I’m still re-reading William Cecil Dampier’s ‘A History of Science, and its Relations with Philosophy and Religion’ (1929). So far, I’ve been doing this slowly, but I have already finished reading the chapter about science in the ancient world. When I first read the book, I found this chapter to be one of the most interesting in the book. Therefore, I will include a number of quotes from it in this post. “Whatever be its value in philosophy, in science the Democritean atomic theory is nearer to the views now held than any of the systems which preceded or replaced it, and its virtual suppression under the destructive criticisms of Plato and Aristotle must, from the scientific standpoint, be counted a misfortune. Platonism in its various forms was left to represent Greek thought to later ages, a fact which was one of the reasons why the scientific spirit vanished from the earth for a thousand years. Plato was a great philosopher, but in the history of experimental science he must be counted a disaster. Between the times of Plato and Aristotle, about 367 B.C., Eudoxus of Cnidos did good work in astronomy, though his cosmogony was a relapse from the ideas of the Pythagoreans with their moving Earth. Eudoxus held that the Earth was the centre of all things, and that the Sun, Moon and planets revolve round it in concentric crystal spheres. This was the first serious attempt to explain the apparently irregular movement of those bodies. The system of Eudoxus led to the more elaborate schemes of Hipparchus and Ptolemy, whose cycles and epicycles satisfied astronomers till the time of Copernicus. In its day, the now discredited geocentric theory, which gave a quantitative explanation of the phenomena, was an immense advance over the ideas which preceded it. A false hypothesis, if it serves as a guide for further enquiry, may be more useful at the time than a truer one for which verifiable evidence is not yet at hand. The literary bent which has characterized modern studies of ancient times has directed attention chiefly to the ages when the poets and sculptors of Athens were putting forth their masterpieces. It would be unfair to say that the classical period of Greece produced no science. There was geometry before Euclid; the medicine of Hippocrates and the zoology of Aristotle were based on sound observation. Yet the philosophic outlook was metaphysical and not scientific; even the atomic theory of Democritus was speculative philosophy and not science. With the marches of Alexander the Great we reach a new epoch. He carried to the East that Greek culture which was already spreading westwards over the Mediterranean, and in return he brought Babylonia and Egypt into closer touch with Europe, while his staff collected vast stores of facts in geography and natural history. Thus began three centuries of Hellenism, from the death of Alexander in 323 to the establishment of the Roman Empire by Augustus in 31 B.C., centuries during which Greek culture, having passed its zenith in its original home, spread to other lands and dominated the known world. A form of the Greek language, the common speech, was understood “from Marseilles to India, from the Caspian to the Cataracts”, and the upper classes from Rome to Asia accepted Greek philosophy and the Greek outlook on life. Commerce became international, and thought was free as it was not to be again till modern days in some nations of the western world. The increased knowledge of the Earth led to more curiosity about natural things, and a more scientific attitude of mind. We are at once conscious of a more familiar atmosphere - indeed there is much resemblance to our own times, though there were then few machines and many slaves. A change in method appears. We pass from general philosophic systems and encyclopaedic surveys of knowledge to more modern specialization. Definite and limited problems are isolated from others and attacked singly, and real progress in natural knowledge is seen. Indeed, the change from the synthetic philosophies of Athens to the analytic science of Archimedes and the early Alexandrians is closely parallel to the change from the Scholasticism of late mediaeval writers to the modern science of Galileo and Newton. The Greek mathematicians and philosophers accepted implicitly the simple intuitional idea, in which the axioms of geometry are taken to be facts self-evident to the mind. But whatever view we may now take of its philosophic meaning, deductive geometry was especially suited to the Greek genius, and, unlike some other products of Greek thought, it marked a permanent step in the advance of knowledge, a step which never had to be retraced. Indeed, Greek geometry may well be considered to share with modern experimental science the highest place among the triumphs of the human intellect. The origins of the sciences of mechanics and hydrostatics are to be sought in the practical arts, rather than in the writings of the early Greek philosophers, but they were placed on a sound footing when observation was allied to the deductive methods learnt in geometry. The first known to have done this was Archimedes of Syracuse (287-212 B.C.), whose work, more than that of any other Greek, shows the true modern combination of mathematics with experimental enquiry; a combination