The First Description Of The
Theory Of Loxodromic Curves
Some Of The Earliest Published
Observations On Copernicus
.
NUÑES, Pedro [Basel, 1566]
Opera: quæ complectuntur, primum, duos libros, in quorum priore tractantur pulcherrima problemata. In altero traduntur ex mathematicis disciplinis regulae & instrumenta artis nauigandi, quibus uaria rerum astronomicarum...
Folio. [31.5 x 21.5 cm]. (6) ff., 307, (1) pp. Bound in contemporary limp vellum, with trace of one tie. Head and tail of spine chipped, repair to bottom corner of back cover. Private library stamps on title, minor worming to initial leaves touching two letters on title. Waterstains affecting blank margins, upper corner. Extensive Marginal annotations, diagrams and calculations in an exuberant early hand. An excellent copy in a contemporary binding.
Rare first Latin edition of Nuñes’ major contribution to the science of navigation, augmenting the Portuguese original of 1537, the work in which he introduced the concept of rhumb lines (predating Mercator), also containing a valued commentary on Peurbach, second only to that of Rheticus in its time, and also containing (as the original Portuguese of 1537 could not) some of the earliest published observations on Copernicus’ De Revolutionibus. It is ironic that some of the earliest published comments on Copernicus should originate from a Portuguese author—one whose country was the most effective regarding censorship in the whole of Europe—, and that the present work, which per force could never have been published in the Iberian peninsula for precisely that reason, should be issued by the same Basel publisher which issued the second edition of the work Nunes attacks. And in the very same year! As Portuguese Royal Cosmographer, Nuñes’ works were standard reading among the navigators and explorers of the mid-16th century (and not only in Portugal), and have become extremely scarce on the market.
In the 1530s Pedro Nuñes was called upon to help his compatriots in their quest for ever more accurate maps and navigational methods. Cartographers and sea captains incorrectly believed that sailing on a single bearing (at equal oblique angles with all meridians) would result in the shortest course between two terrestrial points. In fact, the former type of course, christened a ‘loxodrome’ by Snell in the 17th century (from the Greek ‘oblique course’) is measurably longer than an ‘orthodrome’ (‘straight course’), the most direct route along a ‘great circle’. In 1537 Nuñes published his Tratado da Sphera, including two treatises that differentiated between ‘loxodromic’ and ‘orthodromic’ sailing. He was the first to illustrate the curved ‘loxodromes’, otherwise known as rhumb lines. Mercator would create a loxodromic terrestrial globe, the famed eponymous projection, in 1569 (see Waters, pp. 71-4). Whether Mercator was familiar with Nuñes’ work or developed rhumb lines independently has not been determined. The Tratado, Nuñes’ only work published in Portuguese, also contained vernacular translations of Sacrobosco, Ptolemy and Peurbach.
Nuñes’ Opera, published in 1566, is a substantially expanded Latin translation of the Tratado da Sphera, containing corrected and improved editions of his two treatises on theoretical nautical questions. The second of these treatises in particular elaborates on the theory and practice of rhumb lines. It also contains remarks on other matters besides nautical issues, namely, some observations on Copernicus' De revolutionibus (1543). Although Nuñes’ copy of Copernicus is not extant, according to Prof. Owen Gingerich, he is one of the most frequently mentioned authorities in annotated copies of the first edition, suggesting that his criticisms were widely disseminated. It is significant that among top-level mathematicians, Nuñes is one of the first (excepting Rheticus and a handful of others) to refer, in print, to Copernicus. All the observations by Nuñes on Copernicus are technical. He notes some errors in Copernicus (about trigonometry—these are today well-known errors in De revolutionibus); he disagrees with some of Copernicus’ estimates and he criticizes some aspects of Copernicus’ models, namely about the moon. It is true that from these remarks one can detect the (predictable) opposition of Nuñes to heliocentrism, but it is noteworthy that his objections are always technical, his respect for Copernicus is obvious, and his critiques are always mild.
In addition to the pioneering treatises on navigation and reactions to heliocentrism, Nuñes’ Opera includes a brief annotation on a problem of the Aristotelian Mechanica, about oars. “It is a contribution to the geometry of motion—an attempt to determine, at each moment and in every circumstance, the deviation of the boat in relation to the oars.” – DSB X, p. 161 The work ends with a lengthy and sophisticated commentary on Peurbach's Theoricae novae planetarum.
Nuñes (1502-1578) studied medicine and mathematics at Salamanca and Lisbon. Appointed royal cosmographer in 1529, he became professor of mathematics at Coimbra in 1544. At the court of Lisbon from 1572, he instructed pilots, navigators and cartographers, and invented the ‘nonius’, an instrument for accurately measuring small angles. He is, by all accounts, the greatest Portuguese mathematician, and was the single greatest technical influence on the generation of Portuguese navigators during the 16th century.
We are grateful to Prof. Henrique Leitao, a historian of science at the Universidade de Lisboa and an expert on Nuñes for a brief report on the present work. NUC records NN, NNE, ICN, Minnesota. OCLC adds Smithsonian, Harvard, NYPL, Oxford. The Opera was reprinted in 1573 and 1592. According to the NUC, the first, Portuguese-language edition is held by LC, JCB & Harvard; it is not listed in OCLC). The last copy we have traced on the market was the Horblit copy offered by Kraus in Catalogue 168.113: it had a distinguished provenance from a contemporary Portuguese naval officer, and the price of $95,000 was asked.
Palau y Dulcet (2nd ed.); 196,744; Adams N-370; Kenneth G. McIntyre, The Secret Discovery of Australia (1988) p. 95; A. Fontoura da Costa, Pedro Nunes (1502-1578), Lisbon, 1938/1969; DSB X.160-2; Note: the very rare 1537 ed. earns a mention in Church (76), Borba II, p. 622, Alden-Landis 537/15 and Sabin 56,320 for its references to the newly discovered land of Brazil (ff.B, B7). |
