Regiomontanus Completes the of Ptolemy’s Summary

  • Last updated on November 11, 2022

The first Latin translation of Ptolemy’s Almagest, meticulously revised with new observations and data by Regiomontanus, made widely available for the first time the most important astronomical treatise of antiquity and the Middle Ages, sparking a revolution in astronomy and mathematics.

Summary of Event

Regiomontanus’s Epitome Epitome (Regiomontanus) of Ptolemy’s Almagest (Epytoma in almagestum Ptolomaei; wr. 1462, pb. 1496) brought the Humanist movement to the sciences, changed the course of mathematics, and revolutionized astronomy. Johannes Müller, better known as Regiomontanus (the Latinized name of his hometown, Königsberg), was a prodigy, studying under the astronomer Georg von Peuerbach and receiving his bachelor’s degree from the University of Vienna in 1452 at the age of fifteen. By 1457, he was a professor there, working closely with his mentor von Peuerbach. Astronomy;Austria Regiomontanus Bessarion Peuerbach, Georg von Copernicus, Nicolaus Vespucci, Amerigo Columbus, Christopher Hamman, Johannes Peuerbach, Georg von Bessarion Hamman, Johannes Vespucci, Amerigo Columbus, Christopher Copernicus, Nicolaus

A facsimile page from Regiomontanus’s Epitome of Ptolemy’s Almagest, first printed in 1496.

(Frederick Ungar Publishing Co.)

The inception of the Epitome of Ptolemy’s Almagest came through a fortuitous visit to Vienna in May of 1460 by the Greek cardinal Bessarion, a Byzantine scholar trained in philosophy, and, after the Ottoman invasion of the East, the papal legate to the Holy Roman Empire. Bessarion was an early proponent of the Humanist Humanism movement, which sought the revival, translation, printing, distribution, and reexamination of obscure classical texts. Bessarion supported reconciliation between the Eastern Orthodox and Roman Churches, and he campaigned especially to make Greek texts better known in the Latin West. In Vienna, he persuaded von Peuerbach to begin work on a concise Latin edition of the most influential of Greek astronomical texts, Ptolemy’s Mathēmatikē syntaxis (c. 150). After the twelfth century, it was more commonly known by the title Almagest (English translation, 1952), meaning “the greatest,” a name given to the work by medieval Arabic readers. Almagest was a vast compendium of astronomical observations and tables of calculations based on a geocentric (Earth-centered) model of the cosmos, bringing together the astronomical knowledge of the entire ancient world, from the Babylonians to the Romans. Though he did not know Greek, von Peuerbach had earlier Latin-manuscript translations of the ancient work, and using these he completed Almagest through book VI before he died in April of 1461, just under a year after Bessarion’s arrival.

Upon von Peuerbach’s death, Regiomontanus, his most brilliant student and closest collaborator, inherited the project and began to study Greek under the guidance of Bessarion so that he could read Almagest in its original language. The two traveled together to Rome, where they arrived on November 20, 1461, and they stayed there until 1463. Regiomontanus studied full-time Ptolemy’s language and astronomy, acquiring fluency in Greek and gaining complete mastery of Almagest. He finished the manuscript translation, which he dedicated to Bessarion, at the end of 1462.

At the time of Regiomontanus’s translation, Ptolemy’s Almagest was still considered the most authoritative astronomical reference available. Yet many of the second- and third-generation copies that circulated through Europe were filled with errors. By returning to the original Greek text, and by adding extensive new computations, observations, and commentary, Regiomontanus updated Ptolemy’s system, advancing astronomical knowledge and exposing for the first time some of the crucial flaws in Ptolemy’s astronomy.

In 1463, Regiomontanus followed Bessarion to Venice, and through his patronage began teaching mathematics at Padua. Here, Regiomontanus began pursuing another problem raised in the Epitome. Determining astronomical positions frequently required geometrical calculations comparing angles in spherical triangles. Yet, as Regiomontanus noted in the Epitome, no systematic geometry text was available that allowed for the computation of angles for plane or spherical triangles. To remedy this, Regiomontanus composed his treatise De triangulis omnimodis (wr. 1464, pb. 1533; On Triangles On Triangles (Regiomontanus) , 1967). It was in this text that Regiomontanus became the first scholar in the Latin West to use the then-new mathematical language developed by medieval Islamic scholars—algebra—to solve a trigonometric problem. It was here that Regiomontanus formulated for the first time the cosine law for spherical triangles and created trigonometry as an independent branch of mathematics. Mathematics;Austria

Regiomontanus further developed applied trigonometry in his Tabulae directionum Tabulae directionum (Regiomontanus) (wr. 1467, pb. 1490; tables of directions), introducing a table of tangents in modern form and placing the calculation of celestial positions on a new footing. These innovations influenced astronomers and mathematicians through the next hundred years and spurred the revolution in astronomy that culminated in Isaac Newton’s unified physical system of the cosmos.