in which definite and limited problems are attacked, and hypotheses are set forth only to have their logical consequences first deduced and then tested by observation or experiment. The idea of the relative densities of bodies, which, as we have seen, was unknown to Aristotle, was first formulated clearly by Archimedes, who, moreover, discovered the principle known by this name - that, when a body floats in a liquid, its weight is equal to the weight of liquid displaced, and, when it is immersed, its weight is diminished by that amount. It is said that King Hiero, having entrusted some gold to the artificers who were to make his crown, suspected them of alloying it with silver. He asked Archimedes to test this suspicion. While thinking over the problem, Archimedes noticed in his bath that he displaced water equal in volume to his own body, and saw at once that, for equal weights, the lighter alloy would displace more water than the heavier gold. This flash of insight revealed to Archimedes his principle, but he then proceeded to deduce it mathematically from his fundamental conception of a fluid as a substance that yields to any, even the smallest, shearing stress, that is, a force tending to cause one layer to slide over another. Archimedes also considered the theoretical principle of the lever, the practical use of which must be of immemorial antiquity and is illustrated in the sculptures of Assyria and Egypt two thousand years before the days of Archimedes. Nowadays we treat the law of the lever as a matter for experimental determination, and deduce other, more complicated, results from it. Nevertheless, the co-ordination of the law of the lever with ideas which then seemed simpler was a step in advance. Archimedes’ chief interest lay in pure geometry, and he regarded his discovery of the ratio of the volume of a cylinder to that of a sphere inscribed in it as his greatest achievement. He measured the circle by inscribing and circumscribing polygons, increasing the number of sides till the polygons nearly met on the circle. By this method of exhaustion he showed that the ratio of the circumference to the diameter was greater than 3*10/71 and less than 3*1/7. The mechanical contrivances for which he was famous - compound pulleys, hydraulic screws, burning mirrors - were considered by him as the recreations of a geometer at play. Archimedes was no mere compiler. Nearly all his writings are accounts of his own discoveries. It is a sign of the modernity of his outlook that the greatest man of the Renaissance, Leonardo da Vinci, sought for copies of the works of Archimedes more eagerly than for those of any other Greek philosopher. And nearly indeed were his writings lost to the world. Apparently at one time the only survival was a manuscript, probably of the ninth or tenth century, which has long ago disappeared. But fortunately three copies were made, and are extant; and from these the printed editions have been taken. Archimedes, the first and greatest of physicists of the modern type in the ancient world, who helped with his engines of war to keep the Romans at bay for three years, was killed by a soldier after the storming of Syracuse in the year 212. His tomb was discovered and piously restored in 75 B.C. by Cicero, who was then Quaestor in Sicily. In the fourth century before Christ, geographical discovery made considerable progress. Hanno passed the Pillars of Hercules, and sailed down the west coast of Africa; Pytheas voyaged round Britain towards the polar seas, and also correlated the lunar phases with the tides; Alexander marched to India. It was known that the Earth was a sphere, and some idea of its true size began to be formed. This growth in knowledge was not favourable to the ideas of the counter-earth or central fire imagined by Philolaus, and those parts of Pythagorean astronomy were thenceforward discredited. By the end of the fourth or the beginning of the third century before Christ the intellectual centre of the world had moved from Athens to Alexandria, the city founded in 332 by Alexander the Great. One of Alexander’s generals, Ptolemy (not the astronomer), founded there a Greek dynasty which became extinct on the death of Cleopatra in the year 30 B.C. Among those who made the schools of Alexandria illustrious in the reign of the first Ptolemy, 323 to 285, were the geometer Euclid and Herophilus the anatomist and physician. In the Greek civilization of Alexandria a new and more modern spirit appears, as in other Hellenistic lands. Instead of the complete intellectual systems in which the Athenian philosophers were pre-eminent, the men of Alexandria, following the lead of Aristarchus of Samos and Archimedes of Syracuse, undertook limited and special enquiries, and therefore made more definite scientific progress. About the middle of the third century, the famous Museum, or place dedicated to the Muses, was founded at Alexandria. The four departments of literature, mathematics, astronomy and medicine were in the nature of research institutes as well as schools, and the needs of them all were served by the largest library on the ancient world, containing some 400,000 volumes in rolls. One section of the library was destroyed by the Christian Bishop Theophilus about A.D. 390, and, after the Muslim