis D ni Johannis Henrici Rahn, Secretioris consilij Tigurini ad Theodorum Haak, redditis 

17 o Maij 1671 

Ego praeterito jam aliquo tempore, insistens manuductioni D ni Pellij (cui quicquid in Algebra 

scio, unice acceptum fero) problemata Diophanti Alexandrini ad Speciosam reduxi et constitui. 

nuper etiam tractatum absolvi de Optica, Catoptrica et Dioptrica cum annexa dioptrica 

practica exhibente modum et instrumenta necessaria limandis et poliendis vitris, et haec quidem 

non ex mera ideâ, sed ex ipsa praxi, et usu sese mihi obtulere cum subinde curiositate delecter, 

non tantum tubos majores et minores et microscopia construendi, sed insuper etiam rationem 

invenerim prope partem interiorem, seu circuitum Rotae medium sectiones Hyperbolicas affirmandi, 

quarum beneficio objecta admodum perspicua redduntur, et campus visorius egregie 

dilatatur, Si tibi adlubescit videre Iconismum horum Instrumentorum, aut ejusmodi vitra objectiva 

et ocularia dabo operam ut tibi transmittantur, interim libenter viderem Hookij vestri 

Micrographiam utinam latine loquentem. 

Contigit mihi non ita pridem observare (au Journal des scavants) Figuram ingenti 

admodum formâ minima repraesentantem, 11 sed non constat mihi proportio istius Microscopij, 

quod vitris constet, quis sit uniuscujusq[ue] vitri diameter; et quantum vitra ab invicem distent. 

Nos enim nondum eo usq[ue] progressi sumus, nec cogitata nostra ultra tertium vitrum 

extendimus. 

Si quid aliud etiam vobiscum in Mathematicis prodijt, notatu dignum, ne graveris quaeso 

illud impertiri nobis ad omnia officia paratissimis. 12 

Translation 

From the letter of Mr Johann Heinrich Rahn, Secretary-Councillor of Zurich, to Theodore Haak, 

written on 17 May 1671




Quite some time ago, relying on the training I received from Mr Pell (to whom alone I am 

indebted for whatever I know in algebra), I reduced and arranged the problems of Diophantus of 

Alexandria in algebraic form. 

Recently I have also finished a treatise on optics, catoptrics, and dioptrics, together with 

an appendix on practical dioptrics, showing the method (and the necessary instruments) for grinding 

and polishing glass lenses. These things, indeed, became clear to me not on the basis of mere 

theory, but on the basis of actual practice and use, when I was repeatedly preoccupied by the 

desire not only to know how to construct large and small telescopes, and microscopes, but also— 

above all—when I found a method (to do with the internal part or middle circuit of the wheel) of 

making hyperbolic sections, thanks to which objects are rendered very clear, and the field of 

vision is extraordinarily enlarged. If you would like to see a picture of these instruments, or lenses 

and eye-pieces made of this sort of glass, I shall take care to have them sent to you. Meanwhile 

I should like to see your Hooke’s Micrographia, if only it were translated into Latin. 

Not so long ago I happened to see (in the Journal des sçavans) an illustration of a quite 

prodigious size, representing minute things; 11 but I am not aware of the proportion of that microscope, 

what sort of lenses it consists of, what the diameter is of each lens, and how far apart the 

lenses are from each other. 

For I have not yet advanced as far as that, nor have my thoughts extended beyond a third 

lens. 

If anything else that is noteworthy has been published by your compatriots in the field of 

mathematics, I beg you not to regard it as a burdensome task to share it with me; I am very ready 

to oblige you in all ways. 

One of the treatises by Rahn referred to in this letter has survived: his algebraic version 

of the problems of Diophantus, entitled ‘Solutio Problematum Diophanti Alexandrini’, a 

215-page manuscript dated 1667 and designed to accompany Rahn’s own Latin translation 

(also in manuscript) of his Teutsche Algebra. 13 (This treatment of the Diophantine 

problems was probably inspired by Pell’s work on them: Pell himself is known to have 

prepared an algebraic treatment, the manuscript of which has unfortunately not survived.) 

The titles of two of Rahn’s optical treatises, ‘Tractatus von der Dioptrica oder 

Durchstrahlung’ and ‘Catoptrica oder Gelbstrahlung in ebenen Flächen’, are known from 

the surviving catalogue of his library, but the treatises themselves (and the library) are not 

extant. 14 How exactly he managed the manufacture of hyperbolic lenses—a task that had 

perplexed optical scientists throughout Europe, ever since Descartes had recommended 

such lenses in his ‘Dioptrique’ in 1637—remains, therefore, utterly obscure. 

COLLINS’S DRAFT OF OLDENBURG’S LETTER TO RAHN 

John Collins not only copied out part of Rahn’s letter to Haak; he also composed, for 

Oldenburg’s use, a substantial draft of a reply to it. Responding to the final request in 

Rahn’s letter, his draft began as follows: 

In answer to the letter of Rhonius 

That he hath taken paines to turn Diophantus into the style of the learned Dr Pell will be very 

acceptable to all our Algebraists to hear of, but more to see published in the latine tongue, and as 

concerning Algebraicall affaires we have this account to give. 

