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Encyclopedia > Pedro Nunes

Pedro Nunes (latin, Petrus Nonius), (1502, Alcácer do SalAugust 11, 1578, Coimbra) was a Portuguese mathematician, maybe born from a New Christian (of Jewish origin) family. Download high resolution version (1068x803, 347 KB)Pedro Nunes stamp, Portugal This image of a postage stamp may be copyrighted and/or have other restrictions on its reproduction imposed by the issuing authority. ... Latin is an ancient Indo-European language. ... 1502 was a common year starting on Wednesday (see link for calendar) of the Gregorian calendar. ... Coat of Arms Alcácer do Sal (pron. ... August 11 is the 223rd day of the year (224th in leap years) in the Gregorian Calendar. ... Events January 31 - Battle of Gemblours - Spanish forces under Don John of Austria and Alexander Farnese defeat the Dutch. ... District Coimbra Mayor   - Party Carlos Encarnação PSD Area 316. ... Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... The term New Christian (cristianos nuevos in Spanish, cristãos novos in Portuguese) was used to refer to the Jews and Moors who were converted to Christianity and their baptized descendants. ... This article describes some ethnic, historic, and cultural aspects of the Jewish identity; for a consideration of the Jewish religion, refer to the article Judaism. ...

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. Table of geography, hydrography, and navigation, from the 1728 Cyclopaedia. ... For additional context, see History of Portugal. ... Line crossing all meridians at the same angle. ... A set of vernier calipers. ...



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. The University of Salamanca (Spanish Universidad de Salamanca), located in the town of Salamanca, west-northwest of Madrid, is the second oldest university in Spain (the first one is the university of Palencia, now disappeared), and one of the oldest in Europe. ... Events January 3 - Pope Leo X excommunicates Martin Luther in the papal bull Decet Romanum Pontificem. ... Events January 9 - Adrian Dedens becomes Pope Adrian VI. February 26 - Execution by hanging of Cuauhtémoc, Aztec ruler of Tenochtitlan under orders of conquistador Hernán Cortés. ... The University of Coimbra (Portuguese: Universidade de Coimbra) is a Portuguese public university in Coimbra, Portugal. ... This article is about the field of medical practice and health care. ... Events January 21 - The Swiss Anabaptist Movement was born when Conrad Grebel, Felix Manz, George Blaurock, and about a dozen others baptized each other in the home of Manzs mother on Neustadt-Gasse, Zürich, breaking a thousand-year tradition of church-state union. ... (15th century - 16th century - 17th century - more centuries) As a means of recording the passage of time, the 16th century was that century which lasted from 1501 to 1600. ... Astrology refers to any of several systems, traditions or beliefs in which knowledge of the apparent positions of celestial bodies and related information is held to be useful in understanding, interpreting and organizing knowledge about personality, human affairs and terrestrial events. ... Radio telescopes are among many different tools used by astronomers Astronomy (Greek: αστρονομία = άστρον + νόμος, astronomia = astron + nomos, literally, law of the stars) is the science of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earths atmosphere (such as auroras and cosmic background radiation). ... A moral is a one sentence remark made at the end of many childrens stories that expresses the intended meaning, or the moral message, of the tale. ... Philosopher in Meditation (detail), by Rembrandt. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Events January 6 - Alessandro de Medici assassinated August 25 - The Honourable Artillery Company, the oldest surviving regiment in the British Army, and the second most senior, was formed. ... Events Earliest English slave-trading expedition under John Hawkins. ... Events April 11 - Battle of Ceresole - French forces under the Comte dEnghien defeat Imperial forces under the Marques Del Vasto near Turin. ...

In addition to teaching he was appointed Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547 up to his death. Events April 22 - Treaty of Saragossa divides the eastern hemisphere between Spain and Portugal, stipulating that the dividing line should lie 297. ... Events January 16 - Grand Duke Ivan IV of Muscovy becomes the first Tsar of Russia. ...

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. Events January 26 - Lisbon, Portugal is hit by an earthquake-- thousands die October 1 - Battle of Kappel - The forces of Zürich are defeated by the Catholic cantons. ... John III (Portuguese: João III pron. ... Henry, the cardinal-king or Henrique (in Portuguese) the Chaste (Port. ... Sebastian I the Desired (in Portuguese, Sebastião I o Desejado; born in Lisbon, January 20, 1554; died at Alcazarquivir, August 4, 1578) was the sixteenth king of Portugal. ...

