By the end of the twelfth century many of the important extant works of Greek science had been translated from Arabic to Latin, along with commentaries and original works of many Islamic, as well as Christian, Jewish and Sabian scholars and scientists. The assimilation of Graeco-Arabic science and philosophy at the first European universities sparked a cultural renaissance that began in the twelfth century and lasted until the middle of the following century. This led to the flowering of what we recognise as modern European science, beginning with the studies of Robert Grosseteste (ca. 1168–1253) and his followers at the universities of Oxford and Paris.
Grosseteste, who had been educated at Oxford and later became chancellor of the university, was the leading figure in the rise of the new European philosophy of nature, which although primarily based upon Aristotelianism, differed from some of Aristotle’s doctrines right from the beginning. Although Aristotle’s works formed the basis for most non-medical studies at the new European universities, some of his ideas in natural philosophy and the eternity of the cosmos, particularly as interpreted in commentaries by Averroës (Ibn Rushd), were strongly opposed by Catholic theologians.
Grosseteste believed that the study of optics was the key to an understanding of nature, and this gave rise to his Neoplatonic ‘metaphysics of light’. He believed that light is the fundamental corporeal substance of material things and produces their spatial dimensions, as well as being the first principle of motion and efficient causation. According to his optical theory, light travels in a straight line through the propagation of a series of waves or pulses, and because of its rectilinear motion it can be described geometrically. Grosseteste called this theory the ‘multiplication of species’. Grosseteste does not seem to have been aware of Alhazen’s theory, in which every point in a luminous object emits radiation that propagates rectilinearly. He believed that the ‘multiplication of species’ could be used to explain the propagation of any disturbance, be it light, sound, heat, mechanical action or even astrological influence. Thus he thought that the study of light was of crucial importance for an understanding of nature. He also believed that light, by which he meant not only visible radiation but the divine emanation as well, was the means by which God created the universe, and that through it soul and body interacted in man.
One of Grosseteste’s most interesting optical works is his treatise on The Rainbow, in which he broke with Aristotelian theory by holding that the phenomenon was due to refracted rather than reflected light. Although his theory was incorrect, he posed the problem in such a way that investigations by those who followed after him approached closer to the true solution through criticising his efforts. His work on the rainbow inspired some verses written about 1270 by the French poet Jean de Meun in his continuation of Guillaume de Lorris’ Romance of the Rose. These are in Chapter 83, where Nature explains the influence of the heavens, in which the poet mentions the Optics of Alhazen:
...An optics book
Was written by Alhazen, of the line
Of Huchain, which none but fools neglect.
He who would well this rainbow understand
Should study this, and he should be, besides
A good observer and a careful judge
And learned in nature and geometry...
Grosseteste’s efforts in framing a new philosophy of nature were continued by Albertus Magnus (ca. 1200–80). Albertus played a crucial role in reviving Aristotle and making his philosophy of nature acceptable to the Christian West. The main problem involved in the Christian acceptance of Aristotle was the conflict between faith and reason, particularly in the Averroist interpretation of Aristotelianism with its determinism and purely Aristotelian in its notion of the eternity of the cosmos. Albertus sought to resolve this conflict by regarding Aristotle as a guide to reason rather than an absolute authority, saying that where Aristotle conflicted with either revealed religion or observation then he must be wrong. Albertus held that natural philosophy and theology often spoke of the same thing in different ways, and so he assigned to each of them its own realm and methodology, assured that there could be no contradiction between reason and revelation.
The most brilliant of Albertus’ students was Thomas Aquinas (ca. 1225–74), who came from Italy to study with him, either in Paris or Cologne. Aquinas, like Albertus, tried to resolve the conflict between theology and philosophy, holding that there could be no real contradiction between revelation and reason. Arguing against those who said that natural philosophy was contrary to the Christian faith, he writes in his treatise on Faith, Reason and Theology that ‘even though the natural light of the human mind is inadequate to make known what is revealed by faith, nevertheless what is divinely taught to us by faith cannot be contrary to what we are endowed with by nature. One or the other would have to be false, and since we have both of them from God, he would be the cause of our error, which is impossible.’
One of the works of Averroës, his commentary on the Physica of Aristotle, attacked the theory of Avempace (Ibn Bajja) that motion in a vacuum would be at finite speed, rather than infinitely fast, as Aristotle had maintained. Aquinas argued against Aristotle and Averroës in supporting Avempace’s theory, without mentioning his name. He presented Avempace’s theory that motion through a vacuum would be finite, the moving body passing from one point of the void to the next in finite intervals of time. Thenceforth the idea of motion in a void gained acceptance among European thinkers.
