Pedro Nunes

Little is known about Nunes' early education, life or family background, only that he was born in Alcácer do Sal in Portugal, his origins are possibly Jewish and that his grandchildren spent a few years behind bars after they were accused by the Portuguese Inquisition of professing and secretly practicing Judaism.

[http://cvc.instituto-camoes.pt/ciencia_eng/e42.html Pedro Nunes – A mathematician in a country of navigators] He studied at the University of Salamanca, maybe from 1517 until 1522. He returned to Lisbon c. 1529 and started teaching at the University.

He continued his medical studies but held various teaching posts within the University of Lisbon, including Moral, Philosophy, Logic and Metaphysics. He obtained his doctorate in medicine in 1532. When, in 1537, the Portuguese University located in Lisbon returned to Coimbra, he moved to the re-founded University of Coimbra to teach mathematics, a post he held until 1562.{{Cite web|url=http://www-groups.dcs.st-and.ac.uk/history/Biographies/Nunes.html|title=Pedro Nunes (1502-1578)|website=www-groups.dcs.st-and.ac.uk|access-date=2019-02-08}} This was a new post in the University of Coimbra and it may have been established to provide instruction in the technical requirements for navigation: clearly a topic of great importance in Portugal at this period, when the control of sea trade was the primary source of Portuguese wealth. Mathematics became an independent post in 1544.

In addition to teaching he was appointed Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547: a post which he held until his death.

In 1531, King John III of Portugal charged Nunes with the education of his younger brothers Luís and Henry. Years later Nunes was also charged with the education of the king's grandson, and future king, Sebastian.

It is possible that, while at the University of Coimbra, future astronomer Christopher Clavius attended Pedro Nunes' classes, and was influenced by his works. Clavius, proponent of the Gregorian Calendar, the greatest figure of the Colégio Romano, the great center of Roman Catholic knowledge of that period, classified Nunes as “supreme mathematical genius". Nunes died in Coimbra.

Pedro Nunes lived in a transition period, during which science was changing from valuing theoretical knowledge (which defined the main role of a scientist/mathematician as commenting on previous authors), to providing experimental data, both as a source of information and as a method of confirming theories. Nunes was, above all, one of the last great commentators,{{citation|last1 =Fernández|first1=V.V.|last2=Rodrigues Jr.|first2=W.A.|title=Gravitation as a Plastic Distortion of the Lorentz Vacuum|year = 2010|publisher = Springer-Verlag|location=Berlin Heidelberg|page=5|isbn=978-3-642-13589-7|arxiv=0909.4472|doi=10.1007/978-3-642-13589-7|bibcode=2010gpdl.book.....F|s2cid=115171595 }} as is shown by his first published work “Tratado da Esfera”, enriched with comments and additions that denote a profound knowledge of the difficult cosmography of the period. He also acknowledged the value of experimentation.

In his Tratado da sphera he argued for a common and universal diffusion of knowledge.«o bem, quanto mais comum e universal, tanto é mais excelente» quoted by Calafate, Pedro (see above) Accordingly, he not only published works in Latin, at that time science's lingua franca, aiming for an audience of European scholars, but also in Portuguese, and Spanish (Livro de Algebra).

File:Pedro Nunes April 2009-1a.jpg showing the well-known navigators. Left to right: Jácome de Maiorca (cosmographer and chart maker), Pedro Escobar (navigator), Pedro Nunes (shown holding an armillary sphere), Pero de Alenquer (navigator), Gil Eanes (navigator) and finally João Gonçalves Zarco (navigator)]]

Much of Nunes' work related to navigation. He was the first to understand why a ship maintaining a steady course would not travel along a great circle, the shortest path between two points on Earth, but would instead follow a spiral course, called a loxodrome. These lines —also called rhumb lines— maintain a fixed angle with the meridians. In other words, loxodromic curves are directly related to the construction of the Nunes connection —also called navigator connection.In mathematics, Nunes connection is an example of connection which Cartan showed to Einstein in 1922 when he visited Paris.

In his Treaty defending the sea chart, Nunes argued that a nautical chart should have its parallels and meridians shown as straight lines. Yet he was unsure how to solve the problems that this caused: a situation that lasted until Mercator developed the projection bearing his name. The Mercator Projection is the system which is still used.

