Pedro Nunes

ish origin) family [Martins, Jorge, "Portugal e os Judeus" (3 vol.), Nova Vega, Lisboa, 2006, ISBN 972-699-847-6] .

Pedro Nunes, considered to be one of the greatest mathematicians of his time, is best known for his contributions in the technical field of navigation, which was crucial to the Portuguese period of discoveries. He was the first to propose the idea of a loxodrome and was also the inventor of several measuring devices, including the nonius, named after his Latin surname.

Life

Little is known about Nunes' early education. He studied at the University of Salamanca, maybe from 1521 until 1522, and at the University of Lisbon (this University later become the University of Coimbra) where he obtained a degree in medicine in 1525. In the 16th century medicine used astrology, so he also learned astronomy and mathematics. He continued his medical studies but held various teaching posts within the University of Lisbon, including Moral, Philosophy, Logic and Metaphysics. 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. This was a new post in the University of Coimbra and it was set up to provide instruction in the technical requirements for navigation, clearly a topic of great importance in Portugal at this period when control of sea trade was the chief 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 up to 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's possible that while at the University of Coimbra, Christopher Clavius attended Pedro Nunes' classes, and was influenced by his works.

Work

Pedro Nunes lived in a transition period where science was changing from valuing theoretical knowledge (and thus where the main role of a scientist/mathematician was 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, as his shown by his first published work, but 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, by then science's lingua franca, aiming for an audience of European scholars, but also in Portuguese, and Spanish ("Livro de Algebra").

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. The later invention of logarithms allowed Leibniz to establish algebraic equations for the loxodrome.

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 all the problems this caused, a situation that lasted until Mercator developed Mercator projection, the system which is still used.

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 the astrolabe's accuracy. It consisted of tracing a certain number of concentric circles on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant would have 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. The nonius was used for a while 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 978-0713407273] These were eventually superseded by verniers.

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

He was probably the last major mathematician to make relevant improvements to the ptolemaic system (a geocentric model), however this lost importance because Copernicus heliocentric system replaced it by then. Nunes knew Copernicus' work but he only made a short reference to it in his published works with the objective of correcting some mathematical errors.

He 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, independently, tackled by Johann and Jakob Bernoulli more than a century later with less success. They could find a solution to the problem of the shortest day but failed to determine its duration, possibly because they got lost on details of differential calculus, still a recently developed tool (at that point in time). It also shows Nunes as a pioneer in solving maxima and minima problems, which only became common in the next century using differential calculus.

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.

Bibliography

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

Commented and expanded translations:
*"Tratado da sphera com a Theorica do Sol e da Lua" (Treaty about the Sphere with Theory of the Sun and the Moon), (1537). From "Tractatus de Sphaera" by Johannes de Sacrobosco, "Theoricae novae planetarum" by Georg Purbach and the "Geography" by Claudius Ptolemaeus.

Original work:
*"Tratado em defensão da carta de marear" (Treatise Defending the Sea Chart), (1537).
*"Tratado sobre certas dúvidas da navegação" (Treatise about some Navigational Doubts), (1537)
*"De crepusculis" (About the Twilight), (1542).
*"De erratis Orontii Finei" (About the Errors of Orontii Finei), (1546).
*"Petri Nonii Salaciensis Opera", (1566). Expanded, corrected and reedited as "De arte adque ratione navigandi" in 1573.
*"Livro de algebra en arithmetica y geometria" (Book of Algebra in Arithmetics and Geometry), (1567).

Some modern reprints:
*"Obras" (6 vol.), Academia das Ciências de Lisboa, Lisboa, 1940-1960 (No ISBN at the [http://opac.porbase.org/ipac20/ipac.jsp?uri=full=3100024@!724332@!15 books' record] at the Portuguese National Library)
*"Obras" (3 vol.), Fundação Calouste Gulbenkian, Lisboa, 2002-?, ISBN 972-31-0985-9 and ISBN 972-31-1084-9 (more volumes are likely to be published)

Honours

*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.

References

*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
* [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)

Footnotes