Pedro Nunes | |
|---|---|
 Pedro Nunes, 1843 print | |
| Born | 1502 |
| Died | 11 August 1578 (aged 76) |
| Occupation(s) | Mathematician,cosmographer, andprofessor |
| Signature | |
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Pedro Nunes (Portuguese:[ˈpeðɾuˈnunɨʃ];Latin:Petrus Nonius; 1502 – 11 August 1578)[1] was aPortuguesemathematician,cosmographer, andprofessor, probably from aNew Christian (ofJewish origin) family.[2][3][4]
Considered one of the greatest mathematicians of his time,[5] Nunes is best known for being the first to approach navigation and cartography with mathematical tools. Among other accomplishments, he was the first to propose the idea of aloxodrome (arhumb line), and was the inventor of several measuring devices, including thenonius (from which theVernier scale was derived), named after his Latin surname.[6]
Little is known about Nunes' early education, life or family background, only that he was born inAlcácer do Sal in Portugal, his origins are possiblyJewish and that his grandchildren spent a few years behind bars after they were accused by thePortuguese Inquisition of professing and secretly practicing Judaism.[3][7] He studied at theUniversity 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 variousteaching posts within theUniversity of Lisbon, includingMoral,Philosophy,Logic andMetaphysics. He obtained his doctorate inmedicine in 1532. When, in 1537, the Portuguese University located inLisbon returned toCoimbra, he moved to the re-founded University of Coimbra to teach mathematics, a post he held until 1562.[8] 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 inPortugal at this period, when the control of sea trade was the primary source of Portuguese wealth. Mathematics became an independent post in 1544.[6]
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.[6]
In 1531, KingJohn III of Portugal charged Nunes with the education of his younger brothersLuís andHenry. Years later Nunes was also charged with the education of the king's grandson, and future king,Sebastian.[6]
It is possible that, while at the University of Coimbra, future astronomerChristopher Clavius attended Pedro Nunes' classes, and was influenced by his works.[6] Clavius, proponent of theGregorian Calendar, the greatest figure of the Colégio Romano, the great center of Roman Catholic knowledge of that period, classified Nunes as “supreme mathematical genius".[7] Nunes died inCoimbra.
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 providingexperimental data, both as a source of information and as a method of confirming theories. Nunes was, above all, one of the last great commentators,[9] 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.[7] He also acknowledged the value of experimentation.
In hisTratado da sphera he argued for a common and universal diffusion of knowledge.[10] Accordingly, he not only published works inLatin, at that time science'slingua franca, aiming for an audience of European scholars, but also inPortuguese, andSpanish (Livro de Algebra).
Much of Nunes' work related tonavigation. He was the first to understand why a ship maintaining a steadycourse would not travel along agreat circle, the shortest path between two points on Earth, but would instead follow aspiral course, called aloxodrome.[7] These lines —also calledrhumb lines— maintain a fixed angle with themeridians. In other words, loxodromic curves are directly related to the construction of the Nunesconnection —also called navigator connection.[11]
In hisTreaty defending the sea chart, Nunes argued that anautical chart should have itsparallels and meridians shown as straight lines. Yet he was unsure how to solve the problems that this caused: a situation that lasted untilMercator developed theprojection bearing his name. TheMercator Projection is the system which is still used.
Nunes also solved the problem of finding the day with the shortesttwilight duration, for any given position, and its duration.[7] This problemper se is not greatly important, yet it shows the geometric genius of Nunes as it was a problem which was independently tackled byJohann andJakob Bernoulli more than a century later with less success.[12] They could find a solution to the problem of theshortest day, but failed to determine its duration, possibly because they got lost in the details ofdifferential 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.[13]
He was probably the last major mathematician to make relevant improvements[according to whom?] to theptolemaic system (ageocentric model describing the relative motion of the Earth and Sun). With time, in a slow and complex process, the geocentric model was replaced by theheliocentric system proposed byNicolaus 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 ofspherical trigonometry and his ability to transposePtolemy's adaptations ofEuclidean geometry to it.
Nunes worked on several practical nautical problems concerningcourse correction as well as attempting to develop more accurate devices to determine a ship's position.[13]
He created thenonius to improve instrument (such as thequadrant (instrument)) accuracy. This consisted of a number ofconcentric circles traced on the instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermostquadrant 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 thealidade fell was noted. A table was then consulted to provide the exact measure.[citation needed]
The nonius was used byTycho Brahe, who considered it too complex. The method inspired improved systems byChristopher Clavius andJacob Curtius.[15] These were eventually improved further byPierre Vernier in 1631, which reduced the nonius to theVernier 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.[7] In some languages, the Vernier scale is still named after Nunes, for examplenonieskala in Swedish.
Pedro Nunes also worked on somemechanics problems, from a mathematical point of view.
Nunes was very influential internationally, e.g. on the work ofJohn Dee[16] andEdward Wright.[17]
Pedro Nunes translated, commented and expanded some of the major works in his field, and he also published original research.
Printed work:
Manuscripts:
Some modern reprints:
