The only medieval state that retained an unbroken cultural link with the classical Greek world was the Byzantine Empire, with its capital at Constantinople, ancient Byzantium. The link was very tenuous at times, as when the empire was almost overrun by invaders, losing much of its territory in both Europe and Asia. Constantinople was captured and sacked in 1204 by the army of the Fourth Crusade and the Venetian fleet, after which the Byzantine Empire was reduced to several small states, two of them in Asia Minor. One of these, ruled by the Lascarid dynasty, had its capital at Nicaea, while the Com-neni dynasty reigned from its capital at Trebizond. In 1261 the Greeks of Nicaea recaptured Constantinople, which once again became capital of the Byzantine Empire, a state that was much reduced in size and power compared to what it had been in the reign of Justinian.
During the century prior to the Fourth Crusade several Italian city-states had obtained commercial concessions in the Byzantine Empire, allowing them to set up trading establishments in Constantinople and other cities of the empire. Genoa, Venice, Pisa, and Amalfi had concessions in Constantinople, where they built docks and warehouses along the Golden Horn as well as residences and churches for merchants and their families. These Latin concessions continued in existence until the end of the empire, serving as centers not only for trade but also for cultural interaction between the Greek East and the Latin West.
One important instance of such a cultural interchange occurred in 1136, during the reign of the Byzantine emperor John II Comnenus, when the Holy Roman Emperor Lothair sent a mission to Constantinople to discuss theological differences between the Roman Catholic and Greek Orthodox churches. The mission was headed by Anselm, bishop of Havelberg and later archbishop of Ravenna. After Anselm arrived in Constantinople he and his entourage went to the Pisan quarter on the Golden Horn to discus theology with a group of Greek clerics headed by Nicetas, archbishop of Nicomedia. Anselm writes,
There were present not a few Latins, among them three wise men skilled in the two languages [Latin and Greek] and most learned in letters, mostly James a Venetian, Burgundio a Pisan, and the third, most famous among Greeks and Latins above all others for his knowledge of both literatures, Moses by name, an Italian from the city of Bergamo, and he was chosen by all to be an interpreter for both sides.
The first of these scholars, James of Venice, is known in Latin as Iacobus Veneticus Grecus, which could mean that he was a member of the Greek community of Venice. In any event, he was fluent in both Greek and Latin, as indicated by an entry for the year 1128 in the chronicle of Robert of Torigni, abbot at Mont-Saint-Michel, who writes that “James, a clerk of Venice, translated from Greek into Latin certain books of Aristotle and commented upon them, namely the Topics, the Prior and Posterior Analytics, and the[Sophistici] Elenchi, although there was an older version of these books.”
James was the first European scholar in the twelfth century to introduce the works of Aristotle to the Latin West. Besides the works mentioned by Robert of Torigni, James was the first to translate from the Greek Aristotle's Physica, De Anima, Metaphysica,andParva Naturalia His commentary on the Sophistici Elenchi shows that he was aware of Byzantine scholarship on this subject in Constantinople, which was an unrivaled source for the works of Aristotle and other Greek writers. James's translations, together with their revisions, formed the basis for much of Aristotelian studies in Europe until the sixteenth century.
Burgundio the Pisan traveled frequently from Pisa to Constantinople and to Sicily, another rich source of Greek manuscripts. His translations from the Greek also included the Aphorisms of Hippocrates and ten works of Galen's, as well as Aristotle's Meteorology
Moses of Bergamo, whom Anselm mentions as the interpreter in the theological disputation of 1136, lived at that time in the Venetian quarter of Constantinople. He writes in one of his letters that he learned Greek so that he could translate previously unknown manuscripts into Latin. He spent years collecting Greek manuscripts, for which he paid a total of three pounds of gold, he says, but they were all destroyed in a fire in 1130. The only translations of his that have survived are works of Greek grammarians and early Byzantine theologians.