In Holland diverse bookes of that argument have been published in few yeares but in low 

Dutch 

As Gerard Kinckhuysens Stelkonst, or Introduction to Algebra published in anno 1662 in 

4o…15




A long list of mathematical books now followed (accompanied in some cases by 

Collins’s comments on them), including works by Kinckhuysen, Ferguson, Wilkens, 

Smyters, van der Huyps, Bartholinus, de Sluse, Rinaldini, Fermat, de Billy, Barrow, Dary 

and Wallis. In the next section of the draft, headed ‘As to Opticall affaires’, Collins added 

details of works by Manzini, Eschinardi, de Gottignies, Cherubin, Barrow and 

Bartholinus; he then reproduced some long extracts from a recently published work by 

Johann Heinrich Ott, describing a new method, invented by Ott, of making hyperbolic 

lenses. In a final section he gave details of a number of recent or forthcoming publications 

in Italy, France, and Spain, introducing them with the comment ‘Concerning bookes 

mathematicall we heare of divers lately published in Italy &c. but have seen none of 

them, however thinke fit to give you ane account of them, that we may receive your opinion 

concerning such as you have seen, and be somewhat informed of what argument they 

treat’: in this list he included works by Rosetti, Castelli, Baliani, Borelli, Mengoli, 

Blondel, Milliet de Chales, de Gottignies, Mouton and de la Loubère. 16 With only a handful 

of exceptions (among them, two treatises by Borelli, a work on geodesy by Jean 

Picard and a mathematical treatise by John Kersey), the list of books given here by 

Collins was incorporated by Oldenburg in his letter to Rahn; Ott’s work was mentioned 

there, though the lengthy extracts were not in the end included. 

Collins’s list of recent publications also referred, somewhat casually, to the translation 

of Rahn’s own Teutsche Algebra: ‘In England about 4 yeares since the Introduction written 

by himselfe was translated and printed with divers alterations therein made by D r 

Pell.’ 17 But this comment, and the initial remark about Rahn’s reduction of the 

Diophantine problems into ‘the style of the learned D r Pell’, were not the only references 

to Pell in Collins’s draft. Collins had in fact enjoyed very close relations with Pell; not 

only had he assisted with the preparation of the modified translation of Rahn’s book 

(dealing with the printer in London while Pell was absent from the capital), but when Pell 

returned to London in the late summer of 1669 he became a lodger in Collins’s house. 18 

Collins was especially keen to learn about the advanced algebraic techniques which Pell 

had developed, but which he had not made public; indeed, this desire might have been 

the underlying reason for inviting Pell into his home. But it seems that Pell was reluctant 

to have his secrets wormed out of him, and Collins’s letters to other mathematicians during 

this period are a constant litany of complaints about Pell’s failure to impart any of his 

important discoveries to him. 19 Unable to learn the details of Pell’s methods, Collins 

adopted a strategy of circulating to other mathematicians descriptions of the feats Pell 

claimed to be able to perform, with such hints as he could gather of how he performed 

them, in the hope that they could work out the missing steps in the argument. 20 So it was 

entirely in keeping with Collins’s own epistolary strategy that his draft reply to Rahn 

included another such request. Indeed, making this request—specifying the most useful 

quid pro quo with which Rahn might respond to this deluge of bibliographical information—might 

well have been the most important function of the letter in Collins’s eyes: 

That which we chiefly here desire, is that some easy method might be found and communicated 

for obtaining the rootes of the higher sort of Aequations by logarithmes, and having some kinde 

of intelligence that D r Pell hath attained something extraordinary in that kinde, but hath not as yet 

evulged the same though very desirable, we thought fit to impart to you the Sence of a Member 

of the Society about that affaire, and earnestly covet your observations thereupon. 21




OLDENBURG’S LETTER TO RAHN 

That Henry Oldenburg turned to Collins for assistance in the preparation of his letter to 

Rahn is not in itself surprising. Collins had performed this sort of service for him before 

(producing, for example, a so-called ‘model’ for Oldenburg’s letter to the Liègeois mathematician 

de Sluse a few months earlier), and in subsequent years Oldenburg would 

come to depend on Collins as the drafter of his letters on mathematical subjects to 

Leibniz. 22 However, what is slightly surprising is that Oldenburg seems not to have contacted 

John Pell in this connection—despite Pell’s known links to Rahn, his wide-ranging 

knowledge of contemporary mathematical publications, and the fact that it was in 

response to promptings by Pell that Haak had written to Rahn in the first place. 

