One of the early Islamic scientists, Hunayn ibn Ishaq, writes of going off to bilad-al-Rum, ‘the land of the Greeks’, where he improved his Greek in order to read scientific manuscripts that he eventually translated into Syriac and then into Arabic. The land of Rum was for him Greek-speaking Asia Minor and Constantinople, capital of the Byzantine Empire.
Around the beginning of the first millennium BC there was a great migration that took the Greeks from their homeland in south-eastern Europe across the Aegean to the western coast of Asia Minor and its offshore islands. Three Greek tribes were involved in this migration: the Aeolians to the north, as far as the Hellespont, south of them the Ionians, and farther to the south the Dorians. Together they produced the first flowering of Hellenic culture, the Aeolians giving birth to the lyric poets Sappho and Alcaeus, the Ionians to the natural philosophers Thales, Anaximander and Anaximenes, and the Dorians to Herodotus, the Father of History.
Herodotus tells us that the Ionian cities organised themselves into a confederation called the Panionic League, which comprised the islands of Samos and Chios and ten cities on the mainland of Asia Minor opposite them: Phocaea, Clazomenae, Erythrae, Teos, Lebedus, Colophon, Ephesus, Priene, Myus and Miletus. Miletus surpassed all of the other Greek cities of Asia Minor in its maritime ventures, founding colonies around the shores of the Black Sea as well as along the Hellespont and on the Nile delta. Other cities, most notably Phocaea, established colonies along the western shores of the Mediterranean, particularly in southern Italy and Sicily, which became known as Magna Graecia, or Great Greece, because of the number of Hellenic settlements there.
Miletus was the birthplace of Thales, Anaximander and Anaximenes, who flourished in turn during the first half of the sixth century BC Aristotle refers to them as physikoi, from the Greek physis, meaning ‘nature’ in its widest sense, contrasting them with the earlier theologoi, or theologians, for they were the first who tried to explain phenomena on natural rather than supernatural grounds.
The most enduring idea of the Milesian philosophers proved to be their belief that there was an arche, or fundamental substance, which was at the basis of all matter, enduring through all apparent change. Thales believed that the arche was water, which is normally liquid but when heated appears in the gaseous state as steam and when frozen is solid ice. Anaximander called the fundamental substance apeiron, or the ‘boundless’, meaning that it was not defined by having specific qualities. Anaximenes held that the arche was pneuma, meaning ‘air’ or ‘spirit’, which assumes various forms through its eternal motion.
Ionia was also the birthplace of Pythagoras, who was born on Samos in the mid-sixth century BC and moved to the Greek colony of Croton in southern Italy.
There, it is believed – though we cannot be certain – that he founded a philosophical school and mystical sect, whose beliefs included that of metempsychosis, or the transmigration of souls. Pythagoras and his followers are credited with laying the foundations of Greek mathematics, particularly geometry and the theory of numbers. The most famous of their supposed discoveries is the Pythagorean theorem, which states that in a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides. As we have noted, the Babylonians were aware of this a thousand years earlier, but as a relationship between numbers rather than a geometrical theorem.
According to tradition, their experiments with stringed instruments led the Pythagoreans to understand the numerical relations involved in musical harmony. This made them believe that the cosmos was divinely designed according to harmonious principles that could be expressed in terms of numbers. According to Aristotle, the Pythagoreans ‘supposed the elements of numbers to be the elements of all things, and the whole heavens to be a musical scale and a number’.
The Greek colonies in Magna Graecia rivalled Ionia as a centre of natural philosophy, beginning with the Pythagoreans and continuing with Parmenides and Zeno of Elea in southern Italy, as well as Empedocles of Acragas in Sicily, who flourished around the same time as the Milesian physicists.
Parmenides denied the possibility of motion and any other kind of change, which he said were mere illusions of the senses. The philosophy of Parmenides was defended by his follower Zeno, who proposed several paradoxes designed to show that examples of apparent motion are illusory. Empedocles agreed with Parmenides that there was a serious problem regarding the reliability of our sense impressions, but he said that we are utterly dependent on our senses for they are our only direct contact with nature. Thus we must carefully evaluate the evidence of our senses to gain true knowledge.