Translations from Greek to Latin were also done in Sicily during the reign of William I (r. 1154-66), the son and successor of Roger II; he continued his father's patronage of learning. The two principal translators during his reign were Henricus Aristippus and Eugene the Emir, both of them members of the royal administration who left eulogies of William, commemorating him as a philosopher-king who opened his court to the world's leading scholars. Aristippus became archbishop of Catania in 1156 and four years later was placed in charge of the entire administration of the Sicilian kingdom. He was the first to translate from the Greek two of Plato's dialogues, Meno and Phaedo, as well as the fourth book of Aristotle's Meteorology, works that remained in use until the early Renaissance. Aristippus also served as envoy to the court of Manuel II Com-nenus in Constantinople, where the emperor presented him with a beautiful codex of Ptolemy's Almagest as a present to King William. The first Latin translation of this manuscript from Greek to Latin was made in Palermo by an anonymous visiting scholar circa 1160. Other works translated from Greek to Latin at the Sicilian court by this scholar include Euclid's Optica and Catoptrica, Proclus's De Motu, and Hero of Alexandria'sPneumatica
The unknown scholar who translated these works notes that in doing so he received considerable assistance from Eugene the Emir, “a man most learned in Greek and Arabic and not ignorant of Latin.” Eugene, who held the Arabic title of emir in the royal administration, was probably a Greek, as evidenced by his surviving poetry.
The Dominican monk William of Moerbeke, in Belgium, was the most prolific of all medieval scholars who translated from Greek into Latin. Moerbeke is known to have visited Nicaea in the spring of 1260, when the Byzantines still had their capital there, not recapturing Constantinople until the following year, and he may very well have acquired Greek manuscripts at that time. He took part in the Second Council of Lyons (May-June 1274), whose goal was to bring about a reunion between the Greek and Latin churches, and at a pontifical mass he sang the Credo in Greek together with Byzantine clerics.
Thomas Aquinas is said to have suggested to Moerbeke that he complete the translation of Aristotle's works directly from the Greek. Moerbeke says that he took on this task “in spite of the hard work and tediousness which it involves, in order to provide Latin scholars with new material for study.”
Moerbeke's Greek translations included the writings of Aristotle, commentaries on Aristotle, and works by Archimedes, Proclus, Hero of Alexandria, Ptolemy, and Galen. The popularity of Moerbeke's work is evidenced by the number of extant copies of his translations, including manuscripts from the thirteenth to fifteenth centuries, printed editions from the fifteenth century onward, versions in English, French, Spanish, and even modern Greek done from the fourteenth century through the twentieth. His translations led to a better knowledge of the actual Greek texts of several works, and in a few cases they are the only evidence of lost Greek texts, such as that of Hero's Catoptrica
Moerbeke's only original work is a treatise on divination entitled Geo-mantia, which was evidently quite popular, as demonstrated by the several extant Latin manuscripts and a French translation done in 1347. Witelo, in the dedication to Moerbeke in hisPerspectiva, praises him for his “occult” inquiry into the influence of divine power on humans.
Another Western scholar who visited Constantinople in search of ancient Greek manuscripts was Peter of Abano (1250-ca. 1313), who while there found works by Aristotle, Dioscorides, and Galen, among others. His translations from the Greek include a volume of Aristotle's Problems, the first Latin translation of this work; Aristotle's Rhetoric; Dioscorides's De Materia Medica; and six treatises of Galen's.
The most famous of Peter's original works is his Conciliator Differen-tiarum Philosophorum et Praecipue Medicorum, which he completed in 1303, while he was teaching at the University of Paris. In this enormous tome Peter tries to reconcile the conflicting views of the medical writers and philosophers who had preceded him. The Conciliator comprises more than two hundred questions, or “differences,” which Peter says he and his colleagues had been debating for the past decade. The first and eighteenth questions, for example, concern the differences of opinion about whether the heart is the center of the human nervous system, as Aristotle holds, or whether it is the brain, as Peter says. His conclusion concerning the first question is that “the regulative power of the body resides in the brain;” regarding the eighteenth, he says that “the brain is the seat of sensation and emotion.” Question 67 asks, “Is life possible below the equator?” It seems that this question occurred to Peter after he met Marco Polo, who had returned to Venice in 1295 after his celebrated journey to the Far East.
