Johannes Müller von Königsberg (June 6, 1436 – July 6, 1476), known by his Latin pseudonym Regiomontanus, was an important German mathematician, astronomer and astrologer. He was born near Königsberg, Bavaria and showed his aptitude for astronomy and mathematics while still very young. In 1450 he entered the University of Vienna, where he became a pupil and friend of Georg von Peuerbach. The two men collaborated on astronomical observations and research, and on his deathbed Peuerbach asked Regiomontanus to complete an abridged translation of Ptolemy's Almagest, which included a critique and later led to Copernicus’ refutation of Ptolemy. In 1464, Regiomontanus wrote De Triangulis omnimodus (“On Triangles of All Kinds”) one of the first textbooks presenting trigonometry in its modern form.
Regiomontanus made a number of important observations, including eclipses and the passing of Halley’s comet in January, 1472, which enabled later astronomers to make comparisons. He also observed that the method of lunar distances could be used to determine longitude at sea. Regiomontanus hoped to initiate a reform of observational astronomy, and in 1471 he set up an astronomical observatory in Nuremberg, and his own printing press on which to reproduce scientific texts. His plans were curtailed by his mysterious death at the age for forty while on a visit to Rome; some scholars believe he was murdered by his enemies, while others believe he died in an outbreak of the plague.
Early Life and Education
Johannes Müller von Königsberg was born June 6, 1436, in the Franconian village of Unfinden near Königsberg, Bavaria (not to be confused with the famous East Prussian city of Königsberg (Kaliningrad), nor with Königsberg in der Neumark (Chojna). The son of a miller, his name originally was Johann Müller. He matriculated at university as Johannes Molitoris de Künigsperg, using a Latin form of 'Müller', 'Molitoris.' He was variously known as Johannes Germanus (Johann the German), Johannes Francus (Johannes from Franconia), Johann von Künigsperg (Johann from Königsberg), and his full Latin name, which Gassendi used in his biography, was Joannes de Regio monte, which abbreviated to Regiomontanus (from the Latin for "Königsberg"—"King's Mountain").
He became known as a mathematical and astronomical prodigy while still very young. After receiving some education at home, at the age of eleven, he entered the University of Leipzig, studying dialectics from 1447 to 1450. He then entered the Alma Mater Rudolfina, University of Vienna, on April 14, 1450, where he became a pupil and friend of Georg von Peuerbach. What attracted Regiomontanus to Vienna was principally the eighty-five-year-old University, and especially its activity in mathematical astronomy and cosmology. He was awarded a baccalaureate on January 16, 1452, but the University regulations required him to be twenty-one years of age before he could be awarded a Master's Degree in 1457. On November 11, 1457, he was appointed to the Arts Faculty of the University of Vienna, where he taught a course on perspective in 1458, one on Euclid in 1460, and one on Virgil's Bucolics in 1461, and classes on optics and ancient literature. Regiomantanus collaborated with his former teacher Peuerbach, who showed him how inaccurate the Alphonsine Tables were. They made observations of Mars which showed the planet to be two degrees from its predicted position, and also observed an eclipse of the moon which happened one hour later than the Tables predicted.
Epitome of the Almagest
In 1450 George of Trebizond had translated and commented on Ptolemy's Almagest, attacking the commentary of Theon of Alexandria and antagonizing Cardinal Johannes Bessarion, papal legate to the Holy Roman Empire, who was a great admirer of Theon. Cardinal Bessarion was a scholar and native Greek speaker who wished to promote classical Greek works in Europe. In May of 1460, Bessarion encouraged Peuerbach to produce an abridgment of Ptolemy's Almagest. His desire was to make a more easily understandable version of Ptolemy's work available, and to support Theon of Alexandria against the attack from George of Trebizond. On his deathbed in 1461, Peurbach asked Regiomontanus to complete the work, and Regiomontanus enthusiastically complied. It was finished by 1463, and printed as the Epitome of the Almagest in 1496. In the Epytoma he critiqued the translation, pointing out inaccuracies; it was later used by such astronomers as Copernicus and Galileo and led to Copernicus’ refutation of Ptolemy. Nicolaus Copernicus referred to this book as an influence on his own work.