conquest in the year 640, the Muhammadans, whether accidentally or deliberately is uncertain, destroyed what the Christians left. But for some centuries the Library of Alexandria was one of the wonders of the world, and its destruction was one of the greatest intellectual catastrophes in history. We have already considered the work of Euclid under the head of deductive geometry. He systematized the writings of older geometers and added many new theorems of his own. He also studied optics, realized that light travels in straight lines, and discovered the laws of reflection. The Alexandrian school of medicine was established chiefly by the work of two men, Herophilus and Erasistratus. The former, born at Chalcedon, flourished at Alexandria under Ptolemy I. He was the earliest distinguished human anatomist, and the greatest physician since the days of Hippocrates. His medicine was empirical and almost free from theoretical preconceptions. He gave a good description of the brain, of the nerves and of the eye, of the liver and other internal organs, of the arteries and veins; and he held that the seat of intelligence is the brain, and not the heart as maintained by Aristotle. Erasistratus, a younger contemporary of Herophilus, practised human dissections and made experiments on animals. He was keenly interested in physiology, and was the first to treat it as a separate subject. He added to the knowledge of the brain, of the nerves and of the circulatory system, holding that there are in the body and the brain special vessels for the blood and for the spirit which he identified with air. Taking over from Epicurus the tenets of the atomic theory, Erasistratus was opposed to medical mysticism, though he believed in nature acting as an external power, framing the human body for the ends it is to serve. Herophilus, Erasistratus and a third anatomist, Eudemus, made their century remarkable in the history of medicine. In the latter part of the third century B.C., another group of great men appears, younger contemporaries of Archimedes. Among them was Eratosthenes, born at Cyrene about 273 and died at Alexandria about 192. He was Librarian of the Museum, and the first great physical geographer. He held the Earth to be spheroidal and calculated its dimensions by estimating the latitudes and distances apart of Syene and Meroe, two places on nearly the same meridian. His result was 252,000 stades, equal to about 24,000 miles. These are surprisingly close approximations to the modern estimates of 24,800 and 93 million miles respectively. Eratosthenes argued from the similarity of the tides in the Indian and Atlantic Oceans that those oceans must be connected and the world of Europe-Asia-Africa an island, so that it should be possible to sail from Spain to India round the south of Africa. It was probably he who conjectured that the Atlantic might be divided by land running from north to south and inspired Seneca’s prophecy of the discovery of a new world. Posidonius later rejected this idea, and, underestimating the size of the Earth, said that a man sailing west for 70,000 stades would come to India. This statement gave Columbus confidence. A striking advance in mathematics was made at Alexandria in the latter half of the second century B.C. by Apollonius of Perga, who collected the knowledge of conic sections due to Euclid and his predecessors, and carried the subject much further by his own work. Apollonius showed that all conics could be considered as sections of one cone; he introduced the names parabola, ellipse and hyperbola; he treated the two branches of the hyperbola as a single curve, and thus made clear the analogies between the three kinds of section. He obtained a solution of the general equation of the second degree by means of conics, and determined the evolute of any conic. His treatment of the whole subject is purely geometrical. In the second century at Alexandria we meet again with Hipparchus, whose great work in astronomy has already been described. By this time Alexandria was losing its supremacy in Greek learning, which later was shared with Rome and Pergamos. Of uncertain date, somewhere between the first century B.C. and the third A.D., is Hero, a mathematician, physicist and inventor. He found algebraic solutions of equations of the first and second degree, and worked out many formulae for the mensuration of areas and volumes. He pointed out that the line of a reflected ray of light is the shortest possible path. But he is chiefly remembered for his mechanical contrivances, such as siphons, a thermoscope, the forcing air pump, and the earliest steam engine, in which the recoil of steam issuing from a jet is used to make an arm carrying the jet revolve about an axis, a forerunner of the jet-propelled aeroplane. The chief name which distinguishes later Graeco-Roman Alexandrian science is that of the astronomer Claudius Ptolemy, who must not be confused with the kings of Egypt of the same name. He taught and made observations at Alexandria between the years A.D. 127 and 151. His great work, later called by its contracted Arabic name of Almagest, is an encyclopaedia of astronomy, which was based on and expounded the work of Hipparchus, and remained the standard treatise till the days of Copernicus and Kepler."