Another well-known work by Peter is his Lucidator Dubitabilium Astronomiae, in which he discusses disputed doctrines in astronomy and astrology. Here he suggests that the stars are not fixed in the outermost celestial sphere, as Aristotle has it in his model of the cosmos, but move freely in space, an entirely new idea that would become part of modern cosmology. A number of passages in this work indicate that Peter associated spirits and intelligences with the celestial bodies, one of which he describes as “perpetual and incorruptible, leading through all eternity a life most sufficient unto itself, nor ever growing old.”
Peter's writings on astrology and other occult sciences gave him the reputation of being a magician. Gabriel Naude, in 1625, called Peter “a man who appeared as a prodigy and miracle in his age… he was the greatest magician of his age and learned the seven liberal arts from seven familiar spirits whom he held captive in a crystal.” But Naude went on to say that Peter had in later life abandoned “the idle curiosity of his youth to devote himself wholly to philosophy, medicine and astrology.”
Meanwhile Byzantium was undergoing a cultural revival under the Palaeologues, the dynasty that ruled the Byzantine Empire after its recapture of Constantinople from the Latins in 1261 until its fall to the Turks in 1453. Michael VIII Palaeologus (r. 1259-82), the founder of the dynasty, reestablished the University of Constantinople, which had been closed during the Latin occupation.
The first head of the reopened university was George Acropolites, who lectured on the mathematics of Euclid and Nicomachus as well as the philosophy of Aristotle. Acropolites had been a student of Nicepho-rus Blemmydes (ca. 1197-1272), who wrote a handbook on physics, astronomy, and logic as well as a geographical synopsis and several theological commentaries, all of which were used at the University of Constantinople. Another student of Blemmydes’ who taught at the university was George Pachymeres (1242-1310), who was primarily a historian but who also wrote on mathematics and the theory of music.
A number of scholars from Byzantium went west on diplomatic missions or to teach at European universities. One of the first of the diplomat scholars was the monk Maximos Planudes (1260-1310), who was sent by Andronicus II (r. 1282-1328) on an embassy to Venice in 1296. After his return to Constantinople Planudes translated from Latin to Greek a number of books that he had acquired in Italy, including works by Cicero, Ovid, Saint Augustine, and Boethius. The vast number of extant manuscripts of his translations show that they were often used as texts for teaching Greek at universities in Italy, which began with the emergence of Italian humanism and its interest in reviving classical letters. He also wrote two works on mathematics, one of them a commentary on Diophantus'sArithmetica and the other a treatise on the “Hindu” numbers being used by Arabic mathematics, the first mention of this system of numeration by a Byzantine scholar.
Italian humanism had focused on Latin learning until the time of Petrarch (1304-74) and his pupil Boccaccio (1313-75), who set out to learn Greek so that they could read Homer and Plato and other Greek writers in the original. At Avignon Petrarch began to study Greek with Barlaam of Calabria (d. 1348), who had been sent to the papal court on a diplomatic mission by the emperor Andronicus III (r. 1328-41). But Barlaam died soon afterward and Petrarch never learned proper Greek.
The renowned Byzantine humanist Manuel Chrysoloras (ca. 1350-1417) was sent on a diplomatic mission from Constantinople to Venice in 1390. During his stay in Venice, which ended the following year, Chrysoloras was offered a contract to give Greek lessons in Florence, where he taught from 1396 until 1400. The leading Florentine statesmen and humanists who flocked to his lectures included the chancellor Leonardo Bruni, who is quoted as saying that Chrysoloras inspired him to learn a language that no Italian had understood for seven hundred years.
