LOCOMOTIVE OF THE 1870 PERIOD STILL IN USE IN THE OZARKS
"JOHN BULL," A LOCOMOTIVE BROUGHT FROM ENGLAND AND PUT INTO SERVICE IN AMERICA IN 1831
Pythagoras made similar advances in geometry. He believed that each arithmetical fact had an analogue in geometry, and each geometrical fact a counterpart in arithmetic. He devised a rule by which integral numbers could be found so that the sum of the squares of two of them equaled the square of the third. He also developed the theory of irrational quantities. The first incommensurable ratio discovered is said to have been that of the side of a square to its diagonal which is 1:√2̅.
Euclid (300 B. C.) developed this theory in the tenth book of his geometry as still used.
Pythagoras not only placed mathematics on a solid scientific basis, he also established the fact that the physical phenomena of the world are governed by mathematical laws.
Little progress appears to have been made in astronomy by the Greeks in the time of Pythagoras. The Milesians and the associates of Pythagoras advanced numerous theories, but none of these was better than some of the Egyptian ideas. Hicetas, and others of this period, believed that the sun, moon, stars, and all other bodies in the heavens were stationary and that only the earth moved. The great turning movement of the earth around its axis produced the illusion that it was the heavenly bodies which were moving while the earth remained stationary.
The astronomical theories of Pythagoras, Hicetas, and Philolaus, all affirmed that the universe is composed of the elements earth, air, fire, and water, the whole mass being of spherical shape with the earth at the center and all having life or motion. These early theories, 2,000 years later, did service by aiding to secure acceptance for the Copernican theory. The Pythagorean ideas that the universe is one grand harmonious system, and that thought instead of sense is the sole criterion of truth, have exercised important influence on intellectual speculation throughout the ages.
In order to collect data for testing their theories in the physical and mathematical sciences, the Greeks invented many physical appliances. The monochord, employed in determining the relationships of vibrating harmonic strings is one of the first mechanisms used in practical physics that we have definite information about. An anvil, metal and glass disks, and bell-shaped cylinders were employed in studying the movements of sound waves.
Alcmæon (508 B. C.) was one of the earliest of the Greek anatomists. He was a disciple of Pythagoras and employed the logical research methods of his teacher in the investigation of medical problems. Although the Egyptians had developed medical science to a considerable extent and had taught the Greeks, their methods were not based upon sound principles. The result was that the more analytically minded Greeks could not accept certain Egyptian ideas. The Egyptian anatomical teachings were particularly crude, and Alcmæon began to investigate that science. His discoveries, both in anatomy and physiology, were very great. He outlined the functions of the principal organs of the body, discovered the optic nerve, the difference between the arterial and nervous systems, the Eustachian tube, the two divisions of the brain, the nerves connecting the brain with the organs of sense and with the spinal column. These advances placed the medical sciences on a logical basis similar to that of the physical, mathematical, and astronomical sciences. This first great anatomist and physiologist invented the practice of anatomical dissection and surgical exploration, and advanced the practice of medicine to a higher degree of usefulness.