Oldenburg (who had married the young daughter of one of Pell’s oldest friends, John 

Dury) enjoyed a close friendship with Pell, and, indeed, lived in the same street. 23 In 

April 1670 Pell had performed a useful service for Oldenburg, obtaining a licence from 

the Archbishop of Canterbury ‘to veiw a Parcell of Bookes lately imported from 

Hamborough [sc. Hamburg] … for the use of H. Oldenburg Esq.’. 24 Pell had been a fairly 

active member of The Royal Society, and Oldenburg was evidently keen to make use of 

his mathematical expertise: during the winter of 1672–73, for example, he would pass to 

Pell copies of all the letters he had received from de Sluse and Huygens on the subject of 

‘Alhazen’s problem’, in the hope that Pell would prepare them for publication and add 

his own adjudication of the dispute. 25 And yet there is no sign of Pell’s involvement in 

the preparation of the letter to Rahn; no greetings from Pell were included in the text of 

the letter, and no trace or inkling of its existence is to be found among Pell’s own voluminous 

papers. The reason for this must surely be located in Collins’s request—which 

asked Rahn, in effect, if he could shed some light on Pell’s own method of using logarithms 

in the reduction of higher equations. A letter that thus involved going behind Pell’s 

back could hardly be shown to Pell himself. What scruples Oldenburg might have felt 

about this method of proceeding can only be guessed at; on the one hand there was his 

loyalty to Pell, but on the other hand there were both his cultivation of the ever-helpful 

Collins and his own overriding desire to further the advancement of knowledge. For 

Oldenburg, too, was frustrated by Pell’s incommunicativeness. Four years later, when 

Collins had inserted another reference to this topic in a draft of a letter from Oldenburg 

to Leibniz and the German mathematician had replied that ‘To unravel equations by 

means of a table of logarithmic sines will be a most useful thing’, Oldenburg impatiently 

annotated the margin of Leibniz’s letter: ‘Pell promises much about these things, but 

when?’ 26 The true answer, alas, was ‘never’. 

The text of Oldenburg’s letter to Rahn, as preserved in the surviving scribal copy, is 

as follows. 

Ampliss. o et Consultiss. o Viro Domino Joh. Henrico Rahn, è secretiori Consiliori Tigurino, 

Henricus Oldenburg Soc. Reg. Secr. Salutem 

Cum mihi prae caeteris hîc in Anglia incumbat, Vir Ampliss[im] e , literarium in re Philosophica 

commercium urgere, visum omnino fuit, meam praestantiss[im] o Haakio meo literis tuis nuperrimis 

respondenti, opellam consociare. A principio quidem quam volup[tabile] nob[is] est intelligere, 

p[rae]claros etiam in Helvetia viros (quos inter Tu prima subsellia jure occupas) in 

excolenda Physica et Mathesi mentem et manum addictam habere. Arduum profecto id opus est,




q[uo]d Regis Societas Britannica molit[ur], Naturae scil[icet] penetralia vestigare, atq[ue] Artis 

vires excutere, et utrumq[ue] in vitae humanae usus et commoda transferre. Res equidem non est 

gentis unius; omnium terrarum viri docti et sagaces ingenia et operas jungant necesse est ad tanti 

instituti finem consequendam. Denuo et Te, Vir Consultiss[ime], laude p[er] quam dignum censemus, 

q[uo]d Tuam quoq[ue] Symbolam huc conferre, et studiorum Tuorum rationem nobis communicare 

statuisti. Perplacet, Te Diophantis problemata ad speciosam reduxisse, ejusq[ue] 

editionem Latinam avide praestolamur. Nossi sine dubio, quae novissimis annis in re Algebraica 

ubivis terrarum gesta fuerint. Edidit sc[ilicet] Kinckhusius in Lingua Belgica Introductionem in 

Algebram, excusam 1661; evulgatis jam etiam duobus libris aliis, quorum Tituli; The grondt der 

Metkonst or Analytical [Calculus corrected to Conicks] A 1660 et, Geometrische Problemata met 

haën Analytical Calculus A. 1663 27 Emisit Jacobus Ferguson, Labyrinthum Algebriae; 28 et 

Martinus van Wilkins, Officinam Algebriae. 29 Cui addi possunt Algebra Smyteri, 30 et Algebra 

Francisci van der Huyps. 31 

In Dania prodijt ante aliquot annos Erasmi Bartholini Dioristice sive Methodus aequationum 

prima et secunda; ad cujus Tractatus calcem, Algebrae Systema generale promittit 

Author; 32 qui ex eo tempore Observationib[us] Tychonicis accurate edendis invigilavit. 33 Leodii 

celebrem reddidit Slusium insignis ille liber, cui titulus, Mesolabum, cum parte altera de Analysi 

et Miscellaneis, A. 1661. 34 In Italia lucem vidit Reinaldini Geometra promotus, qui nunc magni 

fiat a doctis, necdum mihi constat. [Marginal note: V. in Ephemer[idibus] Venetis descriptionum 

libri, cui Titulus Analytica Mathematu[m] Caroli Rinaldini in Padoa 1671. In 3 Vol. in fol.] 35 In 