The textbook that Chrysoloras wrote for his lessons, the Erotemata (Questions), was translated into Latin by Guarino of Verona (1374-1460), who studied Greek with him in Constantinople from 1403 to 1408. Guarino went on to teach Greek in Venice, Florence, and Ferrara, where he remained for the last thirty years of his life, attracting students from as far away as England. He was also noted for his translations, which included works by Homer, Herodotus, Plutarch, and Strabo, whose Geography he translated in his latter years.
Chrysoloras was contemporary with the Florentine humanist Poggio Bracciolini, who in 1417 discovered the full text of Lucretius's De Rerum Natura, with its philosophy of nature based on the atomic theory of Democritus. This was printed later in the fifteenth century and reprinted many times thereafter, reviving interest in the atomic theory, which had been in obscurity since antiquity.
By the beginning of the fourteenth century Byzantium was flowering in a last renaissance, even as the empire was being engulfed by the rising tide of the Ottoman Turks. The Ottomans established their first capital in 1326 at Bursa, in northwestern Asia Minor, and crossed over into Europe twenty years later, when they captured the city of Callipolis (Gallipoli), on the Dardanelles. The Turkish capture of Callipolis was recorded by the Byzantine scholar Demetrius Cydones, renowned for his translations from Latin into Greek, most notably the Summa Theolog-ica of Thomas Aquinas. According to Cydones, the fall of Callipolis began an exodus of Greeks from Byzantium to Italy, Spain, and even farther “towards the sea beyond the Pillars [the Strait of Gibraltar].”
The extent of the Palaeologan cultural revival is revealed by the beautiful mosaics and frescoes that have survived in the church of St. Savior in Chora, now known as Kariye Camii, in Istanbul, built in the years 1315-21 by Theodore Metochites (ca. 1250-1332), prime minister under Andronicus II.
Metochites was one of the most renowned figures of his time in Byzantium, the head of the government as well as a distinguished theologian, philosopher, astronomer, mathematician, physicist, poet, and patron of the arts, a leader in the artistic and intellectual renaissance in the early Palaeologan era. His student and protégé Nicephorus Gregoras wrote of him in admiration, “From morning to evening he was most wholly and eagerly devoted to public affairs as if scholarship was absolutely indifferent to him; but later in the evening, having left the palace, he became absorbed in science to such a degree as if he were a scholar with absolutely no connection with any other affairs.”
Metochites’ most important scientific work is his Introduction to Astronomy, which is based on Ptolemy's Almagest He made no astronomical observations, merely recalculating the old parameters for a starting date in 1282, the year that his patron Andronicus II began his reign.
Nicephorus Gregoras (ca. 1290-ca. 1360) was a polymath of remarkable versatility, as evidenced by his writings on history, theology, philosophy, astronomy, geography, and acoustics. His research in astronomy led him to propose a revision of the calendar, a scheme that anticipated the calendar reform carried out in 1582 by Pope Gregory XIII.
The astronomical work of Theodore Metochites and Nicephorus Gregoras was part of a revival of astronomy in Byzantium that had begun at the end of the thirteenth century, when Greek translations of Arabic astronomical treatises and tables became available in Constantinople. One of the first of such translations was done by Gregory Cho-niades, who learned Arabic science in Tabriz and founded a school of astronomy in Trebizond circa 1300. One of his students was Manuel of Trebizond, who taught at his master's school. Manuel's most distinguished student was George Chrysokokkes, who wrote on medicine and geography as well as on astronomy.
By the mid-fourteenth century new “Persian Tables” were substituted for older astronomical tables, as in the Three Books on Astronomy, a compendium of astronomy published in around 1352 by Theodore Melite-niotes, who became head of the Patriarchal School in Constantinople.
