The scientific mood was hardly more popular with the pundits than with the people. The spirit of the age inclined to the “humanities”; even the revival of Greek studies ignored Greek science. In mathematics the Roman numerals obstructed progress; they seemed inseparable from Latin culture; the Hindu-Arabic numerals seemed heretically Mohammedan, and were coldly received, especially north of the Alps; the Cour des Comptes—the French Bureau of Audit—used the clumsy Roman figures till the eighteenth century. Nevertheless Thomas Bradwardine, who died of the plague (a 349) a month after being consecrated archbishop of Canterbury, introduced into England several Arabic theorems in trigonometry. His pupil, Richard Wallingford, Abbot of St. Albans, was the leading mathematician of the fourteenth century; his Quadripartitum de sinibus demonstratis was the first major work on trigonometry in Western Europe. He died of leprosy at forty-three, mourning the time he had taken from theology for science.

Nicole Oresme led an active ecclesiastical career, and yet invaded a dozen sciences successfully. He paved the way for analytical geometry by developing the systematic use of co-ordinates, and by employing graphs to show the growth of a function. He played with the idea of a fourth dimension, but rejected it. Like several of his contemporaries he adumbrated Galileo’s law that the speed of a falling body increases regularly with the duration of its fall.30 In a commentary on Aristotle’s De caelo et mundo he wrote: “We cannot prove by any experiment that the heavens undergo a daily movement and the earth does not”; there are “good reasons indicating that the earth, and not the sky, undergoes a daily motion.”31 Oresme fell back upon the Ptolemaic system, but he had helped to prepare for Copernicus.

When we consider that no telescope or camera existed as yet to watch or record the sky, it is encouraging to note the energy and intelligence of medieval astronomers, Moslem, Jewish, and Christian. Jean de Liniers, after years of personal observations, described the positions of forty-eight stars with an accuracy then rivaled only by Moslems; and he calculated the obliquity of the ecliptic to within seven seconds of the most modern estimate. Jean de Meurs and Firmin de Beauval (1344) proposed to reform the Julian calendar—which was outstripping the sun—by omitting the quadrennial February 29 for the next forty years (which would have erred by excess); the reform had to wait till 1582, and still awaits international and interfaith understandings, William Merle of Oxford rescued meteorology from astrology by keeping record of the weather through 2,556 days. Unknown observers or navigators discovered in the fifteenth century the declination of the magnetic needle: the needle does not point due north, but inclines toward the astronomic meridian at a small but important angle, which, as Columbus noted, varies from place to place.

The peak figure in the mathematics and astronomy of this epoch was Johann Müller, known to history as Regiomontanus from his birth (1436) near Königsberg in Lower Franconia. At fourteen he entered the University of Vienna, where Georg von Purbach was introducing humanism and the latest Italian advances in mathematics and astronomy. Both men matured early and died soon: Purbach at thirty-eight, Müller at forty. Resolved to learn Greek in order to read Ptolemy’s Almagest in the original, Müller went to Italy, studied Greek with Guarino da Verona, and devoured all available texts, Greek or Latin, on astronomy and mathematics. Returning to Vienna, he taught these sciences there, and with such success that he was called to Buda by Matthias Corvinus, and then to Nuremberg, where a rich burgher built for him the first European observatory. Müller equipped it with instruments built or improved by himself. We feel the pure breeze of science in a letter that he wrote to a fellow mathematician in 1464: “I do not know whither my pen will run; it will use up all my paper if I don’t stop it. One problem after another occurs to me, and there are so many beautiful ones that I hesitate as to which I should submit to you.”32 In 1475 Sixtus IV summoned him to Rome to reform the calendar. There, a year later, Regiomontanus died.

The short span of his life limited his achievement. He had planned treatises on mathematics, physics, astrology, and astronomy, and had hoped to edit the classics in those sciences; only fragments of these works found form and survival. He completed Purbach’sEpitome of the Almagest. He composed an essay De triangulis—the first book devoted solely to trigonometry. He was apparently the first to suggest the use of tangents in astronomic calculations, and his tables of sines and tangents facilitated the calculations of Copernicus. He formulated astronomical tables more accurate than any drawn up before. His method of calculating latitude and longitude proved a boon to mariners. Under the title of Ephemerides he issued (1474) an almanac showing the daily position of the planets for the next thirty-two years; from this book Columbus would predict the lunar eclipse that would fill the stomachs of his starving men on February 29, 1504. The observations made of Halley’s comet by Regiomontanus laid the bases of modern cometary astronomy. But his personal and living influence was greater than that of his books. His popular lectures in science helped to raise an intellectual exhilaration in Nuremberg in Dürer’s youth; and he made the city famous for its nautical instruments and maps. One of his pupils, Martin Behaim, drew in color on vellum the oldest known terrestrial globe (1492), still preserved in the Germanisches Museum in Nuremberg.

