Nevertheless, there was great intellectual activity in the Græco-Oriental world, and a certain measure of invention, though little was of a basic kind. Euclid improved the science of geometry, and put it in virtually the same shape as that in which it has been taught since, even to this day. Aristarchus, the astronomer, announced the doctrine that the earth revolves around the sun and rotates on its own axis; and Hipparchus invented the plan of fixing the positions of places on the earth by their latitudes north and south of the Equator and their longitude east or west of a designated meridian. Hippocrates and Galen conceived and developed the foundations of the science of medicine of the present day. Eratosthenes estimated with extraordinary accuracy the circumference of the earth, and founded the science of geography. But the greatest of all of the original workers of that time was Archimedes, who lived at Syracuse in Sicily, and was killed by mistake when Syracuse was captured in the year 212 B. C., while engaged in drawing a geometrical figure on the sand. His principal fame is as a mathematician; but as a great inventor of mechanical appliances, he is the first man recognized as such in history. The invention with which his name is most frequently linked is that of the Archimedean screw. This consisted of a tube, wound spirally around an inclined axle, and so disposed that when the lower end of the tube was dipped into water and the axle was rotated water would rise in the tube--as shavings do when a screw is screwed down into wood. It constituted a very convenient pump and was so used. This was, of course, a mechanical invention of the utmost originality and value, and forms one of the clearly defined stepping-stones to civilization. There seems to be a belief in the minds of some that Archimedes was the inventor of the lever. The lever was, of course, invented long before he lived; but the laws of its operation and the principle that the weight on each side of the fulcrum, multiplied by its distance from the fulcrum, is equal to the weight on the other side, multiplied by its distance (when the lever is in equilibrium), seems to have been established by him. Many stories are told of his exploits when Syracuse was besieged by the Romans, but they are rather vague. The best known story is that he arranged a great many mirrors in such a way that he concentrated so many rays of sunlight on some Roman ships that they took fire. Whether this is true or not is not definitely known; but many centuries later Buffon, the French scientist, made an arrangement of plane mirrors with which he set fire to wood 200 feet away.