Aquinas persuaded the Dominican monk William of Moerbeke (ca. 1220–before 1286) to 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 translations included some of the writings of Aristotle, commentaries on Aristotle, and works of 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 onwards, and 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. His translations of Archimedes were particularly influential in the development of European mathematical physics in the early renaissance.
Meanwhile, translations were still being made from Arabic into Latin in the thirteenth century. Some of these were done under the patronage of King Alfonso X (1221–84) of Castile and Leon, known in Spanish as el Sabio, or the Wise. Alfonso’s active interest in astrology led him to sponsor translations of Arabic works in astronomy and astrology, including a new edition of the Toledan Tables of the eleventh-century Cordoban astronomer al-Zarqallu. This edition, known as the Alfonsine Tables, included some new observations but retained the Ptolemaic system of eccentrics and epicycles.
One of Grosseteste’s most renowned disciples was Roger Bacon (ca. 1219–92), who acquired his interest in natural philosophy and mathematics while studying at Oxford. He received an MA either at Oxford or Paris, around 1240, after which he lectured at the University of Paris on various works of Aristotle. He returned to Oxford around 1247, when he met Grosseteste and became a member of his circle.
Bacon appropriated much of Grosseteste’s ‘metaphysics of light’ with its ‘multiplication of species’, as well as his mentor’s emphasis on mathematics, particularly geometry. In his Opus maius Bacon states that ‘in the things of the world, as regards their efficient and generating causes, nothing can be known without the power of geometry’, and he also says that ‘Every multiplication is either according to lines, or angles or figures’. His ideas on optics also repeat those of Grosseteste. Unlike Grosseteste, he was not only aware of Alhazen’s work but wrote a commentary on his Optics, which influenced his own ideas.
Bacon, in his commentary on ibn al-Haytham – particularly al-Haytham’s theory of the eye as a spherical lense – went beyond what Grosseteste had done basing his own anatomical descriptions on those of Hunayn ibn Ishaq and Avicenna. Bacon used his scientific method to study the rainbow, where he improved on Grosseteste’s theory in his understanding that the phenomena was due to the action of individual raindrops, though he erred in rejecting refraction as part of the process.
Other works by Bacon include the Epistola de secretis operibus artis et naturae et de nullitate magiae, which describes wonderful machines such as self-powered ships, submarines, automobiles and aeroplanes, though it has to be said that many historians believe this to be fantasy. He writes that ‘cars can be made so that without animals they will move with unbelievable rapidity...Also flying machines can be constructed so that a man sits in the midst of the machine revolving some engine by which artificial wings are made to flap like a flying bird...’
Levi ben Gerson (1288–1344) was a Jewish polymath who wrote books on astronomy, physics, mathematics and philosophy, as well as commentaries on the Bible and the Talmud. His greatest work is his Milhamot Adonai (The Wars of the Lord), a philosophical treatise in six books, the fifth of which is devoted to astronomy. Here Levi presents his model of the universe, based on several Arabic sources, principally al-Battani, Jabir ibn Aflah and Ibn Rushd. His model differed in important respects from that of Ptolemy, whose theories did not always agree with observations made by Levi. This was particularly so in the case of Mars, where Ptolemy’s theory had the apparent size of the planet varying by a factor of six, while Levi’s observation found that it only doubled. The instruments used by Levi included one of his own invention, the ‘Jacob’s Staff’, a device to measure angles in astronomical observations. He also employed the camera obscura, an invention of Alhazen, which he used in observing eclipses and in determining the eccentricity of the sun’s orbit. Levi’s astronomical work was influential in Europe for five centuries, and his Jacob’s Staff was used for maritime navigation until the mid-eighteenth century.
Another area in which the new European science developed was optics, the study of light, which had begun at Oxford with the work of Robert Grosseteste and Roger Bacon. The first significant advance beyond what they had done was by the Polish scholar Witelo (b. ca. 1230–35–d. after ca. 1275). Witelo’s best known work is the Perspectiva, which is based on the works of Robert Grosseteste and Roger Bacon as well as those of Alhazen, Ptolemy and Hero of Alexandria. It would seem that the Perspectiva was not written before 1270, since it makes use of Hero’s Catoptrica, the translation of which was completed by William of Moerbeke on 31 December 1269.
