John Dee and Pedro Nunes established a intriguing scientific
connection. This is a point rarely mentioned in international
historiography. Although it is almost certain that Nunes and Dee
never met in person, there are strong evidences that confirm a
strong intellectual link between the two.
John Dee (1527 – 1608/9)
is now viewed as one of the most interesting personalities of
the Elizabethan intellectual world. Within the social context of his
time, he developed a national and international network
of contacts, extending from the Court to the university and to other
institutions that promoted the sharing of knowledge about the
It is not clear when
Dee’s interest for Nunes’ work first came about. It can be argued
that it was during his stay in the Low Countries, first in 1547 and
then later between 1548 and 1550, that the young Dee must have first
heard of Nunes’ work.
It is reasonable to
speculate that Nunes’ writings would have reached Louvain — the city
where Gemma Frisius (1508–1555) had gathered a group to whom he
taught private lessons on geometry and astronomy — without
difficulty. The region had strong commercial connections with
Portugal, and there was also a large community of Portuguese Jews.
One of these, Diogo Pires (or Didacus Pyrrhus Lusitanus), had links
to Portuguese intellectuals at Louvain, such as Amato Lusitano and
Damião de Góis. He also wrote a dedicatory poem included in Gemma’s
1540 edition of Apian’s Cosmography. In the absence of direct
evidence, it is not possible to establish a stronger correlation
between Nunes, Gemma and Pires, but it is interesting to note that
Pires also studied at Louvain, and that he was a friend of the
publisher Rutger Ressen (Rutgerus Rescius), himself a friend of
by 1550/1, John Dee was in Paris where he met,
among others, Oronce Finé. It is very likely that, while in Paris,
Dee became aware of Nunes' book on the Frenchman's mathematical
errors. The reading of this book may well have influenced Dee's
interest on the unsolved problems of squaring of the circle and
doubling the cube and further work on Euclid's Elements.
Dee owned copies of
all of Nunes’ books, with one exception: the Tratado da sphera.
The reason for his failure to acquire this book, aside from
its linguistic relevance, may relate to a recent clue found at
Cambridge University Library.
By 1552, after coming back to England, Dee studied in detail a work
that had been published in Paris in 1549, attacking some of Nunes’
ideas: Diogo de Sá's De nauigatione .
is more interesting in what it attacks than in what it
proposes. Among other things, the author analysed Nunes’ first
treaty step by step according to his own agenda, and launched an all
round assault on what he perceived to be the cosmographer’s
programme: the use of mathematics as a basis for all certain
knowledge about nature, and the mathematization of scientific
However, it may be argued that de Sá’s
attack also backfired, since the second and third books included
fine translations of much of Nunes’ early work,
thus providing Latin versions that could be read by any interested
European scholars who were unable to read Portuguese. John Dee
acquired the book in 1552, and therefore was an early reader of de
Sá’s ideas. His copy and his annotations (mainly underlining, short
marginal comments, marginal pointers and manicules) reveal more
about his interests in the text: in Book One he was above all
interested in the discussion concerning the certainty and
application of mathematics, and on the hierarchy of sciences (Fig.
3). Throughout, de Sá demonstrated that
he knew the basic sources for the discussion on the quaestio very
well and, from his underlining, it seems that Dee also benefited
from this. In Book Two, Dee reveals his interest in the hierarchy of
the sciences and in the mathematical principles of nautical science.
When Sá begins his translation of Nunes’ work, Dee concentrates on
technical aspects of the theory of rhumb lines. In Book Three, he
again shows interest in more technical aspects (of cartography, for
example), paying close attention to the discourse of the "mathematician"
(that is, Nunes’ words and ideas translated and adapted by de Sá)
and showing virtually no interest in the practical applications
proposed by Diogo de Sá. Even if embedded within a philosophical
discussion, the correct translation and adaptation of Nunes’
treatises seems to have enabled Dee to use these works as a textbook
on the topic.