Nunes also solved the problem of finding the day with the shortest twilight duration, for any given position, and its duration. This problem per se is not greatly important, yet it shows the geometric genius of Nunes as it was a problem which was independently tackled by Johann and Jakob Bernoulli more than a century later with less success.[https://books.google.com/books?id=z_BNPYRNmyYC&dq=Bernoulli+pedro+nunes&pg=PA87 Prelúdio para uma história: ciência e tecnologia no Brasil] They could find a solution to the problem of the shortest day, but failed to determine its duration, possibly because they got lost in the details of differential calculus which, at that time, had only recently been developed. The achievement also shows that Nunes was a pioneer in solving maxima and minima problems, which became a common requirement only in the next century using differential calculus.[http://pedronunes.fc.ul.pt/science.html Pedro Nunes (1502 - 1578)(Science)]

He was probably the last major mathematician to make relevant improvements{{According to whom|date=March 2010}} to the ptolemaic system (a geocentric model describing the relative motion of the Earth and Sun). With time, in a slow and complex process, the geocentric model was replaced by the heliocentric system proposed by Nicolaus Copernicus. Nunes knew Copernicus' work but referred only briefly to it in his published works, with the purpose of correcting some mathematical errors.

Most of Nunes' achievements were possible because of his profound understanding of spherical trigonometry and his ability to transpose Ptolemy's adaptations of Euclidean geometry to it.

File:Nonio originale.jpgReis, António Estácio dos, "O nónio de Pedro Nunes", Gazeta de matemática, 143 (2002) 5-19]]

Nunes worked on several practical nautical problems concerning course correction as well as attempting to develop more accurate devices to determine a ship's position.

He created the nonius to improve instrument (such as the quadrant (instrument)) accuracy. This consisted of a number of concentric circles traced on the instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant would comprise 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the alidade fell was noted. A table was then consulted to provide the exact measure.{{Citation needed|date=March 2010}}

The nonius was used by Tycho Brahe, who considered it too complex. The method inspired improved systems by Christopher Clavius and Jacob Curtius.Daumas Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 {{ISBN|978-0-7134-0727-3}} These were eventually improved further by Pierre Vernier in 1631, which reduced the nonius to the Vernier scale that includes two scales, one of them fixed and the other movable. Vernier himself used to say that his invention was a perfected nonius and for a long time it was known as the “nonius”, even in France. In some languages, the Vernier scale is still named after Nunes, for example {{lang|sv|nonieskala}} in Swedish.

Pedro Nunes also worked on some mechanics problems, from a mathematical point of view.

Nunes was very influential internationally, e.g. on the work of John DeeAlmeida, Bruno (September 2012). "On the origins of Dee's mathematical programme: The John Dee–Pedro Nunes connection". Studies in History and Philosophy of Science Part A. 43: 460–469. http://doi:10.1016/j.shpsa.2011.12.004 and Edward Wright.{{cite web|title=Edward Wright and Pedro Nunes|url=http://pedronunes.fc.ul.pt/episodes/edward_wright/edward_wright.htm|work=Pedro Nunes (1502 - 1578)|publisher=Centre for the History of Sciences, Lisbon University|access-date=17 October 2011|author1=Almeida, Bruno |author2=Leitão, Henrique |name-list-style=amp |year=2009}}

• One of the best known Lisbon public Secondary/High Schools is named after Pedro Nunes, Escola Secundária de Pedro Nunes (teaching 7th to 12th grade). It was founded, in 1906, as Lyceu Central da 3ª Zona Escolar de Lisboa (Central Liceum of the 3rd School Area of Lisbon). Over the years had known several designations: Lyceu Central de Pedro Nunes (1911–1930), Liceu Normal de Lisboa (1930–1937), Liceu Pedro Nunes (1937–1956), Liceu Normal de Pedro Nunes (1956–1978) and Escola Secundária de Pedro Nunes (1978–{{as of|2011|alt=present}}), but is still known as Liceu Pedro Nunes. Multiple Portuguese personalities{{Who|date=February 2025}} have studied in Pedro Nunes. The current headquarters commemorated its centenary in 2011, after being refurbished and modernized between 2008 and 2010.
• He was featured on 100 escudos coins.
• The Instituto Pedro Nunes in Coimbra, a business incubator and a center of innovation and technology transfer founded by the University of Coimbra, is named after Pedro Nunes.{{Citation needed|date=March 2010}}
• Asteroid 5313 Nunes is named after him{{Citation needed|date=October 2011}}
• TAP Portugal Airlines has named an Airbus A330-202 airplane after him, registered CS-TOP.