Empedocles proposed that everything in nature is composed of four fundamental substances, earth, water, air and fire. The first three of these correspond, albeit superficially, to the modern classification of matter into three states of matter, earth representing solids, water liquids, and air gases, while fire for Empedocles represented not only flames but phenomena such as lightning and comets. According to Empedocles the four substances alternately intermingled and separated under the influence of what he called Love and Strife, corresponding to the modern concept of attractive and repulsive forces.
A radically different theory of matter was proposed in the mid-fifth century BC by Democritus of Abdera, a Thracian city founded by Ionians from Teos. Democritus thought that the arche exists in the form of atoms, the irreducible minima of all physical substances, which through their endless motion and mutual collisions take on all of the many forms of matter observed in nature. Democritus seems to have learned the theory from his teacher Leucippus, whose only extant fragment states that ‘Nothing occurs at random but everything for a reason and by necessity’, by which he meant that the motion of the atoms is not chaotic but obeys the immutable laws of nature.
The history of Greek medicine begins with Hippocrates, who was born on the island of Kos ca. 460 BC The writings of Hippocrates and his followers, the so-called Hippocratic Corpus, comprises some seventy works dating from his time to ca. 300 BC. They include treatises on all branches of medicine as well as clinical records and notes of public lectures on medical topics. A treatise on Deontology, or Medical Ethics, contains the famous Hippocratic Oath, which is still taken by physicians today.
Athens became the cultural centre of the Greek world during the classical period, 479–323 BC, which began with the end of the Persian Wars and ended with the death of Alexander. The first philosopher to reside in the city was Anaxagoras (ca. 520–ca. 428 BC) of Clazomenae, who left Ionia at the age of twenty and moved to Athens, where he resided for thirty years, becoming the teacher and close friend of Pericles.
Anaxagoras believed that the cosmos had a directing intelligence that he called Nous, or Mind, as Plutarch writes of him in his Life of Pericles: ‘he was the first to enthrone in the universe not Chance, nor yet Necessity, but Mind (Nous) pure and simple, which distinguishes and sets apart, in the midst of an otherwise chaotic mass, the substances which have like elements.’
Anaxagoras believed that the cosmos was filled with an invisible element called the aether, which is in constant rotation and carries with it the celestial bodies. He says in one of his surviving fragments that ‘The sun, the moon and all the stars are red-hot stones which the rotation of the aether carries round with it.’ The nebulous concept of the aether proved to be very enduring, and it keeps reappearing in cosmological theories, as in the nineteenth century when it was thought to be the medium that transmits the electromagnetic force.
The intellectual life of classical Athens was dominated by its two famous schools, the Academy of Plato and the Lyceum of Aristotle. The Academy was founded by Plato ca. 380 BC and functioned more or less continuously until 529 AD, when it was closed by the emperor Justinian. Aristotle was a student at the Academy during the last twenty years of Plato’s life, and then in 335 BC he founded the Lyceum, which he directed until 324 BC, when he returned to his native Macedonia, a year before he died.
Plato’s attitude toward the study of nature is evident from what he has Socrates say in his dialogues. In the Phaedo, Socrates tells of how he had been attracted to the ideas of Anaxagoras because of his concept of Nous. But he was ultimately disappointed, he says, when he ‘saw that the man made no use of Mind, nor gave it responsibility for the management of things, but mentioned as causes air and aether and water and many other strange things’.
Socrates was dissatisfied with Anaxagoras and the other early natural philosophers, because they only told him how things happened rather than why. What he was searching for was a teleological explanation, for he believed that everything in the cosmos was directed toward attaining the best possible end. Plato’s most enduring influence on science was his advice to approach the study of nature as an exercise in geometry, particularly in astronomy. Through this geometrisation of nature, applicable in disciplines such as astronomy that can be suitably idealised, one can arrive at laws that are as ‘certain’ as those in geometry. As Socrates says in the Republic, ‘Let’s study astronomy by means of problems as we do in geometry, and leave the things in the sky alone.’