In a 1558 letter to Mercator, Dee implied that he had been
corresponding with the Portuguese mathematician for some time. The
letter was published in Dee’s first work, Propaedeumata
In this dedicatory letter he recalled the good times both him and
cartographer Gerard Mercator, in which he recalled the good times
they spent ‘philosophizing’ together in Louvain. He also justified
the delay in the completion of his awaited scientific work,
declaring that had fallen severely ill in the previous year. Then,
he makes an unexpected statement
you should know that, besides the extremely dangerous illness from
which I have suffered during the whole year just past, I have also
borne many other inconveniences (from those who, etc.) which have
very much hindered my studies, and that my strength has not yet been
able to sustain the weight of such exertion and labor as the almost
Herculean task will require for its completion. And if my work
cannot be finished or published while I remain alive, I have
bequeathed it to that most learned and grave man who is the sole
relic and ornament and prop of the mathematical arts among us, D. D.
Pedro Nuñes, of Salácia, and not long since prayed him strenuously
that, if this work of mine should be brought to him after my death,
he would kindly and humanely take it under his protection and use it
in every way as if it were his own: that he would deign to complete
it, finally, correct it, and polish it for the public use of
philosophers as if it were entirely his. And I do not doubt that he
will himself be a party to my wish if his life and health remain
unimpaired, since he loves me faithfully and it is inborn in him by
nature, and reinforced by will, industry, and habit, to cultivate
diligently the arts most necessary to a Christian state”.
In general, researchers have passed over more profound implications
of Dee’s declaration. But this connection has not been missed by
some important historians of science: Eva G.R. Taylor and David
Waters have addressed the link between the two men in their
important work on the history of navigation.
Even so, they limit their studies to the influence of Pedro Nunes on
Dee’s work on nautical issues.
Unfortunately, the nature of any correspondence going on between
Nunes and Dee is unknown, but it is very unlikely that a discussed
mathematical topic at the time – the construction of rhumb tables –
was left out of these discussions. On the contrary, John Dee’s
Canon Gubernauticus or an Arithmeticall Resolution of the Paradoxall
, was finished sometime during the period that
Dee often referred Nunes as the “most
learned and grave man”.
According to Eva Taylor: “It was, in fact, a practical development
on the teaching of Pedro Nuñez on this subject, and its invention
belongs to a period when Dee in known to have been in personal touch
with the great Portuguese”.
Between 1556 and 1558,
John Dee was interested in resolving the cartographic problems
introduced by the navigation in high latitudes and calculated a set
of tables known as Canon Gubernauticus. These tables were in
fact aids to what he called "paradoxall navigation".
Prof. E.G.R. Taylor defined the “paradoxall Compas” as a zenithal
equidistant projection chart and the “paradoxal” lines were in fact
rhumb lines, for the first time imagined by Pedro Nunes in 1537.
John Dee's Canon Gubernauticus calculates the latitude and
longitude for the 7 classical rhumbs spiralling across the globe
from a point at the equator to a point at 80º latitude.
Although pursuing this matter in manuscripts and private discussions
in the 40's and 50's, Nunes would only present publicly his full
mathematical theory of the rhumb line in his book printed in 1566 (Petri
Nonii Salaciencis Opera), which Dee also had in his library.
This may also suggest that a sharing of scientific knowledge was
going on between both men at the time that Nunes was almost
finishing the development of his theory.
Certainly gaining from these contacts, John Dee would in time
express his vision of the art of navigation in the 1570’s
“The Arte of Navigation, demonstrated how, by the shortest good way,
by the aptest Direction, and in the shortest time, a sufficient
Ship, between any two places (in passage Navigable) assigned: may be
conducted: and in all storms, and natural disturbances chancing,
how, to use the best possible means, whereby to recover the place
first assigned. What need, the Master Pilot, hath of other Arts,
here before recited, it is easy to know: as, of Hydrography,
Astronomy, Astrology, and Horometry. Presupposing continually, the
common Base, and foundation of all: namely Arithmetic and Geometry.
So that, he be able to understand, and Judge his own necessary
Instruments, and furniture Necessary: Whether they be perfectly made
or no: and also can, (if need be) make them, himself. (…) And also,
be able to Calculate the Planets places for all times.(…)
Sufficiently, for my present purpose, it doth appear, by the
premises, how Mathematical, the Art of Navigation, is: and how it
needed and also used other Mathematical Arts.”
In Dee’s opinion, the “modern” sea pilot should base his everyday
art on scientific knowledge provided by mathematical disciplines, which
is in consensus with Nunes’ own vision of the ratio nauigandi.