His work with Peuerbach brought Regiomontanus into contact with the writings of Nicholas of Cusa (Cusanus), who held a heliocentric view, but he remained a geocentrist after Ptolemy. Regiomontanus worked on mathematics and astronomy, observed eclipses and comets, manufactured astronomical instruments and constructed instruments such as astrolabes. He built astrolabes for Matthias Corvinus of Hungary and Cardinal Bessarion, and in 1465 a portable sundial for Pope Paul II. He was particularly interested in old manuscripts and made copies for his own use, some of which still survive.
From 1461 to 1465 Regiomontanus lived and worked at Cardinal Bessarion's house in Rome. He received instruction from the native Greek speaker Bessarion, and was able to read other important Greek manuscripts. He traveled in Italy with Bessarion, spending the summer of 1462 at Viterbo, Cardinal Bessarion's favourite summer residence, and, when Bessarion left for Greece in the autumn of that year, Regiomontanus went together with him as far as Venice. When Bessarion was appointed as papal legate to the Venetian Republic, Regiomontanus accompanied him and, in the spring of 1464, lectured at the University of Padua (in the Venetian Republic). His lectures on the Muslim scientist al-Farhani have not survived, but his introductory discourse on all the mathematical disciplines was later published. While there, he observed the total eclipse of the moon on April 21, 1464. In August 1464, after the death of the Pope Pius II, Bessarion had to return to Rome to take part in the election of the pope's successor. The astronomer royal for Hungary, Martin Bylica of Olkusz, had also gone to Rome for the election of the new pope, and Bylica and Regiomontanus became friends.
In 1464, Regiomontanus wrote De Triangulis omnimodus (“On Triangles of All Kinds”) one of the first textbooks presenting trigonometry in its modern form. It included lists of questions for review of individual chapters. In it he wrote:
You who wish to study great and wonderful things, who wonder about the movement of the stars, must read these theorems about triangles. Knowing these ideas will open the door to all of astronomy and to certain geometric problems.
De Triangulis was structured in a similar way to Euclid's Elements. It consisted of five books, the first of which gave the basic definitions: quantity, ratio, equality, circles, arcs, chords, and the sine function. He then gave a list of the axioms he would assume, followed by 56 theorems on geometry. In Book II the sine law was stated and used to solve triangles. Books III, IV and V treated spherical trigonometry which was of major importance in astronomy.
In 1467, Regiomontanus left Rome to accept an invitation to work at the court of Matthias Corvinus of Hungary. The King had just returned from a campaign against the Turks with many rare books, and Regiomontanus was appointed to the Royal Library in Buda. There he calculated extensive astronomical tables and built astronomical instruments. Between 1467 and 1471, Regiomontanus worked in Hungary. With some help from his friend, the Hungarian court astronomer Martin Bylica (1433-1493), he compiled various astronomical and trigonometrical tables. He also wrote treatises about and constructed instruments for King Matthias and the Archbishop of Gran.
In 1471, Regiomontanus moved to the Free City of Nuremberg, in Franconia, then one of the Empire's important seats of learning, publication, commerce and art, to undertake the observational reform of astronomy. He associated with the humanist and merchant Bernard Walther, who sponsored an observatory and a printing press. Regiomontanus remains famous for having built at Nuremberg the first astronomical observatory in Germany. He wrote Scipta (published posthumously) giving details of his instruments including dials, quadrants, safea, astrolabes, armillary astrolabe, torquetum, parallactic ruler, and Jacob's staff. In January, 1472, he made observations of a comet, using his Jacob's staff, which were accurate enough to allow it to be identified with Halley's comet 210 years (and three returns of the 70 year period comet) later.
Quite recently I have made observations in the city of Nuremberg... for I have chosen it as my permanent home not only on account of the availability of instruments, particularly the astronomical instruments on which the entire science is based, but also on account of the great ease of all sorts of communication with learned men living everywhere, since this place is regarded as the centre of Europe because of the journeys of the merchants.
The invention of movable type by Johann Gutenberg in 1454 had made possible the first printing of books in Europe. Regiomontanus realized the value of printing for producing identical multiple copies of scientific texts, which could be carefully edited with accurate diagrams. In 1471-1472 he set up a printing press in his own house in Nuremberg, and printed a Prospectus announcing detailed plans for publishing many carefully edited mathematical, astronomical and geographical texts. In 1472 he published the first printed astronomical textbook, the "Theoricae novae Planetarum" (New theory of the planets) of his teacher Georg von Peuerbach, who had worked at the first European observatory, the Observatory of Oradea in Transylvania, and established in his "Tabula Varadiensis" that this Transylvanian town's observatory lay on the prime meridian of Earth. In 1474, he published his own calendar Kalendarium.