The problem for Greek astronomers was to explain the motion of the celestial bodies – the stars, sun, moon and the five visible planets – as seen from the earth, which was believed to be the immobile centre of the cosmos. When these bodies are observed from the earth they appear to be embedded in a globe called the celestial sphere, which seems to rotate daily about a point in the heavens called the celestial pole. This apparent motion is actually due to the rotation of the earth in the opposite direction, the projection of its axis of rotation among the stars forming the celestial pole. The axial rotation of the earth makes it appear as if the sun rises in the east each day and sets in the west. At the same time the orbital motion of the earth around the sun makes it appear as if the sun moves back from west to east among the stars a little less than one degree per day, completing a circuit of the twelve signs of the zodiac in one year. The path of the sun among the stars is called the ecliptic, because solar and lunar eclipses occur when the orbit of the moon crosses the plane of the ecliptic. The ecliptic makes an angle of about 23.5 degrees with the equator of the celestial sphere, due to the fact that the spin axis of the earth is tilted by that amount with respect to the plane defined by its move around the sun. The points where the ecliptic crosses the celestial equator are the spring and fall equinoxes, and the points where it is farthest north and south are the summer and winter solstices, respectively. The five visible planets are also seen to move close to the ecliptic, periodically exhibiting retrograde motion that makes them seem to trace out loops in their motion around the celestial sphere. This happens whenever the planets and the earth pass one another in their orbits around the sun, all of them rotating in the same sense, the inner planets moving more rapidly than the earth and the outer ones more slowly, the effect in both cases making it appear as if the planet is moving backwards for a time among the stars.
Plato believed that all of the celestial bodies were moving with uniform circular motion around the earth, and so, according to Simplicius, a commentator of the sixth century AD, he proposed that astronomers direct their researches to find ‘on what hypotheses the phenomena concerning the planets could be accounted for by uniform and ordered circular motions.’
The astronomer Eudoxus of Cnidus, a younger contemporary of Plato at the Academy, sought to solve the problem by assuming that the path of every celestial body was the resultant motion of four interconnected spheres, all of them centred on the earth, but with their axes inclined to one another and rotating at different speeds. This system may subsequently have been adopted by Aristotle as the physical model for his cosmos, using a total of fifty-six spheres for the celestial bodies, the outermost one containing the fixed stars.
Aristotle’s writings are encyclopaedic in scope, covering the entire spectrum of philosophy and science. The dominant concept in his philosophy of nature is the principle of teleology, the idea that natural processes are directed toward an end, which he states most clearly in the second book of his Physics:
Now intelligent action is for the sake of an end; therefore the nature of things also is so: and as in nature. Thus if a house, e.g., had been a thing made by nature, it would have been made in the same way as it is now by art; and if things made by nature were made also by art, they would come to be in the same way as by nature.
Aristotle’s cosmology and his theories of matter and motion distinguish between the ‘Two Orders of Things’, the imperfect and transitory terrestrial world below the sphere of the moon and the perfect and unchanging celestial region above. He adopted the four elements of Empedocles as the basic terrestrial substances, with concentric spheres of earth, water, air and fire, the latter extending out to the sphere of the moon, while he took the aether of Anaxagoras as the arche of the celestial bodies. The natural movement of earth, water, air and fire was up or down to their natural place among the terrestrial spheres, while the celestial bodies were carried in uniform circular motion around the stationary earth by their aetherial spheres.
Heraclides Ponticus, a contemporary of Aristotle who had also studied at the Academy under Plato, was the first to suggest that the apparent nightly rotation of the stars is actually due to the rotation of the earth on its axis, though the idea never gained general acceptance in the Greek world.
Aristotle was succeeded as head of the Lyceum by his associate Theophrastus (ca. 371–ca. 287 BC) of Erisos on Lesbos. Theophrastus was as prolific as Aristotle, and Diogenes Laertius ascribes 227 books to him, most of which are now lost. Two of his extant works, the History of Plants and the Causes of Plants, have earned him the title Father of Botany, while his book On Stones represents the beginning of geology and mineralogy.
Theophrastus was succeeded in turn as head of the Lyceum by Straton of Lampsacus on the Hellespont (died ca. 268 BC), who had been his student. Straton is credited with forty works, all of which are lost except for fragments.
Diogenes Laertius describes Straton as ‘a distinguished man who is generally known as “the physicist”, because more than anyone else he devoted himself to the study of nature’. One of Straton’s writings on physics is a lost work On Motion, which Simplicius mentions in a commentary on Aristotle. Straton appears to have been the first to demonstrate that falling bodies accelerate, i.e., their velocity increases in time, as Simplicius explains in his commentary: ‘For if one observes water pouring down from a roof and falling from a considerable height, the flow at the top is seen to be continuous, but the water at the bottom falls to the ground in discontinuous parts. This would never happen unless the water traversed each successive space more swiftly.’