As he had stated in 1537 about its mathematical principles:
“(…) And because no rule that is based on speculative or theoretical
knowledge can be well practiced and understood if one doesn’t know
this same principles" since “nothing is most evident than
mathematical demonstration, which, by no means, is possible to be
contested”. This would be reinforced in his 1566 work: “Everything
that we write on these [nautical] subjects must be received without
any hesitation, since nothing exists more exact, nothing more
certain and nothing more evident then mathematical demonstration,
which certainly nobody will ever be able to oppose”.
In fact, the ideas that both men sheared
would echo throughout Europe and were included in many sixteenth and
seventeenth centuries’ navigation textbooks.
In England (and why not to say in Europe), John Dee was one of the
first to consider navigation as a scientific discipline, which
reinforces his important role in what Waters and Taylor called "the
English awakening" in maritime affairs.
Not much has been said about Nunes’ influence on Dee’s mathematical
views, in general, and the use of mathematics to study nature. It is
hard to believe that Dee considered Nunes “that
most learned and grave man who is the sole relic and ornament and
prop of the mathematical arts among us” solely because he had
learned nautical science with him.
In fact, there
is evidence suggesting that this influence was wider. In a letter
from the 1590's, Dee claims to have finished a work in 1560, on the
areas of plane triangles, in three books (De Triangulorum
rectilineorum Areis -- libri -- 3)
 dedicated to Pedro Nunes and, as late as 1584, Dee
and Jacob Kurtz were examining instruments containing improvements
(the nonius scale) proposed by Pedro
“After dinner I went to Dr. Curtz home (…) he showed divers his
labours and inventions mathematical, and chiefly arithmetical
tables, both for his invention by squares to have the minute and
second of observations astronomical, and so for the mending of
Nonnius his invention of the quadrant dividing in 90, 91, 92, 93,
Again in the
Euclide’s Preface, Dee tried to justify and promote the
translation of this classic book to vernacular. He then gave several
examples of similar translation projects going on in Europe, which
included an example for the Iberian Peninsula. He does a very
curious remark by suggesting that Nunes taught themes of his
Portuguese treatises at the University:
"Nor yet the Vniuersities of Spaine, or Portugall, thinke
their reputation to be decayed: or suppose any their Studies to be
hindred by the Excellent P. Nonnius, his Mathematicall workes,
in vulgare speche by him put forth."
We know (as Dee also knew) that this was not true since classes at
the university were delivered in Latin, but this echoes the fact
that Dee was aware of Nunes 1537 works in Portuguese, and very
likely, that he was also conscious of Nunes translation project and
agreed with the ideas behind it.
At the time, this defence of vernaculars as a scientific language
was common all across Europe and Nunes was also involved on it. In
his 1537 book he states: "Science has no language so, by using any
language, it is possible to explain it (...) And therefore, if from
one language to other, one can translate any non scientific text, I
do not know where, so much fear to put a science text in common
language, comes from."
Pedro Nunes developed his “program for the mathematization of the real world”,
a precise, sustained and quite explicit program of promotion of the
mathematical sciences, starting in the mid 30's until 1566. This was
first achieved by applying mathematics to the art of navigation but
throughout all his work, that covers subjects spanning from Algebra
to Geometry, Nautical Science, Astronomy, Cartography, instruments
and even Physics, Nunes extended the “program” with one objective in
mind, that is, to show that Mathematics was the main tool to
describe the real world. This would be one of the distinctive
characteristics of the "scientific revolution" that would have its
peak in the seventeenth century.