It's possible that while at the University of Coimbra, Christopher Clavius attended Pedro Nunes' classes, and was influenced by his works. Christopher Clavius, (March 25, 1538 – February 12, 1612) was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar. ...


Pedro Nunes lived in a transition period where science was changing from valuing theoretical knowledge (and thus where the main role of a scientist 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. The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ... Antipodes (from Greek anti- opposed and pous foot) means diametrically opposed, and more specifically refers to the opposite side of the Earth, the region of the antipodal point, from where one is located. ...

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. Table of geography, hydrography, and navigation, from the 1728 Cyclopaedia. ... A course, in navigation, is the direction of travel. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the... In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way you follow the curve. ... Line crossing all meridians at the same angle. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz)[1] (July 1 (June 21 Old Style) 1646 – November 14, 1716) was a German polymath. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...

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. Portion of chart of Bering Strait, site of former land bridge between Asia and North America. ... The 5 main circles of latitude on Earth A circle of latitude or parallel is an imaginary east-west circle on the Earth, that connects all locations with a given latitude. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... Gerardus Mercator (March 5, 1512 – December 2, 1594) was a Flemish cartographer of German descent, his parents being from Gangelt in the Duchy of Jülich. ... Mercator world map Nova et Aucta Orbis Terrae Descriptio ad Usum Navigatium Emendate (1569) The Mercator projection is a cylindrical map projection presented by the German geographer and cartographer Gerardus Mercator, in 1569, in a large planisphere measuring 202 by 124 cm, printed in eighteen separate sheets. ...

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. A set of vernier calipers. ... A vernier scale lets one read more precisely from a measurement scale. ... A 16th century astrolabe. ... Tycho Brahe Monument of Tycho Brahe and Johannes Kepler in Prague , born Tyge Ottesen Brahe (December 14, 1546 – October 24, 1601), was a Danish (Scanian) nobleman astronomer as well as an astrologer and alchemist. ... Pierre Vernier (1580–1637) was a French mathematician and instrument inventor. ...

Pedro Nunes also worked on some mechanics problems, from a mathematical point of view. Mechanics is the branch of physics concerned with the motion of physical bodies, the forces that cause or limit these motions, and the forces to which bodies may, in turn, give rise. ...

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. Mediaeval drawing of the Ptolemaic system. ... This artistic representation of the geocentric model shows signs of the zodiac and the solar system with world at centre. ... Nicolaus Copernicus (February 19, 1473 – May 24, 1543) was an astronomer who provided the first modern formulation of a heliocentric (sun-centered) theory of the solar system in his epochal book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres). ... Heliocentric Solar System Heliocentrism in comparsion to the geocentric model In astronomy, heliocentrism is the theory that the Sun is at the center of the Universe and/or the Solar 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. It has been suggested that this article or section be merged with Dawn. ... Johann Bernoulli Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician. ... Jakob Bernoulli. ... Differential calculus is the theory of and computations with differentials; see also derivative and 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. Spherical triangle Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. ... Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...


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: Johannes de Sacrobosco or Sacro Bosco (John of Holywood, c. ... Georg Purbach (also Georg von Peuerbach, Peurbach, Purbach, Purbachius, his real surname is unknown) (born May 30, 1423 in Purbach near Linz– April 8, 1461 in Vienna) was an Austrian astronomer/astrologer and mathematician. ... Claudius Ptolemaeus (Greek: ; c. ...

  • 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).


  • Mourão, Ronaldo Rogério de Freitas, Dicionário das Descobertas, Pergaminho, Lisboa, 2001, ISBN 979-711-402-4
  • 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)

  Results from FactBites:
Pedro Nunes - Wikipedia, the free encyclopedia (1064 words)
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.
Pedro Nunes lived in a transition period where science was changing from valuing theoretical knowledge (and thus where the main role of a scientist was commenting on previous authors), to providing experimental data, both as a source of information and as a method of confirming theories.
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.
Pedro - Wikipedia, the free encyclopedia (367 words)
Pedro is the Spanish and Portuguese version of the name Peter, derived from the word Petros (Greek for rock, from πέτρα or Petra, a translation of the Aramaic Kephas or Cephas), through the Latin Petrus.
Pedro Eugenio Aramburu, de facto president of Argentina from 1955 to 1958.
Pedro Rosselló, Governor of Puerto Rico from 1993 to 2001.
  More results at FactBites »



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