Early in the Hellenistic period, the new city of Alexandria in Egypt supplanted Athens as the intellectual centre of the Greek world. The intellectual life of Alexandria was focused on two renowned institutions, the Museum and the Library, founded by Ptolemy I Soter (r. 305–283 BC) and developed by his son Ptolemy II Philadelphus (r. 283–45 BC).
The Museum, dedicated to the Muses, the nine daughters of Zeus and Mnemosyne who were the patron goddesses of the humanities, was patterned on the famous schools of Athens, most notably the Academy and the Lyceum. It was more like a research institute than a college, emphasising science rather than the humanities. The scientific character of the Museum was probably due to Straton of Lampsacus, the Physicist, who in the years 300–288 BC served as tutor to the future Ptolemy II, before returning to Athens to succeed Theophrastus as head of the Lyceum.
The organisation of the Library was probably due to Dimitrios of Phaleron, the former governor of Athens, who fled to Alexandria in 307 BC Dimitrios, a former student at the Lyceum in Athens, is believed to have been the first chief librarian of the library, a post he held until 284 BC According to Aristeas Judeus, Dimitrios ‘had at his disposal a large budget in order to collect, if possible, all the books in the world, and by purchases and transcriptions he, to the best of his ability, carried the king’s objective into execution’. By the time of Ptolemy III Eurgetes (r. 247–21 BC) the Library was reputed to have a collection of half a million parchment rolls, including all the great Greek works in humanities and science from Homer onwards.
The only scientist to serve as chief librarian of the Library was Eratosthenes of Cyrene (ca. 275–ca. 195 BC), a mathematician, astronomer and geographer, who also wrote on literature and history. Eratosthenes was the first to draw a map of the known world based on a system of meridians of longitude and parallels of latitude. He is renowned for his accurate measurement of the earth’s circumference, which he determined by observing that the sun’s noon shadow at the summer solstice in Alexandria made an angle equal to one-fiftieth of a circle, while on the same day the sun was directly overhead at noon in the city of Syene to the south. He concluded that the distance between Alexandria and Syene was one-fiftieth of the earth’s circumference, which he computed by estimating the distance between the two cities and multiplying by fifty, obtaining a result roughly equal to the modern value. Eratosthenes also found that the meridian solar altitude at the summer and winter solstices differed by 11/83 of a circle, which he divided by two to obtain a value of about 23 degrees 51 minutes and 19.5 seconds for the obliquity of the ecliptic.
The great school of mathematics at Alexandria was apparently founded by Euclid, who is believed to have taught at the Museum early in the third century BC, though there are no sources to conclusively prove this. Euclid is renowned for his Elements of Geometry, the earliest extant treatise on the subject, translated in turn into Arabic, Latin, and numerous other languages. Euclid’s extant writings also include a textbook on astronomy, the Phenomena, and a treatise on perspective, the Optica. One of the assumptions made by Euclid in the Optica is that vision involves light rays proceeding in straight lines from the eye to the object. This erroneous idea, known as the extramission theory, was held by many – though not all – subsequent writers on optics up until the seventeenth century.
Greek mathematical physics reached its peak with the works of Archimedes (ca. 287–12 BC), who was born at Syracuse in Sicily. He corresponded with Eratosthenes, to whom he addressed his famous work On Method, lost in antiquity and dramatically rediscovered in 1906. His treatise On Floating Bodies is based on the famous Archimedes’ Principle, which states that a body wholly or partly immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. His book On the Equilibrium of Planes uses the law of the lever to find the centre of gravity of various figures, i.e., the point at which all of their weight is effectively concentrated, a concept that became the basis for all subsequent work in statics, the study of mechanical systems in equilibrium. His treatise On The Measurement of the Circle uses a technique of successive approximations known as the ‘method of exhaustion’ to measure the area of a circle. In his treatise On the Sphere and the Cylinder he found that ratio of the areas of a cylinder and circumscribed sphere was 3/2, and he was so proud of this discovery that he had the figure inscribed on his tomb.
Archimedes was renowned for his inventions, which included catapults, burning mirrors, a system of compound pulleys for moving large ships on land, and a device for raising water known as Archimedes’ Screw, which is still used in Egypt. He also constructed an orrery, or working model of the celestial motions, which was seen by Cicero. According to Pappus of Alexandria, Archimedes wrote a thesis, now lost, describing a celestial globe that he made to represent the motions of the sun and moon and demonstrate solar and lunar eclipses.