Scientific ideas were also coming to Byzantium from the West, as evidenced by a treatise on the astrolabe translated into Greek in Constantinople circa 1309 from a Latin version of the Arabic original. Another astronomical work, the Six Wings, an anonymous thirteenth-century treatise in Hebrew, was translated into Greek in Constantinople in the second quarter of the fifteenth century, apparently having made its way from southern France through Venice to Byzantium.
The fall of Thessalonica to the Ottomans in 1430 led the emperor John VIII (r. 1425-48) to seek help from the West, and he proposed to Pope Martin V that a council be called to help reconcile the Greek and Latin churches. This eventually gave rise to a council that was convened by Pope Eugenius IV in 1438 at Ferrara, moving to Florence the following year. The council ended on 6 July 1439, when a Decree of Union between the Greek and Latin churches was read in Latin and Greek in the cathedral of Florence, Santa Maria del Fiore, in the presence of the emperor John VIII. But most of the people and clergy of Byzantium rejected the Union, dividing the empire in what were to be the last years of its existence.
The delegates to the Council of Ferrara-Florence included four scholars who were leading figures in the cultural interchange between Byzantium and Italy, one of them representing the Latin Catholic Church and the others the Greek Orthodox faith. The Latin delegate was Nicholas of Cusa; the Greeks were George Gemistus Plethon, George Trapezuntios, and Bessarion of Trebizond.
Nicholas of Cusa (1401-1464) was born at Cues, a village on the Moselle. He was educated at the universities of Heidelberg and Padua, where he received a doctorate in 1423. He entered the priesthood circa 1430 and in 1448 Pope Nicholas V made him a full cardinal, with the titular see of St. Peter in Vincoli in Rome.
Cusa's most important work is his De Docta Ignorantia (On Learned Ignorance), completed in 1440. Here he uses mathematics and experimental science in his attempts to determine the limits of human knowledge, particularly in the inability of the human mind to conceive the absolute, which to him was the same as mathematical infinity. He concluded that the universe is infinite in extent, making the idea of a center or of a periphery meaningless. Thus the earth cannot be the center of the universe, and since motion is relative and natural to all bodies, the earth cannot be at rest. A marginal note made by Cusa in one of his manuscripts suggests that the earth cannot be fixed, but rotates on its axis once in a day and a night.
Cusa speculated that the earth might not be the only body on which there were living creatures, and that there might be another earth at the center of the sun's luminous envelope. These and other revolutionary theories led his political rivals to accuse him of pantheism, a charge that he defended himself against in his Apologia Doctae Ignorantia (1440), in which he quoted patristic writings and Christian Neoplatonists as the sources of his ideas.
Ten years later Cusa wrote a work entitled Idiota, a series of dialogues in which a rhetor, or school man, who represents book learning converses with a layman (Idiota) who stresses the importance of quantitative experimental research. According to Idiota, wisdom clamors in the streets and one can find it in the marketplace, where one sees money being counted, merchandise being weighed, oil being measured, and where one can watch human reason performing its most fundamental function: measurement.
George Gemistus Plethon (ca. 1355-1452), whom Sir Steven Runci-man called “the most original of all Byzantine thinkers,” was educated in Constantinople and taught there until about 1392. He then went to Mistra in the Peloponnesus, which at the time was ruled by the despot Theodore Palaeologus, second son of the emperor Manuel II (r. 1391-1425). Plethon taught there for the rest of his days, except for a year that he spent as a member of the Byzantine delegation at the Council of Ferrara-Florence. His teaching was dominated by his rejection of Aristotle and his devotion to Plato, who inspired his goal of reforming the Greek world along Platonic lines. His religious beliefs were more pagan than Christian, as evidenced by his treatise On the Laws, in which he usually refers to God as Zeus and writes of the Trinity as consisting of the Creator, the World-Mind, and the World-Soul. George Trapezuntios writes of a conversation he had at Florence with Plethon, who told him that the whole world would soon adopt a new religion. When asked if the new religion would be Christian or Muhammadan, Plethon replied, “Neither, it will not be different from paganism.”