Gallia Tolosae nup[er] editus fuit Diophantus cum notis Fermati, et hujus Analyticae invento 

novo, ex varijs ipsius Epistolis a Billio Jesuita collecto, quóq[ue] complura Problemata 

Numeralia, ab alijs omissa, solvuntur. 36 Iste Billius edidit duo volumina Diophanti redivivi. 37 

Hic in Anglia, quatuor circiter abhinc annis, Tua ipsius in Algebra[m] introductio, una cum 

plurimis Doctoris Pellii additionibus sermone Anglico in luce[m] prodiit: 38 Atq[ue] ex eo tempore 

lectio de Curvis ad Aequationes solvendas; ad finem Lectionum Geometricarum Dris 

Barrovii, 39 ut M Darii Miscellanea de Curvi-mensoria. 40 Id q[uo]d in Votis praecipue habemus, 

hoc est, invenire scil[icet] et publici Juris facere Methodum facilem, supremarum Aequationum 

radices per Logarithmos consequendi, qua in re cum laborasse utiliter D[omi]num Pellium noverimus, 

nec t[ame]n hactenus qua[m]qua[m] in lucem emisisse, visum fuit id ipsum tibi significare, 

tuaq[ue] de eo cogitata explorare. 

Rem optica[m] q[uo]d spectat, gaudemus, Te de Optica, Dioptrica et Catoptrica Tractatum 

absolvisse, cum annexa Dioptrica practica, morem (modium forte) et instrumenta limandis et 

poliendis necessaria exhibente. 41 Speramus, ejus Exemplaria brevi ad nos transvectum iri. Nota 

tibi haud dubie fuerint Dioptrica Mancini, 42 nec n[on] Problematum Opticorum Centuria 

Eschinardi 43 in Italia; ubi etiam prodijsse nuper accepimus Dioptricam Gottignei, Gregorii de S to 

Vincentio Discipuli, una cum Tractatu de Telescopiis et Microscopiis. 44 Adde synopsin opticam 

Honorati Fabri, ubi de Lente oculari ex duab[us] semi-lentibus, in centro convexitatum conjunctis, 

et extrinsecus utrinq[ue] planis, ceu Eustachii Divini invento praestantissimo, ab Authore primum, 

ut ipse vult, demonstrato, agit[ur]. 45 Accedit elegans P. Cherubini Dioptrica, in Galliis 

nup[er] edita, 46 cui hoc Elogium p[rae]hibet Regnaltius Lugdenensis, q[uo] d scil[icet] bellam 

huj[us] libri Editionem miret[ur], et doctrinam Authoris inibi traditam valde praebet, remq[ue] 

publicam literarium multum ipsi debere arbitret[ur]. 47 Hîc Londini prodiere Lectiones Barrovii 

Dioptricae, 48 quae magni fiunt. In Dania Erasmus Bartholinus Dissert[at]ione[m] edidit de 

Chrystallo Islandico Dis-diaclastico, 49 de quo multa ab ipso et curiose explorata et docte explicata 

sunt. Latere Te no[n] potest, quid gentilis vester, Doctissimus Johannes Ott, Heidelbergae 

nup[er] praestiterit, dum Cogita[ti]ones Physico-Mechanicas de Natura Visionis luci dedit. 50 

De coetero, evulgarunt Itali Tractatum Physico-Mathematicum Rosetti; 51 Bened[icti] 

Castelli opera in unum Volumen collecta; 52 Baliani opuscula posthuma; 53 Borelli motiones naturales 

in Grauitate dependentes; 54 Montanari Exp[er]imenta de ascensu liquorum in tubulis, 

deq[ue] Bullulis vitreis in minutissimas partes, fracta extremitate, dissipantibus. 55 Mengoli opera 

Musica. 56 In Gallia prodierunt Blondellus de Resistentia Corporum Ellipticorum; 57 Milleti de 

[Cales deleted] Chales Euclides, 58 Moutonus de mensura Diametri Solis et Lunae; 59 Antonii 

Lalovera appendices polemicae contra Magnanum; 60 Honorati Fabri commentaria in 

Archimedem. 61 In Anglia vero, D r Wallisius in Motu et Libra; Idem de Calculo Centri Gravitatis;




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 


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




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




Figure 2. Rahn’s letter to Pell (second page): BL, MS Add. 4398, fo. 143 v . (By permission of the British Library.) 

vigere. Cum Residentis caracterem dignè sustineres tot tantaq[ue] beneficia mihi contulisti, ut 

quoties menti observantur, non levi dolore me afficiant, quod retalionis media nulla occurrant, 

obstrictionibus meis respondentia: et hoc magis, quod nouo beneficij genere ita crescant ut ijs 

demerendis nunquam par futurus sim. 

Prorsus sane hujus libri materiam ignorarem, nisi nomen meum in praefatione occurreret, 

et sequentes paginae, methodum à te inventam proderent, adeò linguae Anglicanae rudis sum. 

