18 THE HISTORY OF SCIENCE 



tone of the string of a musical instrument when the 

 length is reduced by one half, and also that strings 

 of like thickness and under equal tension yield har- 

 monious tones when their lengths are related as 

 1 : 2, 2 : 3, 3 : 4, 4 : 5. The Pythagoreans drew from 

 this the extravagant inference that the heavenly 

 bodies would be in distance from the earth as 1, 2, 

 3, 4, 5, etc. Much of their theory must seem to the 

 modern mind merely fanciful and unsupported spec- 

 ulation. At the same time it is only just to this 

 school of philosophers to recognize that their assump- 

 tion that simple mathematical relationships govern 

 the phenomena of nature has had an immense influ- 

 ence on the advance of the sciences. Whether their 

 fanaticism for number was owing to the influence of 

 Egyptian priests or had an Oriental origin, it gave 

 to the Pythagoreans an enthusiasm for pure mathe- 

 matics. They disregarded the bearing of their sci- 

 ence on the practical needs of life. Old problems 

 like squaring the circle, trisecting the angle, and 

 doubling the cube, were now attempted in a new 

 spirit and with fresh vigor. The first, second, and 

 fourth books of Euclid are largely of Pythagorean 

 origin. For solid geometry as a science we are also 

 indebted to this sect of number-worshipers. One of 

 them (Archytas, 428-347 B.C., a friend of Plato) 

 was the first to apply geometry to mechanics. We 

 see again here, as in the case of Thales, that the 

 love of abstract thought, the pursuit of science as 

 science, did not interfere with ultimate practical 

 applications. 



Plato (429-347 B.C.), like many other Greek 

 philosophers, traveled extensively, visiting Asia 



