Pedro Nunes
Encyclopedia
Pedro Nunes (ˈpedɾu ˈnunɨʃ; Latin
, Petrus Nonius), (1502, Alcácer do Sal
– August 11, 1578, Coimbra
) was a Portuguese
mathematician
, cosmographer, and professor
, from a New Christian
(of Jewish origin) family. 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.
of professing and secretly practicing Judaism. 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 established 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 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
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
.
While at the University of Coimbra, Christopher Clavius
attended Pedro Nunes' classes, and was influenced by his works. Clavius, the greatest figure of the Colégio Romano, the great centre of catholic knowledge of that period, classified Nunes as “supreme mathematical genius" .
al 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
, 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 logarithm
s 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 meridian
s 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
bearing his name. The Mercator Projection
is the system which is still used.
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
which, at that time, had only recently been developed. It also shows Nunes was a pioneer in solving maxima and minima problems, which only became a common requirement in the next century using differential calculus.
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 he only made a short reference to it in his published works, with the objective 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.
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. This consisted of a number of concentric
circles traced on an instrument 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. These were eventually improved further by Pierre Vernier
in 1631, which reduced the nonius to Vernier scale
that include 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 the nonius, for example nonieskala in Swedish.
Pedro Nunes also worked on some mechanics
problems, from a mathematical point of view.
and Edward Wright
.
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, Petrus Nonius), (1502, Alcácer do Sal
Alcácer do Sal
Alcácer do Sal is a municipality in Portugal, located in Setúbal District. It has a total area of and a total population of 13,624 inhabitants.-History :-Earliest settlement:...
– August 11, 1578, Coimbra
Coimbra
Coimbra is a city in the municipality of Coimbra in Portugal. Although it served as the nation's capital during the High Middle Ages, it is better-known for its university, the University of Coimbra, which is one of the oldest in Europe and the oldest academic institution in the...
) was a Portuguese
Portugal
Portugal , officially the Portuguese Republic is a country situated in southwestern Europe on the Iberian Peninsula. Portugal is the westernmost country of Europe, and is bordered by the Atlantic Ocean to the West and South and by Spain to the North and East. The Atlantic archipelagos of the...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, cosmographer, and professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
, from a New Christian
New Christian
New Christian was a term used to refer to Iberian Jews and Muslims who converted to Roman Catholicism, and their known baptized descendants. The term was introduced by the Old Christians of Iberia who wanted to distinguish themselves from the conversos...
(of Jewish origin) family. Nunes, considered to be one of the greatest mathematicians of his time , is best known for his contributions in the technical field of navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
, 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
Vernier scale
A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
, named after his Latin surname.
Life
Little is known about Nunes' early education life or family background, only that his origins are Jewish and that his grandchildren spent a few years behind bars after they were accused by the Portuguese InquisitionPortuguese Inquisition
The Portuguese Inquisition was formally established in Portugal in 1536 at the request of the King of Portugal, João III. Manuel I had asked for the installation of the Inquisition in 1515 to fulfill the commitment of marriage with Maria of Aragon, but it was only after his death that the Pope...
of professing and secretly practicing Judaism. He studied at the University of Salamanca
University of Salamanca
The University of Salamanca is a Spanish higher education institution, located in the town of Salamanca, west of Madrid. It was founded in 1134 and given the Royal charter of foundation by King Alfonso IX in 1218. It is the oldest founded university in Spain and the third oldest European...
, 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
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
in 1525. In the 16th century medicine used astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
, so he also learned astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
He continued his medical studies but held various teaching posts within the University of Lisbon, including Moral
Moral
A moral is a message 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...
, Philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, Logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and Metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
. When, in 1537, the Portuguese University located in Lisbon
Lisbon
Lisbon is the capital city and largest city of Portugal with a population of 545,245 within its administrative limits on a land area of . The urban area of Lisbon extends beyond the administrative city limits with a population of 3 million on an area of , making it the 9th most populous urban...
returned to Coimbra
Coimbra
Coimbra is a city in the municipality of Coimbra in Portugal. Although it served as the nation's capital during the High Middle Ages, it is better-known for its university, the University of Coimbra, which is one of the oldest in Europe and the oldest academic institution in the...
, 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
Portugal
Portugal , officially the Portuguese Republic is a country situated in southwestern Europe on the Iberian Peninsula. Portugal is the westernmost country of Europe, and is bordered by the Atlantic Ocean to the West and South and by Spain to the North and East. The Atlantic archipelagos of the...
at this period, when 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 of Portugal
John III , nicknamed o Piedoso , was the fifteenth King of Portugal and the Algarves. He was the son of King Manuel I and Maria of Aragon, the third daughter of King Ferdinand II of Aragon and Queen Isabella I of Castile...
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 of Portugal
Sebastian "the Desired" was the 16th king of Portugal and the Algarves. He was the son of Prince John of Portugal and his wife, Joan of Spain...
.
While at the University of Coimbra, Christopher Clavius
Christopher Clavius
Christopher Clavius was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar...
attended Pedro Nunes' classes, and was influenced by his works. Clavius, the greatest figure of the Colégio Romano, the great centre of catholic knowledge of that period, classified Nunes as “supreme mathematical genius" .
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 experimentExperiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
al 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
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, at that time science's lingua franca
Lingua franca
A lingua franca is a language systematically used to make communication possible between people not sharing a mother tongue, in particular when it is a third language, distinct from both mother tongues.-Characteristics:"Lingua franca" is a functionally defined term, independent of the linguistic...
, aiming for an audience of European scholars, but also in Portuguese, and Spanish (Livro de Algebra).
Navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
. He was the first to understand why a ship maintaining a steady course
Course (navigation)
In navigation, a vehicle's course is the angle that the intended path of the vehicle makes with a fixed reference object . Typically course is measured in degrees from 0° clockwise to 360° in compass convention . Course is customarily expressed in three digits, using preliminary zeros if needed,...
would not travel along a great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...
, the shortest path between two points on Earth, but would instead follow a spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...
course, called a loxodrome. The later invention of logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
s allowed Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
to establish algebraic equations for the loxodrome.
In his Treaty defending the sea chart, Nunes argued that a nautical chart
Nautical chart
A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land , natural features of the seabed, details of the coastline, navigational hazards, locations of natural and man-made aids...
should have its parallels
Circle of latitude
A circle of latitude, on the Earth, is an imaginary east-west circle connecting all locations that share a given latitude...
and meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...
s shown as straight lines. Yet he was unsure how to solve the problems that this caused: a situation that lasted until Mercator
Gerardus Mercator
thumb|right|200px|Gerardus MercatorGerardus Mercator was a cartographer, born in Rupelmonde in the Hapsburg County of Flanders, part of the Holy Roman Empire. He is remembered for the Mercator projection world map, which is named after him...
developed the projection
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
bearing his name. The Mercator Projection
Mercator projection
The Mercator projection is a cylindrical map projection presented by the Belgian geographer and cartographer Gerardus Mercator, in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as...
is the system which is still used.
Geometry
Nunes also solved the problem of finding the day with the shortest twilightTwilight
Twilight is the time between dawn and sunrise or between sunset and dusk, during which sunlight scattering in the upper atmosphere illuminates the lower atmosphere, and the surface of the earth is neither completely lit nor completely dark. The sun itself is not directly visible because it is below...
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
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
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
Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus....
which, at that time, had only recently been developed. It also shows Nunes was a pioneer in solving maxima and minima problems, which only became a common requirement in the next century using differential calculus.
Cosmology
He was probably the last major mathematician to make relevant improvements to the ptolemaic system (a geocentric modelGeocentric model
In astronomy, the geocentric model , is the superseded theory that the Earth is the center of the universe, and that all other objects orbit around it. This geocentric model served as the predominant cosmological system in many ancient civilizations such as ancient Greece...
describing the relative motion of the Earth and Sun). However, this lost importance because Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
introduced his heliocentric system
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...
theory around the same time. 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.
Most of Nunes' achievements were possible because of his profound understanding of spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
and his ability to transpose Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
's adaptations of Euclidean geometry
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
to it.
Inventions
Nunes worked on several practical nautical problems concerning course correctionCourse (navigation)
In navigation, a vehicle's course is the angle that the intended path of the vehicle makes with a fixed reference object . Typically course is measured in degrees from 0° clockwise to 360° in compass convention . Course is customarily expressed in three digits, using preliminary zeros if needed,...
as well as attempting to develop more accurate devices to determine a ship's position.
He created the nonius
Nonius
Nonius can refer to:Persons* Pedro Nunes , Portuguese astronomer and mathematician.* Nonius Marcellus, Latin grammarian and lexicographer, lived at the end of the 3rd or the beginning of the 4th century AD....
to improve the astrolabe
Astrolabe
An astrolabe is an elaborate inclinometer, historically used by astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars, determining local time given local latitude and longitude, surveying, triangulation, and to...
's accuracy. This consisted of a number of concentric
Concentric
Concentric objects share the same center, axis or origin with one inside the other. Circles, tubes, cylindrical shafts, disks, and spheres may be concentric to one another...
circles traced on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant
Circular sector
A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r the radius of the circle, and L is the arc length of the...
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
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...
who, considered it too complex. The method inspired improved systems by Christopher Clavius
Christopher Clavius
Christopher Clavius was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar...
and Jacob Curtius. These were eventually improved further by Pierre Vernier
Pierre Vernier
Pierre Vernier was a French mathematician and instrument inventor. He was inventor and eponym of the vernier scale used in measuring devices....
in 1631, which reduced the nonius to Vernier scale
Vernier scale
A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
that include 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
Vernier scale
A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
is still named after the nonius, for example nonieskala in Swedish.
Pedro Nunes also worked on some mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
problems, from a mathematical point of view.
Influence
Nunes was very influential internationally e.g. on the work of John DeeJohn Dee
John Dee was a Welsh mathematician, astronomer, astrologer, occultist, navigator, imperialist, and consultant to Queen Elizabeth I.John Dee may also refer to:* John Dee , Basketball coach...
and Edward Wright
Edward Wright (mathematician)
Edward Wright was an English mathematician and cartographer noted for his book Certaine Errors in Navigation , which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of...
.
Honours
- One of the best known LisbonLisbonLisbon is the capital city and largest city of Portugal with a population of 545,245 within its administrative limits on a land area of . The urban area of Lisbon extends beyond the administrative city limits with a population of 3 million on an area of , making it the 9th most populous urban...
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 escudoEscudoThe escudo is a unit of currency. Historically it was used in Portugal and in its colonies, and is still used in Cape Verde to this day. Escudo is Portuguese for "shield"...
s coins. - The Instituto Pedro NunesInstituto Pedro NunesInstituto Pedro Nunes 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 Coimbra and worked for the local university.-IPN profile:The...
in CoimbraCoimbraCoimbra is a city in the municipality of Coimbra in Portugal. Although it served as the nation's capital during the High Middle Ages, it is better-known for its university, the University of Coimbra, which is one of the oldest in Europe and the oldest academic institution in the...
, a business incubator and a center of innovation and technology transfer founded by the University of Coimbra, is named after Pedro Nunes. - Asteriod 5313 Nunes5313 Nunes5313 Nunes is a main-belt asteroid discovered on September 18, 1982 by H. Debehogne at the La Silla Observatory in Chile.- External links :*...
is named after him
Other links
- Pedro Nunes page (FCUL) (in English)