Rheticus

Austrian astronomer and mathematician

• Born: February 16, 1514
• Birthplace: Feldkirch, Austria
• Died: December 4, 1574
• Place of death: Kassa, Hungary (now Košice, Slovakia)

Rheticus was instrumental in spreading the heliocentric theory of Nicolaus Copernicus, which argued that the sun rotated around the earth. Rheticus also prepared the first set of mathematical tables with all six trigonometric functions.

Early Life

Rheticus was the son of Georg Iserin, a town physician, and Thomasina de Porris, an Italian. When Iserin was beheaded for sorcery in 1528, it became illegal to use his name. Rheticus’s mother changed the family name, Iserin, to de Porris, which means “of the leeks.” Rheticus translated the Italian name into the German von Lauchen, and added Rheticus, after Rhætia, the ancient Roman name for his birthplace. Later, he dropped the name von Lauchen and assumed Rheticus as his last name.

Rheticus’s father was his first teacher. He continued his schooling at the Feldkirch Latin school and the Frauenmünsterschule in Zürich. Achilles Gasser, who had become the town physician of Feldkirch after the death of Rheticus’s father, provided him with a letter of introduction to Philipp Melanchthon, who was both a noted Protestant (Lutheran) reformer and an educational reformer at the University of Wittenberg. In 1532, Rheticus entered the university, from which he earned a master’s degree in 1536. His thesis argued that Roman law did not prohibit astrological predictions if they were based on physical causes.

Rheticus taught mathematics arithmetic and geometry and astronomy at the University of Wittenberg from 1536 to 1538. In 1538, he took a leave of absence to visit leading astronomers, including Nicolaus Copernicus, and he returned to the University of Wittenberg in 1541, when he was elected the dean of the arts faculty. Rheticus then secured a position as professor of higher mathematics at the University of Leipzig in 1542. The positions at the two universities, and the leave-of-absence, were facilitated by Melanchthon.

Life’s Work

The first part of Rheticus’s work is connected with the Melanchthon circle, a group of young Wittenberg University astronomers, including Erasmus Reinhold, who gathered under the intellectually charismatic Melanchthon. While remaining neutral concerning the truth of geocentrism versus heliocentrism, Reinhold and others focused on the elimination of mathematical errors and the use of Copernican data to construct new planetary tables and to calculate astronomical events and distances more accurately.

Rheticus, in contrast, accepted heliocentrism and emphasized the harmony underlying the Copernican system. In 1539, Rheticus had sought Copernicus at Frombork in Poland to discuss rumors of a revolutionary form of astronomy. Copernicus had resisted publishing his heliocentric theory and saw in Rheticus a means to spread his ideas privately. Rheticus adopted the theory immediately and enthusiastically, and he secured permission from Copernicus to prepare De libris revolutionum Nicolai Copernici narratio prima (1540; The Narratio Prima of Rheticus, 1939; better known as Narratio prima , an introduction to Copernicus’s De revolutionibus orbium coelestium (1543; On the Revolutions of the Heavenly Spheres, 1952; better known as De revolutionibus ). Written in ten weeks, Narratio prima was the first printed announcement of a challenge to Ptolemy’s geocentric astronomy. It was not a mere report, though, for it contained material not found in any of Copernicus’s writings and concentrated on the determination of the relative distances and periodicity of the planets, an emphasis not present in the Copernican treatise. It also contained a few errors.

Rheticus convinced Copernicus to publish De revolutionibus, becoming its first editor. He found a publisher in Nuremberg but had to leave the city before the printing was completed to attend to academic duties. The town theologian, Andreas Osiander, who had experience getting books on mathematics published, then assumed book’s printing and also authored the infamous preface that warned that the book need not be taken seriously, for a hypothesis need not be true. Copernicus had hoped that Narratio prima would have quelled outrage against his theory, but he was wrong.

Rheticus made important contributions to mathematics, particularly trigonometry. In early 1542, he published separately a section on plane and spherical geometry from De revolutionibus entitled De lateribus et anguli triangulorum (on the sides and angles of triangles). The tables of sines employed radii different from those in Copernicus’s tables, however, and, moreover, the table included values for what are now called cosines. Cosines were the work of Rheticus alone. Later, he wrote “Canon of the Doctrine of Triangles” (1551), the first table to provide all six trigonometric functions. This work contained the first extensive table of tangents and the first table of secants ever printed. Here Rheticus defined the trigonometric functions in terms of the sides of triangles, in contrast to earlier definitions based on chords or arcs. He also realized that the functions of angles greater than 45° equaled the cofunctions of the complementary angles of less than 45°. This insight allowed him to halve the length of his tables.