Naturally, John Dee developed his own scientific program which, in a
first stage, was a program based on the use of mathematical
principles as tools to describe the natural world, something that
Dee would start to promote within his role as a consultant on
nautical subjects and go on doing along his life. It is Shumaker and
Heilbron's opinion that "Dee's contributions were promotional and
pedagogical: he advertised the uses and beauties of mathematics,
collected books and manuscripts, and assisted in saving and
circulating ancient texts; he attempted to interest and instruct
artisans, mechanics, and navigators, and strove to ease the
beginner's entry into arithmetic and geometry. It is in this last
role, as pedagogue, that Dee displayed his competence, and made his
occasional small contributions (which he classed as great and
original discoveries) to the study of mathematics as a consultant on
Even agreeing with these words in what concerns Dee's contribution
to pure mathematics, one has to stress that he was perfectly aware
of many scientific developments going on in his time and that he
influenced and worked side by side with some of the most influential
mathematical practitioners in Elizabethan England. His mathematical
program would ultimately be published in the Euclide's Preface,
which Yates considered, in a broad sense, “the manifesto of Dee’s
full article here:
See Chapter XV. Cosmographia Petri Apiani,
per Gemmam Frisium apud Louanienses medicum & mathematicu[m]
insignem, iam demum ab omnibus vindicata mendis, ac
nonnullis quoq[ue] locis aucta, additis eiusdem argumenti
libellis ipsius Gemmae Frisii (Antuerpiae: sub scuto
Basiliensi, Gregorio Bontio, 1545), Chapter XV, fl. 23v-25v.
An unknown detractor wrote a treatise
(nowadays lost) attacking Nunes’ 1537 treatises. Nunes
answered back with a manuscript defence. This document is
presently kept at the Biblioteca Nazionale di Firenze (Codice
modern transcription and study about this manuscript:
Joaquim de Carvalho, “Uma obra desconhecida e inédita de
Pedro Nunes: [defensão do tratado de rumação do globo para a
arte de navegar]”, in: Inedita ac rediuiua, subsídios
para a história da filosofia e da ciência em Portugal,
(Coimbra, 1952), Separata de Revista da Universidade de
Coimbra, n.º 17, (Coimbra: Universidade de Coimbra,
1953), pp. 521-631.
de Sá, De navigatione libri tres quibus mathematicae
disciplinae explicantur ab Iacobo a Saa Equite Lusitano
nuper in lucem editi (Parisiis: officina Reginaldi
Calderii et Claudii eius filii, 1549).
Dee’s copy of this book is today at Cambridge
University Library, shelfmark: CUL, R*.5.27 (F). See note [B
154] of Julian Roberts and Andrew G. Watson, John Dee's
Library Catalogue (London: The Bibliographical Society,
discussion was much alive in sixteenth century Europe and
became known as quaestio de certitudine mathematicarum.
About the quaestio in Portugal and the
role of Diogo de Sá's book in this discussion, see: Bernardo
Machado Mota, O estatuto da matemática em Portugal nos
séculos XVI e XVII, PhD thesis (Universidade de Lisboa,
John Dee on Astronomy. Propaedeumata
Aphoristica (I558 and 1568),
edited and translated with general notes by Shumaker, Wayne,
with introductory essay by Heilbron, John L., (Berkeley:
University of California Press, 1978), «Preface», p. ix.
"paradoxall navigation", see: John Davis,
Secret. Devided into 2. partes, wherein is taught the three
kindes of Sayling, Horizontall, Paradoxall, and sayling upon
a great Circle: also an Horizontall Tyde Table for the easie
finding of the ebbing and flowing of the Tydes, with a
Regiment newly calculated for the finding of the Declination
of the Sunne, and many other most necessary rules and
Instruments, not heeretofore set foorth by any (Londres,
Thomas Dawson, 1595).
The definition provided suggests only a superficial study
from Davis. He certainly owed much of this publication to
the documents taken from Dee’s library.
Pedro Nunes, Obras, Vol. IV, (Lisboa: Fundação
Calouste Gulbenkian, 2008), p. 30.
last known reference comes in a letter from 1592 (printed in
1599). Dee does here a short reference to a work
De Triangulorum rectilineorum Areis -- libri
-- 3 -- demonstrati: ad excellentissimum Mathematicum Petrum
Nonium conscripti -- Anno -- 1560.
In a recent paper presented Stephen Johnson
claimed a correspondence between this work and a lost work
also dedicated to Pedro Nunes. In: Stephen Johnson, «John
Dee’s Tyrocinium Mathematicum: new evidence for a
lost text», John Dee Quatercentenary Conference, 21-22
Nunes, Obras, vol. I, (Lisboa: Fundação Calouste
Gulbenkian, 2002), p. 5.
Dee on Astronomy. Propaedeumata Aphoristica (I558 and 1568),
A. Yates, The Occult Philosophy in the Elizabethan Age
(London: Routledge and Kegan Paul, 1979),
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