File:Nunes - De erratis Orontii Finaei, 1546 - 103782.jpg

File:Nunes, Pedro – De arte atque ratione navigandi, 1573 – BEIC 13151799.jpg

Pedro Nunes translated, commented and expanded some of the major works in his field, and he also published original research.

Printed work:

• Tratado da sphera com a Theorica do Sol e da Lua (Treatise on the Sphere with the theory of the Sun and the Moon), (1537). From Tractatus de Sphæra by Johannes de Sacrobosco, Theoricae novæ planetarum by Georg Purbach and the Geography by Claudius Ptolemaeus. Included original texts: Tratado em defensam da carta de marear (Treatise in defense of the nautical chart), (1537); Tratado sobre certas dúvidas da navegação (Treatise about some doubts of navigation), (1537)
• De crepusculis (About the Twilight), (1542).
• {{Cite book|title=De crepusculis|volume=|publisher=Luiz Rodrigues|location=Lisboa|year=1542|language=la|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=13148868}}
• De erratis Orontii Finæi (About the errors of Oronce Fine), (1546).
• Petri Nonii Salaciensis Opera, (1566). Expanded, corrected and reedited as De arte adque ratione navigandi in 1573.
• [https://purl.pt/40145 Livro de algebra en arithmetica y geometria] (Book of Algebra in Arithmetics and Geometry), (1567).

Manuscripts:

• [Manuscrito de Florença] (Florence manuscript), (written in the period 1537-1540){{Cite thesis |title=A influência da obra de Pedro Nunes na náutica dos séculos XVI e XVII:um estudo de transmissão de conhecimento |url=https://repositorio.ul.pt/handle/10451/6699 |date=2011 |degree=doctoralThesis |first=Bruno José M. G. Pereira de |last=Almeida}}

Some modern reprints:

• Obras (4 vol.), Academia das Ciências de Lisboa, Lisboa, 1940-1960 (No ISBN at the [https://web.archive.org/web/20070927025712/http://opac.porbase.org/ipac20/ipac.jsp?uri=full=3100024@!724332@!15 books' record] at the Portuguese National Library)
• Obras (6 vol.), Fundação Calouste Gulbenkian, Lisboa, 2002–2011, {{ISBN|972-31-0985-9}} and {{ISBN|972-31-1084-9}} (two more volumes are likely to be published)

{{Reflist}}

• Mourão, Ronaldo Rogério de Freitas, Dicionário das Descobertas, Pergaminho, Lisboa, 2001, {{ISBN|972-711-402-4}}
• Dias, J. S. da Silva, Os descobrimentos e a problemática cultural do século XVI (3rd ed.), Presença, Lisboa, 1988
• [https://web.archive.org/web/20050808082934/http://www.instituto-camoes.pt/cvc/filosofia/ren2.html Calafate, Pedro, Pedro Nunes, at Instituto Camões' site] (in Portuguese)
• [http://purl.pt/40/1/pn-impressos-xvi.html Printed works of Pedro Nunes in the 16th century, at Portuguese National Library] (in Portuguese)

• [http://pedronunes.fc.ul.pt/ Pedro Nunes page (FCUL)]

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Category:1502 births

Category:1578 deaths

Category:16th-century Portuguese mathematicians

Category:Portuguese Renaissance humanists

Category:16th-century Portuguese writers

Category:Portuguese geographers

Category:Scientific instrument makers

Category:University of Coimbra alumni

Category:University of Salamanca alumni

Category:Academic staff of the University of Salamanca

Category:Jewish Portuguese writers

Category:People from Setúbal District

Category:People from Coimbra

Category:Portuguese inventors

Category:European Sephardi Jews

Category:Cosmographers