- Latin name of:
- Johannes Müller von Königsberg
- Born:
- June 6, 1436, Königsberg, archbishopric of Mainz [Germany]
- Died:
- July 6, 1476, Rome, Papal States [Italy] (aged 40)
- Notable Works:
- “De triangulis omnimodis”
- “Ephemerides”
Regiomontanus
-
Who was Regiomontanus?
Regiomontanus (1436–1476) was a highly regarded 15th-century German mathematician, astronomer, and astrologer. His birth name was Joannes de K\u00f6nigsberg, which he Latinized to Regiomontanus, meaning "King's Mountain".
He studied at the Universities of Leipzig and Vienna, collaborating with mathematician-astronomer Georg von Peuerbach on astronomical projects. Regiomontanus completed Peuerbach's Epitome, an abridgment of Ptolemy’s Almagest, which offered alternative models for planetary orbits and influenced Nicolaus Copernicus.
Regiomontanus mastered Hellenistic and medieval mathematics, contributing to plane and spherical trigonometry in De triangulis omnimodis. He also established an instrument shop and printing press in N\u00fcrnberg, producing astronomical diagrams and numerical tables.
2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
Where and when did Regiomontanus live?
Regiomontanus, born in Königsberg, archbishopric of Mainz (now Germany), on June 6, 1436, was the foremost mathematician and astronomer of 15th-century Europe. He entered the University of Leipzig at age 11 and, in 1450, went to the University of Vienna. From 1467 to 1471, he lived in Hungary as astrologer to King Matthias I of Hungary and Archbishop János Vitéz. In 1471, he moved to Nürnberg, Germany. Regiomontanus traveled to Rome in 1475 to advise Pope Sixtus IV about calendar reform, where he died on July 6, 1476.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What were Regiomontanus's main contributions to mathematics?
Regiomontanus, the foremost mathematician and astronomer of the 15th century, significantly contributed to mathematics. In De triangulis omnimodis (1464), he formalized plane and spherical trigonometry.
\
Regiomontanus also wrote the first book in the West on plane and spherical trigonometry, which was independent of astronomy. In addition, he published tables of sines and tangents that remained in use for over two centuries. He discovered a Greek manuscript of Arithmetica, by Diophantus of Alexandria. His writings also demonstrated an interest in perfect numbers, Platonic solids, and solving quadratic, cubic, and higher-dimensional equations.2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How did Regiomontanus contribute to the study of astronomy?
Regiomontanus, a prominent 15th-century mathematician and astronomer, significantly contributed to the study of astronomy through his observations of eclipses and comets. He collaborated with Georg von Peuerbach on astronomical projects and later completed Peuerbach's Epitome, an abridgment of Ptolemy’s Almagest, which became a critical introduction to Ptolemy’s astronomy.
Regiomontanus addressed inconsistencies in Almagest by advocating for three-dimensional models using concentric spheres. In N\u00fcrnberg, he established an instrument shop and printing press, publishing works with astronomical diagrams and numerical tables. His Ephemerides showcased his computational skills, and his editions of classical texts influenced the mathematical sciences.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
What important books or works did Regiomontanus write?
Regiomontanus, a prominent 15th-century mathematician and astronomer, authored several significant works. His Epytoma in Almagestum Ptolomei (c. 1462, printed 1496), completing Georg von Peuerbach's abridgment of Ptolemy’s Almagest, became a critical introduction to Ptolemy's astronomy and influenced Nicolaus Copernicus.
His De triangulis omnimodis (1464) formalized plane and spherical trigonometry. Regiomontanus also discovered a Greek manuscript of Diophantus' Arithmetica. Other notable works include Tabulae directionum (1467) and Ephemerides, showcasing his computational skills.
1 Britannica SourceCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles. -
How did Regiomontanus influence later scientists and mathematicians?
Regiomontanus, the foremost mathematician and astronomer of the 15th century, significantly influenced later scientists and mathematicians. His Epitome, an abridgment of Ptolemy’s Almagest, offered an alternative to Ptolemy's models for planetary orbits, providing Nicolaus Copernicus with the geometric key to reorient planetary motions around the Sun.
Regiomontanus mastered Hellenistic and medieval mathematics, contributing to plane and spherical trigonometry in his De triangulis omnimodis. He also published sine and tangent tables that remained in use for over two centuries. His editions also pioneered the printing of astronomical diagrams and numerical tables.