In 1471, Regiomontanus moved to Nuremberg, where he set up a printing press in his house. From here he printed and disseminated a variety of scientific works, becoming the first to turn the new printing Printing;scientific works press into an agent of scientific mass communication. His first published works included a version of von Peuerbach’s Theoricae novae planetarum (1474; English translation, 1987) and the first printed astronomical tables, the Ephemerides (1474). Regiomontanus intended to print his Epitome at his own press, but he died at age forty, before he could do so. The Venetian publisher Johannes Hamman acquired the manuscript of the Epitome and distributed the first printed edition in 1496.

Navigator Amerigo Vespucci was using the tables three years later, comparing the apparent distance between the Moon and Mars to values given in the tables. By calculating the difference between the two values, Vespucci became the first navigator to use lunar distances to determine longitude, among the most reliable methods until the advent of the marine chronometer at the end of the eighteenth century. Christopher Columbus carried a copy of the Ephemerides on his last voyage to the New World in 1504, and he used the power of prediction it gave him to forecast a lunar eclipse, astounding the indigenous peoples of Jamaica and allowing him to take possession of the island. In spite of revolutionary advances in both theoretical and observational astronomy, Regiomontanus’s celestial almanacs remained the standard ones for three centuries after his death.

Some scholars believe Regiomontanus asserted the motion of the earth and thus indirectly influenced Nicolaus Copernicus’s cosmological beliefs. In a letter from the last years of his life, Regiomontanus was reported to have written, “The motion of the stars must vary a tiny bit on account of the motion of the earth.” On the basis of this fragment, a tradition emerged that Regiomontanus might have been the originator or inspiration of the Sun-centered (heliocentric) Copernican system. In the Epitome, however, and in his other known writings, Regiomontanus refrained from explicit critiques of the theoretical assumptions of Ptolemy’s system, focusing instead on improving its calculations. In so doing, however, he made the text all the more accessible to the scrutiny of other astronomers who had more revolutionary approaches and intentions.


As soon as it was published, the Epitome of Ptolemy’s Almagest began to circulate widely among astronomers. At half Almagest’s length, it was considerably less intimidating and more useful. Regiomontanus’s masterful translations and meticulous editing made it a vastly superior tool to the previous Latin translations and other available corrupted copies.

The Epitome revealed technical problems with Ptolemy’s theory that became a central focus for astronomers: According to its formulas, the apparent diameter of the Moon should sometimes vary by up to four times its normal size. This prediction, far from observed values, alerted Copernicus to the fallibility of Ptolemy’s system and began his search for an alternative to the universally accepted, Earth-centered cosmological model at the heart of Almagest.

When the Epitome was published in Venice, Copernicus, then a young student at the nearby University of Bologna, avidly read the new translation. These discrepancies started Copernicus on his lifelong preoccupation with the shortcomings of Ptolemaic astronomy, culminating with the 1543 publication of his solution to the problems, his De revolutionibus orbium coelestium (1543; On the Revolutions of the Heavenly Spheres, 1952; better known as De revolutionibus De revolutionibus (Copernicus) ), which argued against Ptolemy’s model of a geocentric cosmos and replaced it instead with a heliocentric model, where the earth revolved daily about its axis and orbited the sun once a year.

The Epitome fulfilled the Renaissance Humanist dream of reviving the treasures of classical antiquity and making them available for a wide audience. Its prose and organization were unequaled, and it quickly became a model for the new form of scientific communication invented by Regiomontanus himself, the printed scientific book.

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Heilbron, John L. The Sun in the Church: Cathedrals as Solar Observatories. Cambridge, Mass.: Harvard University Press, 2001. Challenges age-old assumptions about the relationship between the Roman Catholic Church and astronomy, showing the importance of Church sponsorship in the research and publications of astronomers from Regiomontanus to Galileo.
  • citation-type="booksimple"

    xlink:type="simple">Hellman, C. Doris. The Comet of 1577: Its Place in the History of Astronomy. New York: Columbia University Press, 1944. Far broader in scope and interest than its title would suggest, this study explores the observational careers of the great European astronomers of the sixteenth century, placing Regiomontanus in the context of his contemporaries.
  • citation-type="booksimple"

    xlink:type="simple">Swerdlow, Noel. “Regiomontanus’s Concentric-sphere Models for the Sun and Moon.” Journal for the History of Astronomy 30 (1999): 1-23. A technical treatment that traces Regiomontanus’s specific alterations to several of Ptolemy’s astronomical models and argues for their importance.
  • citation-type="booksimple"

    xlink:type="simple">Zinner, Ernst. Regiomontanus: His Life and Work. Translated by Ezra Brown. New York: North-Holland, 1990. The definitive study of Regiomontanus, based on a thorough study of the manuscript sources. Followed by a series of essays showing how research since Zinner’s classic 1968 study appeared has revised knowledge of Regiomontanus’s career.

1490’s: Aldus Manutius Founds the Aldine Press

Oct. 12, 1492: Columbus Lands in the Americas

1543: Copernicus Publishes De Revolutionibus

1572-1574: Tycho Brahe Observes a Supernova

1580’s-1590’s: Galileo Conducts His Early Experiments

1582: Gregory XIII Reforms the Calendar

1600: William Gilbert Publishes De Magnete

Categories: History