Georg Joachim Rheticus
Encyclopedia
Georg Joachim von Lauchen, also known as Rheticus (16 February 1514 – 4 December 1574), was a mathematician
, cartographer, navigational-instrument maker, medical practitioner, and teacher. He is perhaps best known for his trigonometric
tables and as Nicolaus Copernicus
's sole pupil. He facilitated the publication of his master's De revolutionibus orbium coelestium
(On the Revolutions of the Heavenly Spheres).
, Austria
. Both his parents possessed considerable wealth, his father, Georg Iserin, being the town physician. However, Georg abused the trust of many of his patients, stealing belongings and money from their homes. In 1528 he was convicted and executed for his crimes, and as a result his family was stripped of their surname
. His son took as his last name a form of the Latin
name for his home region, Rhaetia
, a Roman province
that had included parts of Austria, Switzerland
and Germany
; he would be called Rheticus.
The crater Rhaeticus
is named for him.
took over his medical practice, helping Rheticus to continue his studies and supporting him. Rheticus studied at Feldkirch, Zürich
and the University of Wittenberg, where he received his M.A. in 1536.
During the Reformation
the theologian and educator Philipp Melanchthon
reorganized the whole educational system of Germany, reforming and founding several new universities. In 1536 Melanchthon helped Rheticus to obtain an appointment teaching astronomy and mathematics at the Wittenberg University
.
Two years later, Melanchthon arranged a two-year leave for Rheticus to study with noted astronomers. Rheticus took this opportunity to visit Copernicus in Frauenburg (now Frombork
). Leaving Wittenberg in October 1538, he first went to Nuremberg
to visit the publisher Johannes Schöner
and the printer Petreius. Here Rheticus was given works by Regiomontanus
and others, intended as presents for Copernicus. He went on to Peter Apian in Ingolstadt
and Joachim Camerarius
in Tübingen
, then to Gasser in his hometown.
(Frauenburg), where he spent two years with Copernicus. It is unknown whether he had prior access to Copernicus' Commentariolus
, an unsigned, unpublished outline of Copernicus' revolutionary heliocentric theory
that Copernicus distributed friends and colleagues three decades before he published De revolutionibus.
In September 1539, Rheticus went to Danzig
(Gdańsk) to visit the mayor, who gave him financial assistance to publish his Narratio Prima
(First Report) of Copernicus' forthcoming treatise. Rhode
in Danzig published Narratio Prima in 1540. While in Danzig, Rheticus interviewed maritime pilot
s to learn about their problems in navigation
. Rheticus also visited Copernicus' friend, Tiedemann Giese
, who was Bishop of Culm (now Chełmno).
In August 1541, Rheticus presented a copy of his Tabula chorographica auff Preussen und etliche umbliegende lender (Map of Prussia and Neighboring Lands) to Albert, Duke of Prussia, who had been trying to compute the exact time of sunrise. Rheticus made an instrument for him that determined the length of the day. Rheticus obtained the duke's permission to publish De revolutionibus. Albrecht asked Rheticus to end his travels and return to his teaching position. Rheticus returned to the University of Wittenberg in October 1541. In 1542, he traveled to Nürnberg to supervise the printing by Johannes Petreius
of the first edition of De revolutionibus, which was published shortly before Copernicus' death in 1543.
Georg Donner and the bishop of Warmia Johannes Dantiscus were both patrons of Rheticus. Rheticus was also commissioned to make a staff for king Sigismund II of Poland, while he held a position as teacher in Kraków
for many years. From there he went to Košice
in the Kingdom of Hungary
, where he died.
. In 1542 he had the trigonometric sections of Copernicus' De revolutiobis published separately under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles). In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements.
At his death, the Science of Triangles was still unfinished. However, paralleling his own relationship with Copernicus, Rheticus had acquired a student who devoted himself to completing his teacher's work. Valentin Otto oversaw the hand computation of approximately 100,000 ratios to at least ten decimal places. When completed in 1596, the volume, Opus palatinum de triangulus, filled nearly 1,500 pages. Its tables were accurate enough to be used in astronomical computation into the early twentieth century.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, cartographer, navigational-instrument maker, medical practitioner, and teacher. He is perhaps best known for his trigonometric
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
tables and as Nicolaus 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....
's sole pupil. He facilitated the publication of his master's De revolutionibus orbium coelestium
De revolutionibus orbium coelestium
De revolutionibus orbium coelestium is the seminal work on the heliocentric theory of the Renaissance astronomer Nicolaus Copernicus...
(On the Revolutions of the Heavenly Spheres).
Surname
Rheticus was born at FeldkirchFeldkirch, Vorarlberg
- Schools :* Bundesgymnasium und Bundesrealgymnasium Feldkirch * Bundeshandelsakademie und Bundeshandelsschule Feldkirch* Bundesoberstufenrealgymnasium und Bundesrealgymnasium Schillerstrasse...
, Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
. Both his parents possessed considerable wealth, his father, Georg Iserin, being the town physician. However, Georg abused the trust of many of his patients, stealing belongings and money from their homes. In 1528 he was convicted and executed for his crimes, and as a result his family was stripped of their surname
Surname
A surname is a name added to a given name and is part of a personal name. In many cases, a surname is a family name. Many dictionaries define "surname" as a synonym of "family name"...
. His son took as his last name a form of the 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...
name for his home region, Rhaetia
Raetia
Raetia was a province of the Roman Empire, named after the Rhaetian people. It was bounded on the west by the country of the Helvetii, on the east by Noricum, on the north by Vindelicia, on the west by Cisalpine Gaul and on south by Venetia et Histria...
, a Roman province
Roman province
In Ancient Rome, a province was the basic, and, until the Tetrarchy , largest territorial and administrative unit of the empire's territorial possessions outside of Italy...
that had included parts of Austria, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
and Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
; he would be called Rheticus.
The crater Rhaeticus
Rhaeticus (crater)
Rhaeticus is a lunar crater that lies astride the equator of the Moon, on the southeast edge of the Sinus Medii. To the north-northwest is the crater Triesnecker, and due south can be found the worn remnant of the walled plain Hipparchus...
is named for him.
Patrons
After Georg Iserin's death, Achilles GasserAchilles Gasser
Achilles Pirmin Gasser was a German physician and astrologer. He is now known as a well-connected humanist scholar, and supporter of both Copernicus and Rheticus.-Life:...
took over his medical practice, helping Rheticus to continue his studies and supporting him. Rheticus studied at Feldkirch, Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
and the University of Wittenberg, where he received his M.A. in 1536.
During the Reformation
Protestant Reformation
The Protestant Reformation was a 16th-century split within Western Christianity initiated by Martin Luther, John Calvin and other early Protestants. The efforts of the self-described "reformers", who objected to the doctrines, rituals and ecclesiastical structure of the Roman Catholic Church, led...
the theologian and educator Philipp Melanchthon
Philipp Melanchthon
Philipp Melanchthon , born Philipp Schwartzerdt, was a German reformer, collaborator with Martin Luther, the first systematic theologian of the Protestant Reformation, intellectual leader of the Lutheran Reformation, and an influential designer of educational systems...
reorganized the whole educational system of Germany, reforming and founding several new universities. In 1536 Melanchthon helped Rheticus to obtain an appointment teaching astronomy and mathematics at the Wittenberg University
University of Halle-Wittenberg
The Martin Luther University of Halle-Wittenberg , also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg within Saxony-Anhalt, Germany...
.
Two years later, Melanchthon arranged a two-year leave for Rheticus to study with noted astronomers. Rheticus took this opportunity to visit Copernicus in Frauenburg (now Frombork
Frombork
Frombork is a town in northern Poland, on the Vistula Lagoon, in Braniewo County, Warmian-Masurian Voivodeship. It had a population of 2,528 as of 2005....
). Leaving Wittenberg in October 1538, he first went to Nuremberg
Nuremberg
Nuremberg[p] is a city in the German state of Bavaria, in the administrative region of Middle Franconia. Situated on the Pegnitz river and the Rhine–Main–Danube Canal, it is located about north of Munich and is Franconia's largest city. The population is 505,664...
to visit the publisher Johannes Schöner
Johannes Schöner
Johannes Schöner was a renowned and respected German polymath...
and the printer Petreius. Here Rheticus was given works by Regiomontanus
Regiomontanus
Johannes Müller von Königsberg , today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator and instrument maker....
and others, intended as presents for Copernicus. He went on to Peter Apian in Ingolstadt
Ingolstadt
Ingolstadt is a city in the Free State of Bavaria, in the Federal Republic of Germany. It is located along the banks of the Danube River, in the center of Bavaria. As at 31 March 2011, Ingolstadt had 125.407 residents...
and Joachim Camerarius
Joachim Camerarius
Joachim Camerarius , the Elder was a German classical scholar.-Life:He was born at Bamberg, Bavaria...
in Tübingen
Tübingen
Tübingen is a traditional university town in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, on a ridge between the Neckar and Ammer rivers.-Geography:...
, then to Gasser in his hometown.
Copernicus
In May 1539, Rheticus arrived in FromborkFrombork
Frombork is a town in northern Poland, on the Vistula Lagoon, in Braniewo County, Warmian-Masurian Voivodeship. It had a population of 2,528 as of 2005....
(Frauenburg), where he spent two years with Copernicus. It is unknown whether he had prior access to Copernicus' Commentariolus
Commentariolus
The "Commentariolus" is Nicolaus Copernicus's forty-page outline of an early version of his revolutionary heliocentric theory of the universe...
, an unsigned, unpublished outline of Copernicus' revolutionary heliocentric theory
Copernican heliocentrism
Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets rotating around it in circular paths modified by epicycles and at uniform...
that Copernicus distributed friends and colleagues three decades before he published De revolutionibus.
