geocentric system. To explain the apparent retrograde motion of 

 the planets, Ptolemy not only adopted the eccentrics of Hipparchus 

 but assumed also epicycles for each planet and thus was formed the 

 cumbrous theory which is known to history as the Ptolemaic system. 

 Without a doubt these eccentrics and epicycles are the responses of 

 the astronomers to the demand made by Plato for uniform circular 

 motion, an excellent example, as can now be seen, of an unfortun- 

 ate influence by a philosophic system upon a special science. 



To continue tracing the development of this science is here 

 unnecessary, suffice it to say that the dictatorship of Ptolemy 

 in astronomy remained till with the work of the great Kepler, 

 building upon the achievements of Copernicus and the accurate 

 observations of Tycho Brahe, a new and simpler theory was devised, 

 a theory which treated the earth and planets as moving in ellipses 

 with the sun occupying a non-central position. 



Before the nature of science can be properly understood, it 

 will be advisable to give a brief outline of the development of early 

 mathematics and mechanics, other of the special sciences which 

 have had a long and interesting history. After that is completed, 

 it will then be possible to look back over the development which has 

 taken place and to ask what science actually is. Then, in the 

 following chapter, the philosophic thread may again be taken up 

 with the aim of forming some proper conception of the nature of 

 philosophy. 



That mathematics did not originate in Greece is evident, not 

 only from the testimony of the Greek writers themselves, but also 

 from the documentary evidence which recent scholarship has been 

 able to produce. In Plato's Phaedrus, Socrates is made to say 

 that the Egyptian god Theuth first invented arithmetic, geometry 

 and astronomy, and Aristotle, Meta. I i, tells us that geometry 

 was originally invented in Egypt. Eudemus declares that Thales 

 studied there, while Diodorus and Strabo at later dates both record 

 the tradition that geometry and astronomy are the inventions of 

 the Egyptian priests who claimed Pythagoras, Plato, Democritus, 

 Eudoxus and others as their pupils. But the most interesting 

 statement which bears upon the relation of Grecian and Egyptian 

 mathematics is that found in Herodotus, II ch. 109. The passage 

 reads as follows: "They said also that this king (Sesostris or 



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