[Sidenote: Cultivation of geometry by the Greeks.]

Other famous geometers could also be mentioned, but such men as Euclid, Archimedes, and Apollonius are enough to show that geometry was cultivated to a great extent by the philosophers of antiquity. It progressively advanced, like philosophy itself, from the time of Thales, until it had reached the perfection of which it was capable, when it became merged into astronomical science. It was cultivated more particularly by the disciples of Plato, who placed over his school this inscription, "Let no one ignorant of geometry enter here." He believed that the laws by which the universe is governed are in accordance with the doctrines of mathematics. The same opinion was shared by Pythagoras, the great founder of the science, whose great formula was, that number is the essence or first principle of all things. No thinkers ever surpassed the Greeks in originality and profundity, and mathematics, being highly prized by them, were carried to the greatest perfection their method would allow. They did not understand algebra, by the application of which to geometry modern mathematicians have climbed to greater heights than the ancients. But then it is all the more remarkable that, without the aid of algebraic analysis, they were able to solve such difficult problems as occupied the minds of Archimedes and Apollonius. No positive science can boast of such rapid development as geometry for two or three hundred years before Christ, and never was the intellect of man more severely tasked than by the ancient mathematicians.

[Sidenote: Empirical sciences.]

No empirical science can be carried to perfection by any one nation or in any particular epoch. It can only expand with the progressive developments of the human race itself. Nevertheless, in that science which for three thousand years has been held in the greatest honor, and which is one of the three great liberal professions of our modern times, the ancients, especially the Greeks, made considerable advance. The science of medicine, having in view the amelioration of human misery, and the prolongation of life itself, was very early cultivated. It was, indeed, in old times, another word for physics,—the science of nature,—and the physician was the observer and expounder of physics. The physician was supposed to be acquainted with the secrets of nature—that is, the knowledge of drugs, of poisons, of antidotes to them, and the way to administer them. He was also supposed to know the process of preserving the body after death. Thus Joseph commanded his physician to embalm the body of his father seventeen hundred years before the birth of Christ, and the process of embalming was probably known to the Egyptians beyond the period when history begins. Helen, of Trojan fame, put into wine a drug that "frees man from grief and anger and causes oblivion of all ills." [Footnote: Odyssey, b. iv.] Solomon was a great botanist, with which the science of medicine is indissolubly connected. The "Ayur Veda," written nine hundred years before Hippocrates was born, sums up the knowledge of previous periods relating to obstetric surgery, to general pathology, to the treatment of insanity, to infantile diseases, to toxicology, to personal hygiene, and to diseases of the generative functions. [Footnote: Wise, On the Hindu System of Medicine, p. 12.] The origin of Hindu medicine is lost in remote antiquity.

[Sidenote: Hippocrates.]

Thus Hippocrates, the father of European medicine, must have derived his knowledge, not merely from his own observations, but from the writings of men unknown to us, and systems practiced for an indefinite period. The real founders of Greek medicine are fabled characters, like Hercules and Aesculapius—that is, benefactors whose names have not descended to us. They are mythical personages, like Hermes and Chiron. One thousand two hundred years before Christ temples were erected to Aesculapius in Greece, the priests of which were really physicians, and the temples themselves were hospitals. In them were practiced rites apparently mysterious, but which modern science calls by the names of mesmerism, hydropathy, mineral springs, and other essential elements of empirical science. And these temples were also medical schools. That of Cos gave birth to Hippocrates, and it was there that his writings were commenced. Pythagoras—for those old Grecian philosophers were the fathers of all wisdom and knowledge, in mathematics and empirical sciences, as well as philosophy itself—studied medicine in the schools of Egypt, Phoenicia, Chaldea, and India, and came in conflict with sacerdotal power, which has ever been antagonistic to new ideas in science. He traveled from town to town as a teacher or lecturer, establishing communities in which medicine as well as numbers was taught.

The greatest name in medical science, in ancient or in modern times,— the man who did the most to advance it; the greatest medical genius of whom we have record,—is Hippocrates, born on the island of Cos B.C. 460, of the great Aesculapian family, and was instructed by his father. We know scarcely more of his life than we do of Homer himself, although he lived in the period of the highest splendor of Athens. And his writings, like those of Homer, are thought by some to be the work of different men. They were translated into Arabic, and were no slight means of giving an impulse to the Saracenic schools of the Middle Ages in that science in which the Saracens especially excelled. The Hippocratic collection consists of more than sixty works, which were held in the highest estimation by the ancient physicians. Hippocrates introduced a new era in medicine, which, before his time, had been monopolized by the priests. He carried out a system of severe induction from the observation of facts, and is as truly the creator of the inductive method as Bacon himself. He abhorred theories which could not be established by facts. He was always open to conviction, and candidly confessed his mistakes. He was conscientious in the practice of his profession, and valued the success of his art more than silver and gold. The Athenians revered him for his benevolence as well as genius. The great principle of his practice was trust in nature. Hence he was accused of allowing his patients to die; but this principle has many advocates among scientific men in our day, and some suppose the whole philosophy of homeopathy rests on the primal principle which Hippocrates advanced. He had great skill in diagnosis, by which medical genius is most severely tested. His practice was cautious and timid in contrast with that of his contemporaries. He is the author of the celebrated maxim, "Life is short and art is long." He divides the causes of disease into two principal classes,—the one comprehending the influence of seasons, climates, and other external forces; the other from the effects of food and exercise. To the influence of climate he attributes the conformation of the body and the disposition of the mind. He also attributes all sorts of disorders to a vicious system of diet. For more than twenty centuries his pathology was the foundation of all the medical sects. He was well acquainted with the medicinal properties of drugs, and was the first to assign three periods to the course of a malady. He knew, of course, but little of surgery, although he was in the habit of bleeding, and often employed his knife. He was also acquainted with cupping, and used violent purgatives. He was not aware of the importance of the pulse, and confounded the veins with the arteries. He wrote in the Ionic dialect, and some of his works have gone through three hundred editions, so highly have they been valued. His authority passed away, like that of Aristotle, on the revival of European science. Yet who have been greater ornaments and lights than these distinguished Greeks?

[Sidenote: Galen.]

The school of Alexandria produced eminent physicians, as well as mathematicians, after the glory of Greece had departed. So highly was it esteemed that Galen went there to study five hundred years after its foundation. It was distinguished for inquiries into scientific anatomy and physiology, for which Aristotle had prepared the way. He was the Humboldt of his day, and gave great attention to physics. In eight books he developed the general principles of natural science known to the Greeks. On the basis of the Aristotelian researches, the Alexandrian physicians carried out extensive inquiries in physiology. Herophilus discovered the fundamental principles of neurology, and advanced the anatomy of the brain and spinal cord.

[Sidenote: Medical science among the Romans.]