Modern geography was created not by geographers but by sailors, merchants, missionaries, envoys, soldiers, and pilgrims. Catalonian skippers made or used excellent maps; their portolani—pilot guides to Mediterranean ports—were in the fourteenth century almost as accurate as the navigation charts of our time.33 Old trade routes to the East having fallen into Turkish hands, European importers developed new overland routes through Mongol territory. The Franciscan friar Oderic of Pordenone, after spending three years in Peking (c. 1323–26), wrote an illuminating record of his trip to China via India and Sumatra, and of his return via Tibet and Persia. Clavijo, as we shall see, gave a fascinating account of his embassy to Timur. Johann Schnittberger of Bavaria, captured by the Turks at Nicopolis (1396), wandered for thirty years in Turkey, Armenia, Georgia, Russia, and Siberia, and wrote in his Reisebuch the first West-European description of Siberia. In 1500 Juan de la Cosa, one of Columbus’ pilots, issued an extensive map of the world, showing for the first time in cartography the explorations of his master, of Vasco da Gama, and others. Geography was a moving drama in the fifteenth century.

In one particular the most influential medieval treatise on geography was the Imago mundi (1410) of Cardinal Pierre d’Ailly, which encouraged Columbus by describing the Atlantic as traversable “in a very few days if the wind be fair.” 34 It was but one of half a dozen works that this alert ecclesiastic wrote on astronomy, geography, meteorology, mathematics, logic, metaphysics, psychology, and the reform of the calendar and the Church. Reproached for giving so much time to secular studies, he replied that a theologian should keep abreast of science.35 He saw some science even in astrology; and on astrological grounds he predicted a great change in Christianity within a hundred years, and world-shaking events in 1789.36

The best scientific thought of the fourteenth century was in physics. Dietrich of Freiburg (d. 1311) gave essentially our modern explanation of the rainbow as due to two refractions, and one reflection, of the sun’s rays in drops of water. Jean Buridan did excellent work in theoretical physics; it is a pity that he is famous only for his ass, which may not have been his.* Born near Arras before 1300, Buridan studied and taught at the University of Paris. He not only argued for the daily rotation of the earth, but he eliminated from astronomy the angelic intelligences to which Aristotle and Aquinas had ascribed the guidance and motion of the heavenly bodies. Nothing more is needed to explain their movements, said Buridan, than a start originally given them by God, and the law of impetus—that a body in motion continues its motion except as hindered by some existing force; here Buridan anticipated Galileo, Descartes, and Newton. The motions of planets and stars, he added, are governed by the same mechanical laws that operate on earth.37 These propositions, now so trite, were deeply damaging to the medieval world view. They almost date the beginning of astronomical physics.

Buridan’s ideas were taken to Germany and Italy by his pupils, and influenced Leonardo, Copernicus, Bruno, and Galileo.38 Albert of Saxony carried them to the university that he founded at Vienna (1364), Marsilius von Inghen to the university that he founded at Heidelberg (1386). Albert was one of the first to reject the Aristotelian notion that a vacuum is impossible; he developed the idea of a center of gravity in every body; he anticipated Galileo’s principles of static equilibrium and the uniform acceleration of falling bodies; and he held that the erosion of mountains by water, and the gradual or volcanic elevation of the land, are compensating forces in geology39—an idea that fascinated Leonardo.