In September 1539, Rheticus went to Danzig
History of Gdansk
This article is about the History of Gdańsk , a Polish city located on the Baltic Sea.- Early times :The area around the Vistula delta was inhabited by populations belonging to the various archaeological cultures of the Stone Age, Bronze Age, and Iron Age...
(Gdańsk) to visit the mayor, who gave him financial assistance to publish his Narratio Prima
Narratio Prima
De libris revolutionum Copernici narratio prima, usually referred to as Narratio Prima , is an abstract of Nicolaus Copernicus' heliocentric theory, written by Georg Joachim Rheticus in 1540. It is an introduction to Copernicus's major work, De revolutionibus orbium coelestium, published in 1543,...
(First Report) of Copernicus' forthcoming treatise. Rhode
Franz Rhode
Franz Rhode was a German printer of the 16th century.Having been active in Marburg between 1529 and 1534, he went to Hamburg in 1536 to print Latin works of the theologist Urbanus Rhegius from Celle...
in Danzig published Narratio Prima in 1540. While in Danzig, Rheticus interviewed maritime pilot
Maritime pilot
A pilot is a mariner who guides ships through dangerous or congested waters, such as harbours or river mouths. With the exception of the Panama Canal, the pilot is only an advisor, as the captain remains in legal, overriding command of the vessel....
s to learn about their problems in 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...
. Rheticus also visited Copernicus' friend, Tiedemann Giese
Tiedemann Giese
Tiedemann Giese Tiedemann Giese Tiedemann Giese (1 June 1480 – 23 October 1550, Heilsberg (Lidzbark), was a member of the patrician Giese family of Danzig (Gdańsk). The brother of the Hanseatic League merchant Georg Giese and relative of Albrecht Giese he became Bishop of Culm (Chełmno) first...
, who was Bishop of Culm (now Chełmno).
In August 1541, Rheticus presented a copy of his Tabula chorographica auff Preussen und etliche umbliegende lender (Map of Prussia and Neighboring Lands) to Albert, Duke of Prussia, who had been trying to compute the exact time of sunrise. Rheticus made an instrument for him that determined the length of the day. Rheticus obtained the duke's permission to publish De revolutionibus. Albrecht asked Rheticus to end his travels and return to his teaching position. Rheticus returned to the University of Wittenberg in October 1541. In 1542, he traveled to Nürnberg to supervise the printing by Johannes Petreius
Johannes Petreius
Johann Petreius was a German printer in Nuremberg.-Life:...
of the first edition of De revolutionibus, which was published shortly before Copernicus' death in 1543.
Later years
The canon of WarmiaWarmia
Warmia or Ermland is a region between Pomerelia and Masuria in northeastern Poland. Together with Masuria, it forms the Warmian-Masurian Voivodeship....
Georg Donner and the bishop of Warmia Johannes Dantiscus were both patrons of Rheticus. Rheticus was also commissioned to make a staff for king Sigismund II of Poland, while he held a position as teacher in Kraków
Kraków
Kraków also Krakow, or Cracow , is the second largest and one of the oldest cities in Poland. Situated on the Vistula River in the Lesser Poland region, the city dates back to the 7th century. Kraków has traditionally been one of the leading centres of Polish academic, cultural, and artistic life...
for many years. From there he went to Košice
Košice
Košice is a city in eastern Slovakia. It is situated on the river Hornád at the eastern reaches of the Slovak Ore Mountains, near the border with Hungary...
in the Kingdom of Hungary
Kingdom of Hungary
The Kingdom of Hungary comprised present-day Hungary, Slovakia and Croatia , Transylvania , Carpatho Ruthenia , Vojvodina , Burgenland , and other smaller territories surrounding present-day Hungary's borders...
, where he died.
Trigonometry
For much of his life, Rheticus displayed a passion for the study of triangles, the branch of mathematics now called trigonometryTrigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
. In 1542 he had the trigonometric sections of Copernicus' De revolutiobis published separately under the title De lateribus et angulis triangulorum (On the Sides and Angles of Triangles). In 1551 Rheticus produced a tract titled Canon of the Science of Triangles, the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements.
At his death, the Science of Triangles was still unfinished. However, paralleling his own relationship with Copernicus, Rheticus had acquired a student who devoted himself to completing his teacher's work. Valentin Otto oversaw the hand computation of approximately 100,000 ratios to at least ten decimal places. When completed in 1596, the volume, Opus palatinum de triangulus, filled nearly 1,500 pages. Its tables were accurate enough to be used in astronomical computation into the early twentieth century.
Works
- Narratio prima de libris revolutionum Copernici (1540)
- Tabula chorographica auff Preussen und etliche umbliegende lender (1541)
- De lateribus et angulis triangulorum (with Copernicus; 1542)
- Ephemerides novae (1550)
- Canon doctrinae triangulorum (1551)
External links
- Scienceworld article on Rheticus
- Narratio Prima - Full digital facsimile, Linda Hall Library.
- Christian Pinter: Der erste Kopernikaner