Multa jam jam vidi, quae negotio grande lumen afferunt, brevi ergò translationem procurabo. Pro 

munere tam grato acceptoq[ue], quantas possum gratias ago. Liber iste animum dat, si Deus otia 

mihi fecerit, ad studium Analyticum denuò me convertere, quod genus semper mihi dulcissimum




fuit. Quae tuae nunc occupationes, planè me latet, non tamen nisi graves et splendidae esse possunt, 

ubicunq[ue] terrarum degas, modò genio atq[ue] merito tuo congruant. 

Antequam negotia publica me obruerent, exercitationes opticae ferè totum me occupârunt, 

quo verò successu illi judicent, qui tubos à me fabrefactos vident, Exemplar tubi [retinui], 69 qui 

à sex usq[ue] ad viginti quinq[ue] pedes usui est: nam ope variorum ductuum facile producitur, 

retrahiturq[ue]. Quatuor lentibus convexo-convexis constat, unâ quidem objectivâ, et 3 ocularibus 

quae parvo tubulo immissae, seorsum majori inserantur; sed quo artificio singula adaptentur, 

non attinet hic referre, quoniam universa recensere, nimis longum foret. 

Amicus quidam mihi persuadere voluit, quasi Secretarius Societatis Regiae Britannicae, 

ante biennium et quod excurrit, literas ad me dedisset, quas apud Mercatores nostros atq[ue] 

Basileenses frustrà quaesivi, ne itaq[ue] suspicio sit, quasi ex proposito responsum intermiserim, 

etiam atq[ue] etiam rogo, ut talem inurbanitatis notam, à me semovere non 70 designeris. 

Hisce vale, Vir celeberrime, meiq[ue] memor esse perge. 

Famigeratissimi nominis tui devotissimus cultor 

Henr. Rhonius Tig: Senator Quaestor et rerum criminaliu[m] praeses 

Tiguri d. 17 Aprilis 1675. 

[annotated by Pell:] Doctor Pel received this letter, May XI. 1675 71 


I have received the Algebra—no longer ‘my’ Algebra, but rather, on many accounts, yours— 

which, thanks to your generosity, was sent to me by a certain scholar; from it, I gather that my 

memory is still flourishing with you, after the passing of so many years. When you were worthily 

fulfilling the role of [English] Resident, you conferred so many favours on me, so often, that 

whenever they come to mind, it causes me no slight pain to think that I have no ways of repaying 

them that would suitable to my obligations—all the more so, since they are so augmented by 

this favour of a new kind, that I shall never be capable of deserving them. 

I am so unskilled in the English language that I would indeed be completely ignorant of 

the contents of that book, were it not for the fact that my name occurs in the preface, and that the 

pages that follow expound the method which you invented. I have immediately observed many 

things which cast great light on the subject; so I shall shortly procure a translation. I thank you 

as much as I can for such a pleasing and welcome gift. That book encourages me—if God gives 

me leisure—to go back to the study of algebra, a field of study in which I always took extreme 

delight. I am completely in the dark about what your present occupation is, but I am sure that, 

wherever in the world you are living, it must be important and distinguished—so long as it suits 

your talent and your merit. 

Before I was overwhelmed by public business, I was almost completely absorbed in optical 

researches; how successful I was therein, those people may judge who saw the telescopes I 

made. I have kept an example of a telescope which can be used at a length of from six to twentyfive 

feet: for by means of various parts that can be drawn out, it can easily be extended or 

retracted. It comprises four convexo-convex lenses: one, indeed, is the objective, and three are 

eye-pieces which, placed inside the small tube, can be inserted separately into the larger one. But 

it would be out of place to describe here the way in which the individual parts may be fitted 

together, as it would take much too long to explain everything. 

A certain friend has given me to understand that the Secretary of the British Royal Society 

sent me a letter more than two years ago; I enquired for it in vain among the merchants of both 

Zurich and Basel. So let it not be suspected that I deliberately delayed replying; I urgently beg 

you not to attribute such a sign of impoliteness to me. 

With this I say farewell, most famous man, and ask you to continue to remember me—the 

most devoted cultivator of your reputation, about which so much is said, 

Heinrich Rahn, Senator of Zurich, Judge and President of the Criminal Court 

Zurich, 17 April 1675




Given the existence of a copy of Oldenburg’s letter in a collection of Rahn’s correspondence, 

Rahn’s comment on it here must be viewed with considerable suspicion. It is 

of course conceivable that Oldenburg’s letter was not delivered until four years after it 

was sent; but the scenario is an unlikely one. And the fact that Rahn so vaguely misrepresented 

the date of Oldenburg’s attempted communication with him (‘more than two 

years ago’) seems consistent with a deliberate tactic of obfuscation; had he genuinely 

been informed of the existence of an undelivered letter, and genuinely instituted a search 

for it, there would seem to be no reason why he should not have remembered the dates 

of those occurrences with reasonable accuracy. Whether any further attempt was now 

made at an exchange of letters between Oldenburg and Rahn is not known, but it also 

appears unlikely: Johann Heinrich Rahn died in 1676, and Henry Oldenburg died in the 

following year. 

