GEOMETRY 



2443 



GEOMETRY 



EOMETRY, jeom'etri. A great city 

 had fallen, and soldiers were rushing through 

 its streets, putting to death all who gave them 

 the slightest excuse. As one burly soldier 

 crossed the market-place he saw, seated on the 

 ground, an old man whose ears seemed deaf 

 to the tumult around him and who' seemed to 

 see nothing but the figures he was tracing with 

 his finger in the sand. The soldier stopped, 

 wondering whether these might perhaps be 

 magic figures, and as his shadow fell upon the 

 markings the old man looked up. "Don't 

 touch my circles!" he cried; but the soldier, 

 angered at the commanding tone, ran him 

 through the body with his sword. The general 

 in command grieved over the death of this 

 old man, took upon himself the support of his 

 relatives, and erected in his honor a stately 

 tomb. He did this despite the fact that the 

 old man had done all in his power against the 

 invaders in aiding in the defense of the city; 

 for in such reverence did the ancients hold 

 learning, and especially the marvelous science 

 of circles and angles and spheres, which is 

 called geometry, or earth-measuring. 



The sacked city was Syracuse, in Sicily, 

 which fell before the Romans in 212 B.C.; the 

 drawer of the mystic figures was Archimedes, 

 one of the greatest mathematicians of an- 

 tiquity (see ARCHIMEDES). Geometry is not 

 like that simpler form of mathematics which 

 we call arithmetic a comparatively modern 

 science; the former existed in a fairly complete 

 form two thousand years ago. 



The Story of Geometry. It is probably true 

 that geometry had its beginnings in practical 

 problems. The ancient Egyptians, for instance, 

 had great difficulty in preserving boundary 

 lines between the fields which each year were 

 flooded by the Nile, and when the waters sub- 

 sided they had to make new surveys or "land- 

 measures" and hence the name geometry. 

 Now in making these surveys it was very nec- 

 essary that they know how to mark off cor- 

 rectly right angles. Th,e Egyptians had never 

 heard the rule which every student of arith- 



metic learns that the square of the hypotenuse 

 of a right-angled triangle is equal to the sum 

 of the squares of the other two sides; but they 

 had worked out, no one knows how, the fact 

 that if they measured off with their ropes a 

 three-sided figure whose sides were in the rela- 

 tion of 3, 4, 5, the large enclosed angle would 

 be a right angle. 



In their plans for the pyramids, too, the 

 Egyptians must have made use of many of the 

 principles with which geometry concerns itself, 

 but it cannot be said that they ever really 

 developed a science of geometry. This was 

 left for the Greeks 

 to do. Thales was 

 the first Greek to 

 make a systematic 

 study of the sub- 

 ject, but more fa- 

 mous than he was 

 his disciple Pythag- 

 oras (which see)7 

 who worked out 

 that proposition 

 about right-angled 



triangles which the 

 T-> i. A fig" 1 " 6 which shows that 



Egyptians had felt the square drawn upon the 

 ti - ui;~,4i,, ~A hypotenuse of a right-angled 

 after blindly, and t ^ ngle ls equal to the sum 

 which is still called of like squares drawn upon 



the other two sides, 

 for him the Pytha- 

 gorean Theorem. Philosophers found this new 

 subject quite to their taste, and Plato and 

 Aristotle contributed much to its development ; 

 but it was left for Euclid, a Greek of Alexan- 

 dria who lived about 300 u. c., to win the title 

 of "father of geometry" (see EUCLID). He or- 

 ganized everything that his predecessors had 

 discovered, added new problems, and set forth 

 all his knowledge in his Elements, a book on 

 which the teaching of geometry has ever since 

 been based. Indeed, his name is practically 

 a synonym for geometry. "To-morrow's Euclid 

 is hard," says the English schoolboy, and no 

 one misunderstands him. 



The next really great geometrician was 

 Archimedes, who died, as related above, in 



PYTHAGOREAN 

 THEOREM 



