Georg Joachim von Lauchen, also known as Rheticus (February 16, 1514 – December 4, 1574), was a mathematician, cartographer, navigational and other instrument maker, medical practitioner, and teacher. He is perhaps best known for his trigonometric tables, and for facilitating the publication of Nicolaus Copernicus' De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). February 16 is the 47th day of the year in the Gregorian calendar. ... 1514 was a common year starting on Thursday (see link for calendar) of the Gregorian calendar. ... December 4th redirects here. ... Year 1574 was a common year starting on Friday (link will display the full calendar) of the Julian calendar. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Cartography is the study of map making and cartographers are map makers. ... Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek Trigona = three angles and metron = measure[1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled triangles). ... It has been suggested that Copernicus and coin reform be merged into this article or section. ... Title page of De revolutionibus De revolutionibus orbium coelestium (English: On the Revolutions of the Heavenly Spheres, Polish: O obrotach sfer niebieskich) is the seminal work on heliocentric theory and the masterpiece of the great Polish astronomer Nicolaus Copernicus. ...

New surname

Rheticus was born at Feldkirch, Austria. Rheticus' parents both possessed considerable wealth and his father, Georg Iserin, was the town doctor of Feldkirch. Iserin, however, abused the trust of many of his patients, stealing items and money from many of their homes. He was convicted and executed for his crimes in 1528, and his family was stripped of their surname as a result. The 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. Feldkirch is a medieval city in the western Austrian state of Vorarlberg, at 47°15′ N 9°35′ E, on the border with Switzerland and Liechtenstein. ... The Roman Empire ca. ...

Patrons

After Iserin's death, Achilles Gasser took over his medical practice. Gasser helped Rheticus continue his studies and was a strong support to him. Rheticus studied at Feldkirch, Zürich and the University of Wittenberg, where he received his M.A. in 1536. View of the inner city with the four main churches visible, and the Albis in the backdrop Zürich (German: , Zürich German: Züri , French: , in English generally Zurich, Italian: ) is the largest city in Switzerland (population: 366,145 in 2004; population of urban area: 1,091,732) and... The Martin-Luther-University of Halle-Wittenberg is located in the German cities of Halle, Saxony-Anhalt and Wittenberg. ...

Philipp Melanchthon, the theologian and educator, greatly assisted Rheticus in obtaining appointments at several universities. During the Reformation, Melanchthon reorganized the whole educational system of Germany, reforming and founding several new universities. In 1536 Rheticus was aided by Melanchthon in obtaining appointment to a teaching position in astronomy and mathematics at Wittenberg University. Portrait of Philipp Melanchthon, by Lucas Cranach the Elder. ... The Protestant Reformation was a movement which began in the 16th century as a series of attempts to reform the Roman Catholic Church, but ended in division and the establishment of new institutions, most importantly Lutheranism, Reformed churches, and Anabaptists. ... Wittenberg University is a private, four-year liberal arts college of the Evangelical Lutheran Church in America located in Springfield, Ohio. ...

Two years later, Melanchthon arranged for Rheticus to visit and study with noted astronomers of the day. Rheticus took this opportunity to visit Copernicus in Frauenburg, Prussia (now Frombork, Poland). On the way he first went to Nuremberg and visited the publisher Johannes Schöner and the printer Petreius. From there he proceeded on to Peter Apian in Ingolstadt and Joachim Camerarius in Tübingen, then to Achilles Gasser in his hometown. Frombork Cathedral, with the Vistula Lagoon in the background Frombork (German: ) is a town in northern Poland, on the Vistula Lagoon in the Warmian-Masurian Voivodship, with a population of 2,602 in 2005. ... Nuremberg (German: Nürnberg, Polish: Norymberga) is a city in the German state of Bavaria, in the administrative region of Middle Franconia. ... Johannes Schöner (January 16, 1477 – January 16, 1547) was a German astronomer and cartographer. ... Apianus on an 18th century engraving Petrus Apianus (April 16, 1495 – April 21, 1552; also known as Peter Apian) was a German humanist, famous for his works in mathematics, astronomy and cartography. ... Ingolstadt is a city in the Federal State of Bavaria, Germany. ... Joachim Camerarius (April 12, 1500 - April 17, 1574), German classical scholar, was born at Bamberg. ... Tübingen, Neckar front Tübingen, a traditional university town of Baden-Württemberg, Germany, is situated 20 miles southwest of Stuttgart, on a ridge between the River Neckar and the Ammer. ...