While the council was deliberating in Florence Plethon delivered a lecture at the palace of Duke Cosimo de’ Medici, the subject being the philosophical and religious differences between Platonism and Aris-totelianism, in which he eulogized Plato. Cosimo was so inspired by Plethon that he founded a Platonic academy in Florence, which became the center of Renaissance Platonism. Plethon's writings also inspired Marsilio Ficino (1433-99), the first of the great Renaissance Platonists.
During his stay in Florence, Plethon recommended the study of Strabo's Geography as a supplement to that of Ptolemy. One of those to whom he spoke of this may have been Paolo Dal Pozzo Toscanelli, whom he met in Florence. Toscanelli later passed the suggestion on to Christopher Columbus, who would have read Strabo in Guarino's Latin translation. Columbus, according to the biography written by his son, was directly influenced by two passages of Strabo's. These were quotes from Eratosthenes and Poseidonus, the first being “If the immensity of the Atlantic did not prevent us, we could sail from Iberia to India along the same parallel,” and the second, “If you sail from the west using the east wind you will reach India at a distance of 70,000 stades.”
George Trapezuntios (1395-1486) was born on Crete to a family who had moved there from Trebizond; hence his last name. He was a prolific translator from Greek into Latin, which he studied under Guarino in Venice in 1417-18. He taught in Venice, Vicenza, and Mantua before going to Rome, where he served in the papal bureaucracy under Euge-nius IV (r. 1431-47) and then taught under Nicholas V (r. 1447-55). He severely criticized Plethon for his attack on Aristotelianism, portraying himself as the champion of medieval scholasticism against its humanist critics, and singling out for special praise Albertus Magnus and Thomas Aquinas, which brought him into conflict with Bessarion, among others.
Bessarion (1403-1472) was born into a family of manual laborers at Trebizond. The metropolitan of Trebizond noticed the boy's intelligence and sent him to school in Constantinople. While at the university he met the Italian humanist Francesco Filelfo, who had been inspired to study in Constantinople after attending the classes of Manuel Chrysoloras in Italy.
At the age of twenty Bessarion became a monk and spent some years at a monastery near Mistra, where he studied under Plethon. He then returned to Constantinople and won renown as a professor of philosophy. He was chosen as one of the delegates to the Council of Ferrara-Florence, and was appointed metropolitan of Nicaea so that he would have appropriate status at the conclave. When the agreement of union was formally proclaimed on 6 July 1439 in the cathedral in Florence, it was first read in Latin by Cardinal Cesarini and then in Greek by Bessarion.
Bessarion's stay in Italy convinced him that Byzantium could survive only in alliance with the West, not just politically, but also by sharing in the cultural life of Renaissance Italy. Disheartened by opposition to the union in Constantinople, he returned to Florence at the end of 1440, by which time he had already been made a cardinal in the Roman Catholic Church. He spent some time traveling on papal diplomatic missions and served as governor of Bologna from 1450 to 1455, but otherwise from 1443 on he resided in Rome. He was nearly elected pope in 1455, but he lost out when his enemies warned of the dangers of choosing a Greek, and so the cardinals turned to the Catalan Alfonso de Borgia, who was elevated as Callisto III.
Much of Bessarion's energy was spent trying to raise military support in Europe to defend Byzantium against the Turks, but his efforts came to naught since the Ottomans captured Constantinople in 1453 and then took his native Trebizond in 1461, ending the long history of the Byzantine Empire. Thenceforth Bessarion sought to find support for a crusade against the Turks, but to no avail.