In a work called The Sand Reckoner Archimedes describes a method for expressing extremely large numbers, which could not be done with the system then used by the Greeks, where numbers were written using letters of the alphabet. As an example, Archimedes computes the number of grains of sand in ‘a volume equal to that of the cosmos’, which he takes to be a sphere whose radius is the distance between the centres of the earth and sun. He then makes reference to a new astronomical theory that had been proposed by Aristarchus of Samos, a slightly younger contemporary: ‘Aristarchus of Samos has, however, enunciated certain hypotheses in which it results from the premises that the universe is much bigger than that just mentioned. As a matter of fact he supposes that the fixed stars and the sun do not move, but the earth revolves in the circumference of a circle about the sun, which lies in the middle of the orbit.’
This is the first mention of a heliocentric theory, eighteen centuries before Copernicus. Cleanthes of Assos, a contemporary of Archimedes, wrote a tract condemning the theory, remarking that Aristarchus should be charged with impiety, on the grounds ‘that he was disturbing the hearth of the universe’. Some contemporary classicists consider this passage to be a later addition by a philologist of the seventeenth century, still others believe it to be genuine. The only ancient astronomer known to have accepted the heliocentric theory of Aristarchus was Seleucus the Babylonian, who flourished in the second century BC, but otherwise it was ignored and forgotten until it was revived by Copernicus in the sixteenth century.
The only work of Aristarchus that has survived is his treatise On the Sizes and Distances of the Sun and Moon. Here he used geometrical demonstrations together with three astronomical observations to calculate the solar and lunar distances and their sizes relative to the earth. All of his values are greatly underestimated, because of the crudeness of his observations, but he did demonstrate that the sun is much larger than the earth, which may have been the main reason he put it at the centre of the cosmos rather than the earth.
The only other Hellenistic mathematician comparable to Euclid and Archimedes is Apollonius of Perge, born ca. 262 BC, who studied in Alexandria and was an honoured guest in the court of King Attalus I (r. 241–197 BC) of Pergamum in north-western Asia Minor. The only major work of Apollonius that has survived is his treatise On Conics, though even there the last book is lost. This is a comprehensive analysis of the four types of conic sections: the circle, the ellipse, the parabola and the hyperbola. On Conics was translated in turn into both Arabic and Latin, the latter used by Johannes Kepler in his second law of planetary motion and by Isaac Newton in his analysis of the motion of both planets and terrestrial projectiles.
Apollonius is also credited with formulating two mathematical theories to explain the apparent retrograde motion of the planets. One of these is the epicycle theory, in which the planetary motion is the resultant of two circular motions, one centred on the earth, and the second on the circumference of the first circle, the so-called deferent. The second theory has the planet moving on the circumference of an eccentric circle, i.e., one that is not centred on the earth. He also showed that these two theories were equivalent to one another, so that either one could be used in describing retrograde planetary motion.
Ctesibus of Alexandria, a contemporary of Archimedes, was famous as an inventor of machines, mechanical gadgets and pneumatic devices. Among other things, he is credited with inventing a force pump, a catapult, a fire-engine, an hydraulic organ, a water-clock, and a singing statue, which he made for the empress Arsinoe, sister and wife of Ptolemy II. All of his writings are now lost, but his ideas and inventions were revived by his two most notable followers, Philo of Byzantium and Hero of Alexandria.
The extant writings of Philo, who flourished in the mid-third century BC, comprise three books from a large work on mechanics: On Catapults, On Pneumatics, and On Besieging and Defending Towns. In the first of these books Philo states that he travelled to Alexandria and saw a bronze spring catapult made by Ctesibus. This second book described a number of demonstrations almost certainly taken from Ctesibus, including pneumatic toys. The third book, the earliest work on military engineering, describes the use of and defence against various engines of war, as well as the use of secret messages, cryptography and poisons.
Hero of Alexandria flourished ca. 62 AD. His longest extant work by far is the Pneumatica, the first chapters of which describe experiments demonstrating that air is a body, evident through the pressure that it exerts, and showing that it is possible to produce a vacuum, contrary to Aristotelian doctrine. The book also describes his famous steam-engine, in which a glass bulb is made to rotate by jets of steam directed tangentially in opposite directions from the two ends of a diameter.