Service to Copernicus

In May 1539 he arrived in Frauenburg, (Warmia) and spent two years there with Copernicus. In September 1539 Rheticus went to Danzig (Gdańsk, just west of Frombork), and visited the mayor who gave Rheticus some financial assistance to publish the First Report or Narratio Prima. This Narratio Prima, published by Rhode in Danzig in 1540, is still considered to be the best introduction to Copernicus' De revolutionibus orbium coelestium. While in Danzig he interviewed the pilots to find out navigational problems. Rheticus had also visited the bishop of Chełmno Tiedemann Giese of Danzig. Warmia in 1547 Warmia (Polish: , German: , Latin: Varmia, also historically known as Ermeland) is a region between Pomerania and Masuria in northeastern Poland. ... GdaÅ„sk ( ; IPA: ), also known by its German name Danzig ( ) and several other names, is the sixth-largest city in Poland and is Polands principal seaport and the capital of the Pomeranian Voivodeship. ... Georg Joachim von Lauchen a. ... In Greek mythology, Rhode was the oldest Oceanid, a daughter of Tethys and Oceanus. ... Tiedemann Giese (June 1, 1480 - October 23, 1550) of the Patrician family Giese from Gdańsk became bishop of Chełmno, then bishop of Warmia. ...

In August 1541 Rheticus presented a copy of his work Tabula chorographica auff Preussen und etliche umbliegende lender (Map of Prussia and Neighboring Lands) to Duke Albrecht 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 asked and received the permission of the duke for the publication of the Copernicus De revolutionibus. Albrecht requested of Rheticus that he return to his teaching position. He returned to the University of Wittenberg in October 1541, after earlier publishing the trigonometrical sections of the Copernicus De revolutionibus. In 1542 he traveled to Nürnberg to supervise the printing of the Copernicus material, published upon Copernicus' death in 1543. Albert (May 16, 1490 - March 20, 1568), (Albertus in Latin, Margrave Albrecht of Brandenburg in German) Grand Master of the Teutonic Order and first duke of Ducal Prussia, was the third son of Frederick of Hohenzollern, prince of Ansbach and Bayreuth, and Sophia, daughter of Casimir IV Jagiello Grand Duke...

Later years

The canon of Warmia 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. Warmia in 1547 Warmia (Polish: , German: , Latin: Varmia, also historically known as Ermeland) is a region between Pomerania and Masuria in northeastern Poland. ... Prince Bishops / Bishops of Warmia: 1250-1274 Anselm of Meissen 1278-1300 Heinrich I Fleming 1301-1326 Eberhard of Neisse 1327-1328 Jordan 1329-1334 Heinrich II Wogenap 1337-1349 Herman of Prague 1350-1355 Joannes I of Meissen 1355-1373 Joannes II Stryprock 1373-1401 Heinrich III Sorbom 1401... Poeta Laureatus Johannes Dantiscus, also Johann(es) von Höfen or Johann(es) Flachsbinder, Polish: , was born 1 October 1485 in Danzig (GdaÅ„sk) and died 27 October 1548 in Lidzbark WarmiÅ„ski (Heilsberg) and is known as a Father of Polish Diplomacy. ... Wawel Hill, Old Town, Kraków. ... Statue of KoÅ¡ices coat of arms St. ... The Kingdom of Hungary (Hungarian: Magyar Királyság) is the name of a multiethnic kingdom that existed in Central Europe from 1000 to 1918. ...

Science of triangles

For much of his life, Rheticus displayed a passion for the study of triangles, or trigonometry. In 1542 he had the trigonometric sections of Copernicus' Revolutions (chapters 13 and 14) published separately under the title, De lateribus et angulis triangulorum (On the Sides and Angles of Triangles). In Leipzig in 1551, Rheticus produced a tract titled, Canon of the Science of Triangles, the first publication of six-function trigonometric tables, though the term trigonometry was not used until 1595. This pamphlet was to be an introduction to Rheticus' greatest work, a full set of tables to be used in angular astronomical measurements. (Danielson, 140-141)

At his death, the Science of Triangles was still unfinished, but, 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 one hundred thousand ratios to at least ten decimal places. When completed in 1596, the volume, Opus palatinum de triangulus, filled nearly fifteen hundred pages. Its tables of values were accurate enough to be used as the basis for astronomical computation into the early twentieth century. (Danielson, 194-201)

References

• Richard S. Westfall, Indiana University. Rheticus, George Joachim. "Catalog of the Scientific Community of the 16th and 17th Centuries," The Galileo Project.
• J.J. O'Connor and E.F. Robertson, University St. Andrews, Scotland.
• Dennis Danielson (2006). The First Copernican: Georg Joachim Rheticus and the Rise of the Copernican Revolution. Walker & Company, New York. ISBN 0-8027-1530-3

External links

• O'Connor, John J.; Edmund F. Robertson "Georg Joachim Rheticus". MacTutor History of Mathematics archive.  
• Scienceworld article on Rheticus
• Narratio Prima