Witelo adopted the ‘metaphysics of light’ directly from Grosseteste and Bacon, and in the preface to the Perspectiva he says that visible light is simply an example of the propagation of the power that is the basis of all natural causes. But he disagrees with Grosseteste and Bacon where they say that light rays travel from the observer’s eye to the visible object, and instead follows al-Haytham in holding that the rays emanate from the object to interact with the eye.
The Perspectiva describes experiments performed by Witelo in his study of refraction. Here his method is similar to that of Ptolemy, where he measures the angle of refraction for light in passing from air into glass and also into water, for angles of incidence ranging from ten to eighty degrees. He tried to explain the results by a number of mathematical generalisations, attempting to relate the differences in refraction to the difference in the densities of the two media. He also produced the colours of the spectrum by passing light through an hexagonal crystal, observing that the blue rays were refracted more than the red.
Witelo also studied refraction in lenses, where he made use of the concept later known as the principle of minimum path. He justified this by the metaphysical notion of economy, saying that ‘It would be futile for anything to take place by longer lines, when it could better and more certainly take place by shorter lines.’
Witelo followed Grossteste in holding that the ‘multiplication of species’ could be used to explain the propagation of any effect, including the divine emanation and astrological influences. In the preface to the Perspectiva, which he addresses to William of Moerbeke, he writes ‘of corporeal influences sensible light is the medium’, adding that ‘there is something wonderful in the way in which the influence of divine power flows in to things of the lower world passing through the powers of the higher world.’
The next advances in optics were made by Dietrich of Freiburg (ca. 1250–ca. 1311). Dietrich’s principal work is his treatise On the Rainbow and Radiant Impressions, the latter term meaning phenomena produced in the upper atmosphere by radiation from the sun or any other celestial body. He was one of the first to realise that the rainbow is due to the individual drops of rain rather than the cloud as a whole. This led him to make observations with a glass bowl filled with water, which he used as a model raindrop, for he writes ‘that a globe of water can be thought of, not as a diminutive spherical cloud, but as a magnified raindrop’. His observations and geometrical analysis led him to conclude that light is refracted when it enters and leaves each raindrop, and that it is internally reflected once in creating the primary bow and twice for the secondary arc, the second reflection reversing the order of the colours in the spectrum. Although he made a number of errors in his analysis, his theory was far superior to those of any of his predecessors, and it paved the way for researches by his successors.
Dietrich’s theory of the rainbow is very similar to that of his Persian contemporary, Kamal al-Din al-Farisi. In any event, it seems that the emerging European science had by the beginning of the fourteenth century reached a level comparable to that of Arabic scientific research, at least in optics. But whereas the work of al-Farisi was the last great achievement of Arabic optics, Dietrich’s researches would be an important stage in the further development of European studies in the science of light, culminating in the first correct theories of the rainbow and other optical phenomena in the seventeenth century.
The march of Ottoman conquest leading to the fall of Constantinople in 1453 forced a number of Greek scholars to flee from the Byzantine capital to Italy. Basilios Bessarion (ca. 1403–72), a Greek from Trebizond who became a cardinal in the Roman Catholic Church and was nearly elected pope in 1455, had left Constantinople in 1438 and become a cardinal in the Roman Catholic Church, nearly becoming Pope in 1453. 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 nought, as 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 he commissioned to translate Ptolemy’s Almagest from Greek into Latin.
One of Bessarion’s diplomatic missions took him in 1460 to Vienna, whose university had become a centre 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, while in the interim he had travelled 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 Muller, took his last name from the Latin for his native Königsberg in Franconia. He studied first at the University of Leipzig from 1447–50, 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 programme 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. Regiomontanus 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 of 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 Mathias 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 that he printed before his premature death in 1476 was Peurbach’s Theoricae novae planetarum, reprinted in nearly sixty editions up to 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 1504 to frighten the hostile natives of Jamaica into submission.
Regiomontanus’ most important mathematical work is his De triangulis omnimodis, a systematic method for analysing triangles, which, 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 work 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 al-Qushji, and may have been transmitted to Regiomontanus by Bessarion. If so, this would place Bessarion, Regiomontanus and Ali al-Qushji in the long chain that leads, albeit in a convoluted and punctuated way, from Aristarchus of Samos to Copernicus through the Arabic and Latin scholars of the Middle Ages to the dawn of the Renaissance.