NOTES 

1 H. Oldenburg, The Correspondence (ed. A. R. Hall and M. B. Hall), 13 vols (Madison, WI, 

University of Wisconsin Press and London, Mansel; Taylor & Francis, 1965–86). [hereafter: OC]. 

2 Zentralbibliothek, Zurich, MS S. 353, fos. 137–138. The permission of the Zentralbibliothek to 

publish the text of this letter is very gratefully acknowledged. 

3 See W. Schnyder-Spross, Die Familie Rahn von Zürich (Zurich, Schulthess, 1951), pp. 125–169 

(father), 262–279 (son). See also R. Wolf, Biographien zur Kulturgeschichte der Schweiz (Zurich, 

Orell, Füssli & Co., 1858–62), iv, pp. 55–66. 

4 British Library, London [hereafter: BL], MS Add. 4423, fos. 50–51, referring to Pell’s gift as ‘that 

dispute about the measurement of the circle’ (‘Certamen illud cyclometricum’): this was Pell’s 

Controversiae de vera circuli mensura … pars prima (Amsterdam, 1647). 

5 Bodleian Library, Oxford [hereafter: Bodl.], MS Aubrey 6, fo. 55 r ; BL, MS Add. 4424, fo. 260 r 

(‘Pellij discipulus’); BL, MS Add. 4278, fo. 80 r (Pell to Thomas Brancker, 5 March 1666 (quotation) 

(unfortunately these ‘coppies’ have not survived). Cf. also the other evidence cited in N. 

Malcolm, ‘The Publications of John Pell F.R.S. (1611–1685): some new light, and some old confusions’, 

Notes Rec. R. Soc. Lond. 54, 275–292 (2000), here pp. 286–287. 

6 BL, MS Add. 4365, fos. 5–6, Rahn to Pell, 3 Mar. 1658 (fo. 5 r : ‘quot horas dulcissimas’). 

7 Rahn, Teutsche Algebra, sig. XX2 r (‘In den Solutionen, und grad auch in der Arithmetic bediene 

ich mich einer ganz neuen manier … die ich von einer hohen und sehr gelehrten Person erstmals 

erlehnet hab … Dieser form bestehet in einem dreyfachen Margine’); pp. 8 (division sign), 187 

(Pell’s theorem). On Pell’s tri-columnar method see J. A. Stedall, A Discourse concerning algebra: 

English algebra to 1685 (Oxford University Press, 2002), pp. 137–138. 

8 See the letter from Pell to Haak of 13 June 1666, cited below at note 10. 

9 J. H. Rahn [‘Rhonius’], An Introduction to Algebra, Translated out of the High-Dutch into 

English, by Thomas Brancker, M. A., Much Altered and Augmented by D. P. [ sc. Doctor Pell] 

(London, 1668); for details of the history of the project see ibid., sig. A2 r (‘The Translator’s 

Preface’); BL, MS Add. 4414, fo. 10 r (Collins, ‘The Publisher’s preface’, annotated by Pell ‘not 

sent, not printed’); C. J. Scriba, ‘John Pell’s English Edition of J. H. Rahn’s Teutsche Algebra’, 

in For Dirk Struik: scientific, historical and political essays in honor of Dirk J. Struik (ed. R. S. 

Cohen, J. J. Stachel and M. M. Wartofsky), pp. 261–274 (Dordrecht, Reidel, 1974); and the 

account given in N. Malcolm and J. A. Stedall, John Pell (1611–1685) and his correspondence 

with Sir Charles Cavendish: the mental world of an early modern mathematician (Oxford 

University Press, in the press). 

10 Bodl., MS Aubrey 13, fo. 91 v ; ‘Graffschaft’ means ‘county’. 

11 This refers to the large illustrations (copied from Hooke) in the review of Hooke’s Micrographia




in the Journal des sçavans, no. 42, 10 December 1666 (reprinted in Le Journal des sçavans, ed. 

‘le sieur de Hedonville’ [D. de Sallo] (Amsterdam, 1685), i, pp. 738–749). 

12 St Andrews University Library [hereafter: StAUL], MS 31009, fo. 32 v . This is printed, but with 

some serious inaccuracies (e.g. ‘Pahn’ for ‘Rahn’, ‘vitri’ for ‘Rotae’) in James Gregory 

Tercentenary Memorial Volume (ed. H. W. Turnbull), pp. 202–203 (London, 1939). The italics in 

the final sentence here represent underlining in the MS. In this and the other letters transcribed 

in this article, expanded contractions are placed in square brackets. The long sentence in the second 

paragraph of the letter is somewhat ungrammatical in its construction; this is reflected in the 

translation here. 