Bessarion devoted much of his time to perpetuating the heritage of Byzantine culture by adding to his collection of ancient Greek manuscripts, which he bequeathed to Venice, where they are still preserved in the Marciana Library. The group of scholars who gathered around Bessarion in Rome included George Trapezuntios, whom Bessarion commissioned to translate Ptolemy's Almagest from Greek into Latin. Then in 1459 Trapezuntios published an attack on Platonism, suggesting that it led to heresy and immorality. Bessarion was outraged and wrote a defense of Platonism, published in both Greek and Latin. His aim was not only to defend Platonism against the charges made by Trapezuntios, but to show that Plato's teachings were closer to Christian doctrine than those of Aristotle. His book was favorably received, for it was the first general introduction to Plato's thought, which at the time was unknown to most Latins; earlier scholarly works on Platonism had not reached a wide audience.
In 1460 one of Bessarion's diplomatic missions took him to Vienna, where the university had become a center of astronomical and mathematical studies through the work of John of Gmunden (d. 1442), Georg Peurbach (1423-61) and Johannes Regiomontanus (1436-76). John had built astronomical instruments and acquired a large collection of manuscripts, all of which he had bequeathed to the university, thus laying the foundations for the work of Peurbach and Regiomontanus.
Peurbach was an Austrian scholar who had received a bachelor's degree at Vienna in 1448 and a master's in 1453; in the interim he had traveled in France, Germany, Hungary, and Italy. He had served as court astrologer to Ladislaus V, king of Hungary, and then to the king's uncle, the emperor Frederick III. His writings included textbooks on arithmetic, trigonometry, and astronomy, his best-known works being his Theoricae Novae Planetarum (New Theories of the Planets) and his Tables of Eclipses
Regiomontanus, originally known as Johann Müller, took his last name from the Latin for his native Königsberg in Franconia. He studied first at the University of Leipzig, from 1447 to 1450, and then at the University of Vienna, where he received his bachelor's degree in 1452, when he was only fifteen, and his master's in 1457. He became Peurbach's associate in a research program that included a systematic study of the planets as well as observations of astronomical phenomena such as eclipses and comets.
Bessarion was dissatisfied with the translation of Ptolemy's Almagest that had been done by George Trapezuntios, and he asked Peurbach and Regiomontanus to write an abridged version. They agreed to do so, for Peurbach had already begun work on a compendium of the Almagest, but it was unfinished when he died in April 1461. Regiomontantus completed the compendium about a year later in Italy, where he had gone with Bessarion. He spent part of the next four years in the cardinal's entourage and the rest in his own travels, learning Greek and searching for manuscripts by Ptolemy and other ancient astronomers and mathematicians.
Regiomontanus left Italy in 1467 for Hungary, where he served for four years in the court of King Matthias Corvinus, continuing his researches in astronomy and mathematics. He then spent four years in Nuremberg, where he set up his own observatory and printing press. One of the works he printed before his premature death in 1476 was Peurbach's Theoricae Novae Planetarum; it would be reprinted in nearly sixty editions until the seventeenth century. He also published his own Ephemerides, the first planetary tables ever printed, giving the positions of the heavenly bodies for every day from 1475 to 1506. Columbus is said to have taken the Ephemerides with him on his fourth and last voyage to the New World, and to have used its prediction of the lunar eclipse of 29 February 15 04 to frighten the hostile natives of Jamaica into submission.
Regiomontanus's most important mathematical work is his De Trian-gulis Omnimodis, a systematic method for analyzing triangles that, together with his Tabulae Directionum, marked what a modern historian of mathematics has called “the rebirth of trigonometry.”
The astronomical writings of Regiomontanus include the completion of Peurbach's Epitome of Ptolemy's Almagest, which he dedicated to Bessarion, a book noted for its emphasis on mathematical methods omitted in other works of elementary astronomy. Copernicus read the Epitome when he was a student in Bologna, and at least two propositions in it influenced him in the formulation of his own planetary theory. These propositions seem to have originated with the fifteenth-century Arabic astronomer Ali Qushji and may have been transmitted to Regiomontanus by Bessarion. If so, this would place Bessarion and Regiomontanus in the long chain that leads from Aristarchus of Samos to Copernicus through the Arabic and Latin scholars of the Middle Ages and to the dawn of the Renaissance.