Pedro Nunes (
pron. IPA:
['pedɾu 'nunɨʃ];
Latin, Petrus Nonius),
(
1502,
Alcácer do Sal –
August 11,
1578,
Coimbra) was a
Portuguese mathematician,
cosmographer, and
professor, born from a
New Christian (of
Jewish origin) family
[1].
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.
[2] 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).
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.
[3] 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.
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:
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
books' record at the Portuguese National Library)
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
Footnotes
1-
^ Martins, Jorge, Portugal e os Judeus (3 vol.), Nova Vega, Lisboa, 2006,
ISBN 972-699-847-62-
^ «o bem, quanto mais comum e universal, tanto é mais excelente» quoted by Calafate, Pedro (see above)
3-
^ Daumas Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989
ISBN 978-0713407273
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