Pedro Nunes
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Pedro Nunes (pron. IPA: ['pedɾu 'nunɨʃ]; Latin, Petrus Nonius), (1502, Alcácer do Sal – August 11, 1578, Coimbra) was a Portuguese mathematician, cosmographer, and professor, maybe born from a New Christian (of Jewish origin) family.
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.
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[edit] 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.
[edit] 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/mathmatician 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. For example, he saw the importance of the Portuguese navigators being able to sail south of the equator despite previous author's assurances that it was impossible, thereby demonstrating that the antipodes existed and that men lived there just as in Europe, something that even the saints deemed as impossible.
Nunes believed that scientific knowledge should be shared. So his original printed works were written in three different languages, some in Portuguese, some in Latin, aiming for a broader audience of European scholars; and even one (Livro de algebra en arithmetica y geometria) in Spanish, which is considered as surprising by some historians, given that Spain was Portugal's main rival in a fight for world dominance of the seas.
Many 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, later known as vernier, to improve the astrolabe's accuracy. The nonius was used for a while by Tycho Brahe who, however, considered it too complex. Later it was perfected by Pierre Vernier to its present form.
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, stating that it was a mathematically correct model. In doing so he apparently wished to avoid giving an opinion on the question on whether the Earth or the Sun was the centre of the system.
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.
[edit] 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).
[edit] Trivia
- 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.
[edit] 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
- Printed works of Pedro Nunes in the 16th century, at Portuguese National Library (in Portuguese)
- Pedro Nunes biography, by Pedro Calafate, at Instituto Camões (in Portuguese)