Hero describes other inventions in his treatise On Automata-Making, most notably the thaumata, or ‘miracle-working’ devices such as one that opened and closed the doors of a temple using steam generated by fire in an altar. Hero also made important contributions in optics as well as applied mathematics.
Hipparchus of Nicaea, the greatest astronomer of antiquity, flourished in the third quarter of the second century BC What little is known of his life comes from the geographer Strabo, who says that Hipparchus worked in the Library at Alexandria, and from the astronomer Claudius Ptolemaeus, who refers frequently to his theories and observations and often quotes him directly.
All of the writings of Hipparchus have been lost except for his first work, a commentary on the Phainomena of Aratus of Soli, a poem describing the constellations. The commentary contains a catalogue of some 850 stars, for each of which Hipparchus gives the celestial coordinates and relative brightness, including those of a ‘nova’ or ‘new star’, which suddenly appeared in 134 BC within the constellation Scorpio.
Hipparchus is renowned for his discovery of the precession of the equinoxes, i.e., the slow movement of the celestial pole in a circle about the perpendicular to the ecliptic. He discovered this effect by comparing his star catalogue with observations made 128 years earlier by the astronomer Timocharis, which enabled him to compute that the annual precession was 45.2 seconds of arc. The currently accepted value is about 50 seconds of arc per year, which gives a precessional period of about 25,800 years. The effect of this precession is to make the tropical year about 20 minutes shorter than the sidereal year.
Hipparchus is also celebrated as a geographer and mathematician, his greatest achievement in the latter field being the development of spherical trigonometry and its application to astronomy, which was continued by Claudius Ptolemaeus.
Theodosius of Bithynia, a younger contemporary of Hipparchus, is known for his Sphaerica, a treatise on the application of spherical geometry to astronomy, which was translated into Arabic and Latin and remained in use until the seventeenth century.
Strabo (63 BC–ca. 25 AD) was born in Amasia on the Black Sea coast of Asia Minor and studied in both Alexandria and Rome. His major work is his seventeen-volume Geography, which covers the whole of the known world, describing, as he says in his introduction, ‘things on land and sea, animals, plants, fruits and everything else to be seen in various regions’.
The beginning of pharmacology comes with the work of Dioscorides Pedanius, from Anazarbus in south-eastern Asia Minor, who served as a physician in the Roman army during the reigns of Claudius (r. 41–54) and Nero (r. 54–68). His De Materia Medica contains a description of some 600 medicinal plants and nearly 1,000 drugs. This was subsequently translated from Greek into Arabic and Latin, becoming the basis for all subsequent work in pharmacology both in Islam and Christian Europe.
Nicomachus of Gerasa (fl. 100 AD) is noted for his Introduction to Arithmetic, an elementary handbook on the parts of mathematics that were needed for an understanding of Pythagorean and Platonic philosophy. His work was translated into both Arabic and Latin in turn, and was influential in both the Islamic world and the West. Menelaus of Alexandria, a contemporary of Nicomachus, wrote on mathematics and made astronomical observations at Rome; his Spherics, which applies spherical trigonometry to astronomy, survives only in Arabic.
Ancient Greek astronomy culminated with the work of Claudius Ptolemaeus, known more simply as Ptolemy. All that is known of his life is that he worked in Alexandria during the successive reigns of Hadrian (r. 117–38) and Antoninus Pius (r. 138–61), presumably at the Museum and Library. The most famous of his writings is his Mathematiki Syntaxis, better known by its Arabic name, the Almagest, a detailed description of the motion of the celestial bodies, based largely on the observations of Hipparchus and using the epicycles and eccentric circles formalised by Ptolemy. The principal modification made by Ptolemy is that the centre of each epicycle moves uniformly (though this is not true for all planets), with respect to a point called the equant, which is displaced from the centre of the deferent, the inner circle, a concept that was to be the subject of controversy in later times. Ptolemy’s mapping of the celestial sphere led him to develop spherical trigonometry and the technique of stereographic projection, the basis of the instrument later known as the astrolabe, which Arabic astronomers were to use with great effectiveness.
