right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides) was the discovery of Pythagoras; while Theon of Alexandria is known to have added certain definitions on his own account.
But even when we deduct all those portions of Grecian geometry declared by scholars to be earlier or later than Euclid, we are left paralyzed in admiration of the mind of the one man who was author of what is left.
We have no details of the life of Euclid; only one of his sayings has come down to us. When Ptolemy asked him if a person could not understand geometry without reading all his books—an enquiry with which many school boys in all ages have been in the deepest sympathy—Euclid replied: "There are no royal roads to geometry," alluding to those straight roads in Persia which were reserved for the king alone to travel over.
After Euclid, probably the next best known Greek mathematician is Archimedes, who in his youth studied at the Alexandrian School. Unquestionably the most original of the Greeks. Archimedes invented appliances and enunciated principles which remain of the utmost utility at the present day. The endless or Archimedean screw, although not now used for the purpose for which it was originally devised (raising water from the hold of a ship), is the parent of such diverse mechanisms as screw-nails and the steam-turbine. Archimedes made the first planetarium. His "Eureka" on discovering a method to detect alloy in the gold crown of Hiero of Syracuse, has become as hackneyed phrase. While we need not believe all that was told of him, of his engines for prolonging the siege of Syracuse, of the mirrors with which he set fire to the ships of the Roman fleet, etc., yet we may freely admit Archimedes to have been a mathematician and engineer of the first rank. The Archimedean principle of flotation underlies the possibility of things heavier than water floating in water. One of the sayings of Archimedes is in praise of the lever, a mode of the application of force which we have good reason to believe was known to the Egyptians long before Greece was civilized. Archimedes wrote, or to his inspiration are attributed, quite a number of books on pure mathematics, both of surfaces and solids, one of them, a treatise on the center of inertia, being of practical value at the present day. This book is regarded as the foundation of the theory of mechanics and it is a great advance on what Aristotle wrote on the same subject. By his own desire, the figure of a sphere within a cylinder was engraved on his tomb, for it was the relationship of these which Archimedes considered his greatest discovery. Archimedes was killed by a Roman soldier on the fall of Syracuse in 212 B.c. Cicero in 75 B.c, found the tomb overgrown with vegetation. Hero of Alexandria in his "Pneumatica" describes at least two devices