In 1475, Regiomontanus was called to Rome to work with Pope Sixtus IV on calendar reform. On his way, he published "Ephemeris" in Venice; both Christopher Columbus and Amerigo Vespucci used Regiomontanus's Ephemerides to measure longitudes in the New World. Regiomontanus died mysteriously in Rome on July 6, 1476, a month after his fortieth birthday. Rumors circulated that he had been assassinated by the sons of George of Trebizond, because he had promised to publish a work demonstrating the worthlessness of Trebizond’s commentary on Ptolemy’s Syntaxis. It is more likely that Regiomontanus became a victim of the outbreak of plague which occurred after the Tiber overflowed its banks in January of 1476.
Regiomontanus's interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. It was many years, however, before the position of the Moon could be predicted accurately enough to make the method practical.
A prolific author, Regiomontanus was already internationally famous during his lifetime. Despite having completed only a quarter of what he had intended to write, he left a substantial body of work. Domenico Maria Novara da Ferrara, the teacher of Nicolaus Copernicus, referred to Regiomontanus as having been his own teacher.
He is known for having built one of the most famous automata, the wooden eagle of Regiomontanus, which flew from the city of Koenigsberg to meet the emperor, saluted him, and returned. He also built an iron fly of which it is said it flew out of Regiomontanus's hands at a feast, and taking a round, returned to him.
Regiomontanus crater, on the Moon, is named after him.
Regiomontanus and Astrology
In his youth, Regiomontanus had cast horoscopes (natal charts) for famous patrons, including the court of Emperor Frederick III. His Tabulae directionum, completed in Hungary, were designed for astrological use and contained a discussion of different ways of determining astrological houses. The calendars for 1475-1531 which he printed at Nuremberg contained only limited astrological information, a method of finding times for bloodletting according to the position of the moon; subsequent editors added material.
The works most indicative of Regiomontanus' hopes for an empirically sound astrology were his almanacs or ephemerides, produced first in Vienna for his own benefit, and printed in Nuremberg for the years 1475-1506. Weather predictions and observations were juxtaposed by Regiomontanus in his manuscript almanacs, and the form of the printed text enabled scholars to enter their own weather observations in order to likewise check astrological predictions; extant copies reveal that several did so. Regiomontanus' Ephemeris was used in 1504, by Christopher Columbus when he was stranded in Jamaica, to intimidate the natives into continuing to provision him and his crew from their scanty food stocks, when he successfully predicted a lunar eclipse for February 29, 1504.
Regiomontanus did not live to produce the special commentary to the ephemerides that he had promised would reveal the advantages the almanacs held for the activities of physicians, for human births and the telling of the future, for weather forecasting, for the inauguration of employment, and for a host of other activities, although this material was supplied by subsequent editors. Nevertheless, Regiomontanus' promise suggests that he either was as convinced of the validity and utility of astrology as his contemporaries, or was willing to set aside his misgivings for the sake of commercial success.
One biographer has claimed to have detected a decline in Regiomontanus' interest in astrology over his life, and came close to asserting that Regiomontanus had rejected it altogether. But more recent commentators have suggested that the occasional expression of skepticism about astrological prognostication was directed towards the procedural rigor of the art, not its underlying principles. It seems plausible that, like some other astronomers, Regiomontanus concentrated his efforts on mathematical astronomy because he felt that astrology could not be placed on a sound footing until the celestial motions had been modeled accurately.
- Boyer, Carl B., and Uta C. Merzbach. 1991. A history of mathematics. New York: Wiley. ISBN 0471543977
- Folkerts, Menso. 2006. The development of mathematics in medieval Europe: the Arabs, Euclid, Regiomontanus. Aldershot: Ashgate Variorum. ISBN 0860789578
- Regiomontanus, Joannes, Johann Schöner, and Barnabas Hughes. 1967. Regiomontanus: On triangles. De triangulis omnimodis. Madison: University of Wisconsin Press.
- Zinner, Ernst. 1990. Regiomontanus. North-Holland. ISBN 044488792X
All links retrieved July 27, 2019.
- Adam Mosley. Regiomontanus Biography, web site at the Department of History and Philosophy of Science of the University of Cambridge.
- John J. O'Connor and Edmund F. Robertson. Regiomontanus at the MacTutor archive
- The Rare book collection, The Vienna University Observatory. See under "digital book collections."
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