The extant writings of Ptolemy also include other treatises on astronomy: the Handy Tables, Planetary Hypothese, Phases of the Fixed Stars, Analemma, and Planisphaerium; a work on astrology called the Tetrabiblos, and treatises entitled Optica, Geographia, and Harmonia, the latter devoted to musical theory.
Ptolemy’s researches on light are presented in the Optica, which is only preserved in a Latin translation of an Arabic translation. His most important accomplishment in this work is the demonstration of an empirical relation for the law of refraction, the bending of a ray of light when it passes from one medium to another, the correct theory for which was not given until the seventeenth century. Neugebauer remarks that ‘we see here the progress from a strictly geometrical optics to a theory of binocular vision and physiological optics based on empirical data and systematic experimentation.’
Ptolemy’s Geographia is the most comprehensive work in theoretical geography that has survived from antiquity, with maps of the known world on a grid of longitudes and latitudes. The Geographia was translated into Arabic and then into Latin and served as the basis for all subsequent works on mathematical geography up until the European renaissance.
Galen of Pergamum (130–ca. 204), the greatest physician of antiquity, was a younger contemporary of Ptolemy. He served his medical apprenticeship at the healing shrine of Asclepius at Pergamum, where his work treating wounded gladiators gave him first-hand knowledge of human anatomy, physiology and neurology. After further studies in Smyrna, Corinth and Alexandria he moved to Rome, where he spent most of the rest of his life, serving as physician to the emperors Marcus Aurelius (r. 161–80), Lucius Verus (r. 161–69) and Commodus (r. 180–92).
Galen’s writings, translated successively into Arabic and Latin, formed the basis of medical literature in both Islam and Christian Europe up until the seventeenth century. His medical writings are deeply philosophical, including interpretations of Plato, Aristotle, Epicurus and others. This is also evident from the title of one of his treatises, That the best doctor is also a philosopher, as well as those of his treatises On Scientific Proof and Introduction to Logic. He wrote on psychology as well, including the interpretation of dreams, predating Freud by seventeen centuries.
Diophantus of Alexandria (fl. ca. 250 AD) did for algebra and number theory what Euclid had done for geometry and Apollonius for conics. His most important work is the Arithmetica, of which six of the original thirteen books have survived. The surviving books of the Arithmetica were translated from Greek to Latin in 1621, and six years later they inspired the French mathematician Pierre de Fermat to create the modern theory of numbers.
Pappus of Alexandria, who flourished in the first half of the fourth century AD, wrote works in mathematics, astronomy, music and geography. His treatise entitled Synagogue (Collection), is the principal source of knowledge of the accomplishments of many of his predecessors in the Hellenistic era, most notably Euclid, Archimedes, Apollonius and Ptolemy. His own work in mathematics, translated in turn into Arabic and Latin, influenced both Descartes and Newton, and one of his discoveries, known as the Theorem of Pappus, is still taught in elementary calculus courses.
The last scientist known to have worked in the Museum and Library was Theon of Alexandria, who in the second half of the fourth century wrote commentaries on Euclid’s Elements and Optica as well as on Ptolemy’s Almagest and Handy Tables. In the latter work Theon notes that ‘certain ancient astrologers’ believed that the points of the spring and autumn equinox oscillate back and forth along the ecliptic, moving through an angle of eight degrees over a period of 640 years. This erroneous notion was revived in the so-called ‘trepidation theory’ of Islamic astronomers, and it survived in various forms up to the sixteenth century, when it was discussed by Copernicus.
Theon’s daughter Hypatia was a professor of philosophy and mathematics, and around 400 she became head of the Platonic Academy in Alexandria, the only woman academic in the history of ancient science. She revised the third book of Theon’s commentary on Ptolemy’s Almagest, and she also wrote commentaries on the works of Apollonius and Diophantus, now lost. Her lectures on pagan philosophy aroused the anger of Saint Cyril, bishop of Alexandria, who in 415 instigated a riot by fanatical Christians in which Hypatia was killed.
The Library of Alexandria survived almost to the end of the fourth century, by which time the museum seems to have vanished. The emperor Theodosius I issued a decree in 391 calling for the destruction of all pagan temples throughout the empire. Theophilus, bishop of Alexandria, took this opportunity to lead his fanatical followers in destroying the temple of Serapis, which had housed the Library since the reign of Ptolemy III. The ancient world was coming to an end, though its philosophy and science would eventually be transmitted through the land of the Greeks to the newly emergent world of Islam.