Practical mechanics made some modest advances. Complicated windmills were used to pump water, drain soil, grind grain, and do other chores. Water power was employed in smelting and sawing, in driving furnace bellows, tilt hammers, silk-spinning machines. Cannon were cast and bored. Steel was made in sizable quantities; large blast furnaces were set up in northern Europe in the fourteenth century. Well boring is mentioned in 1373; wiredrawing was practiced at Nuremberg in the fifteenth century; a pump composed of buckets on an endless chain is pictured in a manuscript of 1438.40 In a drawing by the Hussite engineer Conrad Keyser (c. 1405) occurs the earliest known representation of reciprocating motion converted into rotary motion: two arms, moving in alternation, revolve a shaft precisely as the pistons turn the crankshaft of an automobile.41

Better mechanisms for measuring time were demanded as commerce and industry grew. Monks and farmers had divided the daylight into the same number of periods in all seasons, making the periods longer in summer than in winter. City life required more uniform divisions of time, and in the thirteenth and fourteenth centuries clocks and watches were made that divided the day into equal parts throughout the year. In some places the hours were numbered from one to twenty-four, as in the military chronometry of our time; and as late as 1370 some clocks, like that of San Gotardo in Milan, struck the full number. This proved to be a noisy extravagance. By 1375 the day was regularly divided into two halves of twelve hours each.

The essential principle of the mechanical clock was a weight slowly turning a wheel, whose revolution was checked by an escapement tooth sufficiently resistant to allow the wheel to turn by only one cog in a given interval of time. Such a timepiece had been described about 1271. The first mechanical clocks were set up in church towers or belfries visible through large areas of a town. One of the earliest was installed (1326–35) in the abbey of St. Albans by Richard Wallingford; it showed not only the hours and minutes of the day but the ebb and flow of the tide, and the motions of the sun and moon. Later clocks added a medley of gadgets. The clock (1352) in Strasbourg Cathedral showed a crowing cock, the three Magi, and a human figure on which were indicated, for each part of the body, the proper time for bloodletting. The cathedral clock at Wells used a moving image of the sun to point the hour, and a small star, moving on an inner circle, to indicate the minute; a third circle gave the day of the month; and on a platform above the dial four horsemen emerged and charged as each hour struck. On a fifteenth-century clock at Jena a buffoon’s head opened its monstrous mouth to receive a golden apple from a pilgrim, only to have the apple snatched away as his mouth began to close upon it; this comedy was performed every hour of every day for hundreds of years; and the clock still exists. A similar clock at Nuremberg, set up in 1506 and rudely interrupted by the second World War, resumed its theatrical performances in 1953.

To make watches a spiral spring was substituted (c. 1450) for the hanging weight: a band of fine steel, rolled up into a small circle or drum, produced, by its gradual unwinding, the effect of the weight on the retarded wheel. By the end of the fifteenth century watches were numerous, some as large as a hand, some as small as an almond, many ovoid like the “Nuremberg eggs” made by Peter Hele (1510). The principle of weight, escapement, and wheel was applied to other purposes, so that the mechanical clock became the parent of a myriad diverse machines.

While physics thus foreshadowed the Industrial Revolution, alchemy slowly grew into chemistry. By the close of this age the alchemists had discovered and described zinc, bismuth, liver of sulfur, regulus of antimony, volatile fluorine of alkali, and many other substances. They distilled alcohol, volatilized mercury, and made sulfuric acid by the sublimation of sulfur. They prepared ether and aqua regia, and a scarlet dye superior to those now used.42 They bequeathed to chemistry the experimental method that would prove the greatest gift of medieval science to the modern mind.

Botany was still mostly confined to manuals of husbandry or to herbals describing medicinal plants. Henry of Hesse (1325–97) suggested that new species, especially among plants, might evolve naturally from old ones;43 this 500 years before Darwin. Royal or papal menageries, animal breeding, veterinary medicine, treatises on hunting or fishing or the culture of bees or silkworms, bestiaries that told animal stories to insinuate morality, and books on falconry, like the Miroir de Phoebus (1387) of Gaston III Count of Foix, half unwittingly gathered material for a science of zoology.

Anatomy and physiology had for the most part to depend upon the dis section of animals, the wounds of soldiers, and occasional cases where the law required post-mortem autopsy. Honest Christians felt reasonable objections to the dissection of human bodies which, however dead, were supposed to rise intact from the grave at the Last Judgment. All through the fourteenth century it was difficult to get cadavers for anatomical study; north of the Alps very few physicians, before 1450, had ever seen a dissected human corpse. Nevertheless, about 1360, Guy de Chauliac persuaded the authorities at Avignon (then ruled by the papal court) to turn over to medical schools, for dissection, the bodies of executed criminals.44 Dissections were performed before medical students at Venice in 1368, Montpelier in 1377, Florence in 1388, Lérida in 1391, Vienna in 1404; and in 1445 the University of Padua built the first known anatomical theater. The results for medicine were endless.

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