Taking a leave from the University of Leipzig in 1545, Rheticus traveled throughout Italy, but he also suffered a severe mental disorder in early 1547. He recovered sufficiently to teach at Constance later that year. Then he studied medicine in Zürich with Conrad Gesner, from 1547 to 1548, before returning to Leipzig, where he was chosen dean of the faculty of arts.

In 1551, Rheticus had to flee from Leipzig because of a homosexual relationship with a male student, homosexuality being illegal at the time. He first left for Chemnitz, then to Prague, where he resumed medical studies, and he settled finally in Krákow in 1554. The authorities in Leipzig tried him in absentia, sentenced him to 101 years of exile, and impounded all his possessions. At this point, Melanchthon and the members of his circle stopped their association with him.

In Krákow, Rheticus practiced medicine for twenty years. During this period, he rekindled his interest in astrology, following up on his master’s thesis. In 1562, he was still contemplating the possibility of constructing a chronology of the world from its creation to its end. In 1571, he correctly predicted that King Sigismund II Augustus of Poland would have a short reign, thus attaining a reputation as a great seer. He also constructed instruments, made astronomical observations, and performed experiments in alchemy.

During these last years of his life, Rheticus continued the painstaking work on trigonometric tables. Holy Roman Emperor Maximilian II’s funding of his work enabled Rheticus to employ six assistants. In 1574, a young student of mathematics at the University of Wittenberg, Valentin Otto, visited Rheticus. Recalling his service to Copernicus, Rheticus hoped to see him arrange for the publication of his tables. Unfortunately, Rheticus died, and Otto, after some difficulties, found a patron in Palatinate elector Frederick IV, for whom he became the official mathematician. Otto finished the tables and named them in honor of his backer Opus palatinum de triangulis (the palatine work on triangles) (1596).

Significance

There was deep enmity between science and religion during Rheticus’s time. Copernicus feared that people would reject his heliocentric system because it contradicted Scripture. As a member of Melanchthon’s circle, Rheticus a Lutheran and a Copernican wrote an anonymous treatise on the Holy Scripture and the motion of Earth, published only a century later. On one hand, Rheticus had argued that the Bible is authoritative only in matters of ethics and salvation, but not in science; while on the other hand, he attempted to find evidence in Scripture suggesting that Earth does move. Such attempts to reconcile science and religion appeared much more frequently after the arrest of Galileo.

Rheticus has had a lasting significance in mathematics because of his preparation of trigonometric-functions tables and the painstaking efforts he took to the end of his life to refine them further. The first trigonometry textbook appeared soon thereafter, and Rheticus’s tables helped lay the foundation for the discovery of logarithms.

Bibliography

Barker, Peter. “The Role of Religion in the Lutheran Response to Copernicus.” In Rethinking the Scientific Revolution, edited by Margaret J. Osler. New York: Cambridge University Press, 2002. Describes Rheticus’s role in the publication of Copernicus’s work and reevaluates the Lutheran response to it.

Blumenberg, Hans. The Genesis of the Copernican World. Translated by Robert M. Wallace. Cambridge, Mass.: MIT Press, 1987. A massive work on the Copernican revolution and its significance for understanding modernity. Places Rheticus in the context of its supporters.

Hooykaas, R. G. J. Rheticus’s Treatise on Holy Scripture and the Motion of the Earth, with Translation, Annotations, Commentary, and Additional Chapters on Ramus-Rheticus and the Development of the Problem Before 1650. New York: North Holland, 1984. Includes a discussion of religious issues created by scientific developments in the sixteenth century, especially among Copernicus’s circle.

Motz, Lloyd, and Jefferson Hane Weaver. The Story of Astronomy. New York: Plenum Press, 1995. A short history of astronomy from the time of antiquity, useful for understanding the issues surrounding Copernicus.

Westman, Robert S. “The Melanchthon Circle, Rheticus, and the Wittenberg Interpretation of the Copernican Theory.” Isis 66 (1975): 165-193. Examines the social context of the early reaction to Copernican astronomy and explains the appeal of Copernican theory in terms of Rheticus’s personal history.