Pedro Nunes (; Latin: ''Petrus Nonius''; 1502 – 11 August 1578) was a Portuguese mathematician, cosmographer, and professor, from a New Christian (of Jewish origin) family. Considered one of the greatest mathematicians of his time, Nunes is best known for his contributions to the nautical sciences (navigation and cartography), which he approached, for the first time, in a mathematical way. He was the first to propose the idea of a loxodrome, and was the inventor of several measuring devices, including the nonius (from which Vernier scale was derived), named after his Latin surname.

Life

Little is known about Nunes' early education, life or family background, only that he was born in Alcácer do Sal, his origins are 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.Pedro Nunes – A mathematician in a country of navigators
/ref> 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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

. He continued his medical studies but held various teaching posts within the University of Lisbon, including

Moral A moral (from Latin ''morālis'') is a message that is conveyed or a lesson to be learned from a story or event. The moral may be left to the hearer, reader, or viewer to determine for themselves, or may be explicitly encapsulated in a maxim. A ...

Philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

, Logic and Metaphysics. When, in 1537, the Portuguese University located in

Lisbon Lisbon (; pt, Lisboa ) is the capital and largest city of Portugal, with an estimated population of 544,851 within its administrative limits in an area of 100.05 km2. Grande Lisboa, Lisbon's urban area extends beyond the city's administr ...

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 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 John III ( pt, João III ; 7 June 1502 – 11 June 1557), nicknamed The Pious (Portuguese: ''o Piedoso''), was the King of Portugal and the Algarves from 1521 until his death in 1557. He was the son of King Manuel I and Maria of Aragon, the thi ...

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 Sebastian may refer to: People * Sebastian (name), including a list of persons with the name Arts, entertainment, and media Films and television * ''Sebastian'' (1968 film), British spy film * ''Sebastian'' (1995 film), Swedish drama film ...

. 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.

Work

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, 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. Accordingly, he not only published works in Latin, at that time science's

lingua franca A lingua franca (; ; for plurals see ), also known as a bridge language, common language, trade language, auxiliary language, vehicular language, or link language, is a language systematically used to make communication possible between groups ...

, aiming for an audience of European scholars, but also in Portuguese, and Spanish (''Livro de Algebra'').

Navigation

Much of Nunes' work related to navigation. He was the first to understand why a ship maintaining a steady

course Course may refer to: Directions or navigation * Course (navigation), the path of travel * Course (orienteering), a series of control points visited by orienteers during a competition, marked with red/white flags in the terrain, and corresponding ...

would not travel along a

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...

, the shortest path between two points on Earth, but would instead follow a

spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:loxodrome. The later invention of logarithms allowed Leibniz to establish algebraic equations for the loxodrome. These lines —also called

rhumb line In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true north. Introduction The effect of following a rhumb li ...

s— 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 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 Projection, projections or projective may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphic ...

bearing his name. The

Mercator Projection The Mercator projection () is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and sou ...

is the system which is still used.

Geometry

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. 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 In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...

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.Pedro Nunes (1502 - 1578)(Science)
/ref>

Cosmology

He was probably the last major mathematician to make relevant improvements to the ptolemaic system (a

geocentric model In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...

describing the relative motion of the Earth and Sun). However, this lost importance because Copernicus introduced his heliocentric system theory around the same time. 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.

Inventions

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 An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستاره‌یاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclin ...

's accuracy. This consisted of a number of

concentric In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center point ...

circles traced on the astrolabe 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. 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 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 ' in Swedish. Pedro Nunes also worked on some mechanics problems, from a mathematical point of view.

Influence

Nunes was very influential internationally, e.g. on the work of

John Dee John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, astrologer, teacher, occultist, and alchemist. He was the court astronomer for, and advisor to, Elizabeth I, and spent much of his time on alchemy, divinatio ...

and Edward Wright.

Honours

*One of the best known

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–), but is still popularly known as Liceu Pedro Nunes. Many well known Portuguese personalities have studied in Pedro Nunes. The current headquarters commemorated its centenary in 2011, after being totally refurbished and modernized between 2008 and 2010. *He was featured on 100 escudos coins. *The

Instituto Pedro Nunes Instituto Pedro Nunes (IPN) is a non-profit private organization for innovation and technology transfer based in Coimbra, Portugal. It is named after the Portuguese 16th century mathematician and professor Pedro Nunes, who lived in the city of C ...

in Coimbra, a business incubator and a center of innovation and technology transfer founded by the University of Coimbra, is named after Pedro Nunes. *Asteroid 5313 Nunes is named after him * TAP Portugal Airlines has named an Airbus A330-202 airplane after him, registered CS-TOP.

Bibliography

Nunes - De erratis Orontii Finaei, 1546 - 103782

Nunes, Pedro – De arte atque ratione navigandi, 1573 – BEIC 13151799

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 Sphæra ''De sphaera mundi'' (Latin title meaning ''On the Sphere of the World'', sometimes rendered ''The Sphere of the Cosmos''; the Latin title is also given as ''Tractatus de sphaera'', ''Textus de sphaera'', or simply ''De sphaera'') is a medieval ...

'' by Johannes de Sacrobosco, ''Theoricae novæ planetarum'' by

Georg Purbach Georg von Peuerbach (also Purbach, Peurbach; la, Purbachius; born May 30, 1423 – April 8, 1461) was an Austrian astronomer, poet, mathematician and instrument maker, best known for his streamlined presentation of Ptolemaic astronomy in the ''Th ...

and the ''Geography'' by Claudius Ptolemaeus. Original work: *''Tratado em defensam 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 Finæi'' (About the Errors of Orontius Finæus), (1546). *''Livro de algebra en arithmetica y geometria'' (Book of Algebra in Arithmetics and Geometry), (1567). *''Petri Nonii Salaciensis Opera'', (1566). Expanded, corrected and reedited as ''De arte adque ratione navigandi'' in 1573. * Some modern reprints: *''Obras'' (4 vol.), Academia das Ciências de Lisboa, Lisboa, 1940-1960 (No ISBN at th
books' record
at the Portuguese National Library) *''Obras'' (6 vol.),

Fundação Calouste Gulbenkian The Calouste Gulbenkian Foundation ( pt, Fundação Calouste Gulbenkian), commonly referred to simply as the Gulbenkian Foundation, is a Portuguese institution dedicated to the promotion of the arts, philanthropy, science, and education. One of ...

, Lisboa, 2002-2011, and (more volumes are likely to be published)

Notes

References

*Mourão, Ronaldo Rogério de Freitas, ''Dicionário das Descobertas'', Pergaminho, Lisboa, 2001, *Dias, J. S. da Silva, ''Os descobrimentos e a problemática cultural do século XVI'' (3rd ed.), Presença, Lisboa, 1988
Calafate, Pedro, ''Pedro Nunes'', at Instituto Camões' site
(in Portuguese)

(in Portuguese)

External links

Pedro Nunes page (FCUL)
{{DEFAULTSORT:Nunes, Pedro 1502 births 1578 deaths 16th-century Portuguese mathematicians Portuguese Renaissance humanists Portuguese Renaissance writers Portuguese geographers Scientific instrument makers University of Coimbra alumni University of Salamanca alumni University of Salamanca faculty Jewish Portuguese writers Portuguese exploration in the Age of Discovery People from Setúbal District People from Coimbra School of Salamanca Portuguese inventors European Sephardi Jews