13 Zentralbibliothek, Zurich, MSS C 114b and C 114a, respectively; the latter is also dated 1667. 

14 The catalogue is in the Stadtbibliothek, Winterthur, MS Folio 12 (cited in E. Fueter, ‘Hans 

Heinrich Rahn als Wissenschafter’, in Schnyder-Spross, op. cit. (note 3), pp. 286–293; here p. 

290). 

15 StAUL, MS 31009, fo. 31 r . 

16 Ibid., fos 31–32 (printed, with minor inaccuracies, in Turnbull, op. cit. (note 12), pp. 198–204; 

Turnbull also misidentifies the entire draft by Collins as ‘the transcript of the letter from Rhonius 

to Haake’ (p. 205, n. 13)). 

17 StAUL, MS 31009, fo. 31 r . 

18 BL, MS Add. 4278, fo. 129r (Pell to Collins, 5 July 1669, thanking him for the offer of ‘a chamber 

in your house’); Correspondence of Scientific Men of the Seventeenth Century (ed. S. J. 

Rigaud), 2 vols (Oxford University Press, 1841), ii, p. 197 (Collins to John Beale, 20 August 

1672: ‘he boarded long at my house’). 

19 See, for example, Rigaud, op. cit. (note 18), i, pp. 149 (Collins to de Sluse, October 1670), 196 

(Collins to Beale, 20 August 1672); ii, p. 220 (Collins to Gregory, 25 March 1671). 

20 See, for example, Rigaud, op. cit. (note 18), i, 149 (Collins to de Sluse, October 1670); ii, 

303–304 (Collins to Newton, 19 July 1670); ii, p. 526 (Collins to Wallis, 21 March 1671). 

21 StAUL, MS 31009, fo. 31 v . 

22 For the ‘model’ and letter to de Sluse see OC vii, pp. 501–504; viii, pp. 15–22. 

23 Some time after leaving Collins’s house, Pell took a room in an inn in Pall Mall, the street where 

Oldenburg lived: see BL, MS Add. 4424, fo. 78 r (a note recording Pell’s presence there in 

September 1671). 

24 BL, MS Add. 4278, fo. 149 r . 

25 See StAUL, MS 31009, fo. 47 (Collins to Gregory, 8 Nov. 1672) (printed, with minor inaccuracies, 

in Turnbull, op. cit. (note 12), p. 247). 

26 Royal Society, MS 81 (Commercium epistolicum), no. 26, 1st leaf, recto: ‘Pellius promittit multa 

de his, sed quando’; for Collins’s draft see OC xi, pp. 256–257, and for the text of Leibniz’s reply, 

ibid., xi, pp. 395–396. 

27 Gerard Kinckhuysen, Algebra, ofte stel-konst, beschreven tot dienst van de leerlinghen (Haarlem, 

1661); De grondt der meet-konst, ofte een korte verklaringe der keegel-sneeden, met een byvoeghsel 

(Haarlem, 1660). The identity of the third work mentioned here is less certain. The 

review of Ferguson’s work in Philosophical Transactions of The Royal Society (see below, note 

28) referred to one book by Kinckhuysen as ‘A Collection of Geometrical Problems, Analytically 

solv’d’ (p. 998); this was apparently the same work as the one listed here by Oldenburg, and from 

this it would also appear that the title used by Oldenburg was more a description than a reproduction 

of the title page. The book was probably Kinckhuysen’s Geometria ofte meet-konst 

(Haarlem, 1663), which does contain some geometrical problems as examples in the text. 

28 Johan Jacob Ferguson, Labyrinthus algebriae … verhandelende de ontbindinge der … vergelijckingen 

(The Hague, 1667). This work had attracted the interest of both Collins and Oldenburg, 

being favourably reviewed in Philosophical Transactions, no. 49 (19 July 1669), pp. 996–999. On 

17 June 1669 Collins had described it in a letter to John Wallis as ‘a book called Labyrinthus 

Algebrae, wherein he solves cubic and biquadratic equations by such new methods as render the 

roots in their proper species, when it may be done … and likewise improves the general method ….




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).




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




Padua in the period 1665–69, was a younger relative (nephew or cousin) of the prominent Zurich 

church historian and Hebrew scholar Johann Heinrich Ott (1617–82), who was a friend and correspondent 

of Rahn (see A Calendar of the Correspondence of J. H. Ott, 1658–1671 (ed. L. 

Forster), Publications of the Huguenot Society of London, xlvi (Frome, 1960), pp. xiv, 14, 17, 28, 

40, 46). Oldenburg had been notified of his work by Leibniz’s letter of 29 April 1671 (OC viii, 

p. 25); he published a notice of Ott’s Cogitationes (probably by Collins) in Philosophical 

Transactions, no. 71 (22 May 1671), pp. 2163–2165; and on 15 January 1671 he sent a letter to 

Ott, requesting further information about his inventions (OC viii, pp. 474–475). Ott’s only other 

published work was a long letter on the physics of sound (commenting on the theories of 

Athanasius Kircher and Sir Samuel Morland), printed in J. J. Wepfer, Observationes anatomicae 

ex cadaveribus eorum, quos sustulit apoplexia (Amsterdam, 1681), pp. 440–464. 

51 This might refer to either of two works by Donato Rossetti: Antignome fisico-mathematiche, con 

il nuovo orbe, e sistema terrestre (Livorno, 1667; 2nd edn Florence, 1668); Dimostrazione fisicomathematica 

delle sette proposizioni che promesse D. Rossetti (Florence, 1668). The former is on 

cosmology, meteorology, and earthquakes; the latter is mostly on barometrics. Collins’s draft 

(StAUL, MS 31009, fo. 32 v ) shows that it was the former that was intended. 

52 Benedetto Castelli, Alcuni opuscoli filosofici del padre abbate D. Benedetto Castelli (Bologna, 

1669). 

53 Giovanni Battista Baliani, Opere diverse (Genoa, 1666). 

54 Giovanni Alfonso Borelli, De motionibus naturalibus a gravitate pendentibus (Reggio di 

Calabria, 1670). 

55 Geminiano Montanari, Pensieri fisico-matematici sopra alcune esperienze fatte in Bologna … 

intorno diversi effetti de’liquidi in cannuccie di vetro, & altri vasi (Bologna, 1667); Speculazioni 

fisiche … sopra gli effetti di que’ vetri temprati, che rotti in una parte si risolvono tutti in polvere 

(Bologna, 1671). The latter work was devoted to the phenomenon known in England as ‘Rupert’s 

drops’. 

56 Pietro Mengoli, Speculationi di musica (Bologna, 1670). 

57 François Blondel, Epistola ad P.W. [Paulum Wurzium], in qua famosa Galilaei propositio discutitur, 

circa naturam lineae qua trabes secari debent ut sint aequalis ubique resistentiae et in qua 

lineam illam non quidem parabolicam, ut ipse Galilaeus arbitratus est, sed ellipticam esse 

demonstratur (Paris, 1661). 

58 Claude François Milliet de Chales, Euclidis elementorum libri octo. Ad faciliorem captum 

accommodati (Lyon, 1660). 

59 Gabriel Mouton, Observationes diametrorum solis et lunae apparentium (Lyon, 1670). 

60 Antoine de la Loubère, Veterum geometria promota in septem de cycloide libris. Et in duabus 

appendicibus (Toulouse, 1660). The appendices contained criticisms of the Minim friar 

Emmanuel Maignan. 

61 Knowledge about Fabri’s work on Archimedes was derived originally from Bertet’s 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). This was then confirmed by Dodington’s letter to 

Oldenburg of 20 January 1671, which declared that ‘Padre Fabri hath lately putt forth a most 

accurate peece intituled Commentarij novi in Archimedem’ (OC vii, p. 405). Possibly 

Dodington’s information (which he said came from ‘some letters from Rome’) and Bertet’s 

derived from the same source. (Cf. note 44 above, on de Gottignies.) In February 1672, however, 

Collins wrote (in a draft for a letter from Oldenburg to de Sluse) that ‘of the Comments on 

Archimedes by … Honorato Fabry we hear nothing’ (OC viii, p. 546); the work appears never to 

have been published. 

62 These titles correspond to section or chapter headings in the three parts (separately published, but 

with continuous pagination) of John Wallis, Mechanica, sive de motu, tractatus geometricus 

(London, 1670–71); the copyist has mistakenly written ‘ie Percussionis’. 

63 James Gregory, Exercitationes geometricae: appendicula ad veram circuli et hyperbolae quadraturam. 

N. Mercatoris quadratura hyperbolae geometrice demonstrata (London, 1668).




64 Nicolaus Mercator, Logarithmo-technia (London, 1668). 

65 Jeremy Horrox [‘Jeremias Horroxius’], Opera posthuma, ed. John Wallis (London, 1672). 

66 This responds to Rahn’s request for information about the specifications of the microscope used 

by Hooke (see his letter to Haak, above). 

67 The dash appears to have been left by the copyist for an illegible word. 

68 Zentralbibliothek, Zurich, MS S. 353, fos. 137–138. 

69 Rahn wrote ‘retiaui’; Pell has written ‘retinui’ above the line. 

70 This ‘non’ is superfluous, and is not reflected in the translation. 

71 BL, MS Add. 4398, fo. 143 (original). This letter is cited, but with the incorrect statement that it 

is tipped in to a copy of Rahn’s Introduction to Algebra (see above, note 9) in the British Library, 

in G. Wertheim, ‘Die Algebra des Johan Heinrich Rahn (1659) und die englische Übersetzung 

derselben’, Bibliotheca Mathematica: Z. Geschichte Math. Wiss. (3) 3, 113–126 (1902), here pp. 

122–123 (n.).

an unpublished letter from henry oldenburg to johann heinrich rahn

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