2 Britannica SourcesCreated from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.
Regiomontanus (born June 6, 1436, Königsberg, archbishopric of Mainz [Germany]—died July 6, 1476, Rome, Papal States [Italy]) was the foremost mathematician and astronomer of 15th-century Europe, a sought-after astrologer, and one of the first printers.
Königsberg means “King’s Mountain,” which is what the Latinized version of his name, Joannes de Regio monte or Regiomontanus, also means. A miller’s son, he entered the University of Leipzig at the age of 11 and in 1450 went to the University of Vienna. Regiomontanus was awarded a baccalaureate in 1452, but university regulations forced him to wait until he turned 21 to receive his master’s degree. He eventually collaborated with his teacher, the mathematician-astronomer Georg von Peuerbach (d. 1461), on various astronomical and astrological projects, including observations of eclipses and comets, the manufacture of astronomical instruments, and the casting of horoscopes for the court of the Holy Roman Emperor Frederick III.
The papal legate to the Holy Roman Empire, Cardinal Bessarion, during a diplomatic visit to Vienna (1460–61), asked Peuerbach to write an epitome, or abridgment, of Ptolemy’s Almagest to remedy the problems in George of Trebizond’s 1450 translation of and commentary on that great work. When Peuerbach died in 1461, Regiomontanus left for Rome as a member of Bessarion’s extended household and completed Peuerbach’s half-finished Epitome (c. 1462; first printed in 1496 as Epytoma…in Almagestum Ptolomei). His demonstration of an alternative to Ptolemy’s models for the orbits of Mercury and Venus with respect to the Sun gave Nicolaus Copernicus (1473–1543) the geometric key to reorient planetary motions around the Sun. The Epitome is still one of the best critical introductions to Ptolemy’s astronomy.
Although he admired the Almagest, Regiomontanus was keenly aware that its geometric models led to inconsistencies (notably between predictions of planetary position and predictions of planetary size). To remedy these inconsistencies, he tried to eliminate the nonconcentric, two-dimensional eccentrics and epicycles that were the mainstays of Ptolemy’s models. Three-dimensional models using concentric spheres would, he believed, yield good mathematical predictions of planetary positions without jeopardizing the physical principles of natural philosophy.
In Italy (1461–c. 1465), Regiomontanus perfected his Greek, lectured at the University of Padua, read widely in Bessarion’s Greek library, and fought in the latter’s long feud with George of Trebizond. The controversy prompted Regiomontanus to write his longest expository work, the “Defense of Theon Against George of Trebizond,” which later fueled rumours, entirely unsubstantiated, that George’s sons had him poisoned.
Regiomontanus thoroughly mastered Hellenistic and medieval mathematics. His own contributions to the subject range from the formalization of plane and spherical trigonometry in De triangulis omnimodis (1464; “On Triangles of All Kinds”) to his discovery of a Greek manuscript (incomplete) of Arithmetica, the great work of Diophantus of Alexandria (fl. c. ad 250). His writings also show his interest in perfect numbers (numbers equal to the sum of their proper divisors), the Platonic solids, and the solution of quadratic, cubic, and higher-dimensional equations.
From 1467 to 1471 Regiomontanus lived in Hungary as astrologer to King Matthias I of Hungary and Archbishop Janós Vitéz. In 1471 he moved to Nürnberg, Germany, where he established an instrument shop, set up a printing press, and continued his planetary observations in collaboration with the merchant Bernhard Walther. He announced plans to print 45 works, mostly in the classical, medieval, and contemporary mathematical sciences. However, only nine editions appeared, including Peuerbach’s Theoricae novae planetarum (1454; “New Theories of the Planets”), his own attack (“Disputationes”) on the anonymous 13th-century Theorica planetarum communis (the common “Theory of the Planets”), his German and Latin calendars, and his 896-page Ephemerides (daily planetary positions for 32 years, which showcase his computational skills). His editions pioneered the printing of astronomical diagrams and numerical tables. Several of the works that he prepared and had hoped to print, including editions of Euclid and Archimedes, his own astronomical Tabulae directionum (1467; “Tables of Directions”), and a table of sines that he had computed to seven decimal places, proved influential when circulated in the 15th and 16th centuries in manuscript and in print.
The trusted destination for professionals, college students, and lifelong learners.
SUBSCRIBE
In 1475 Regiomontanus traveled to Rome to advise Pope Sixtus IV about calendar reform. He died there the following year, probably from the plague precipitated by the Tiber River overflowing its banks.