INTRODUCTION. 25 



What progress the Chaldeans and Egyptians had made in astronomy, 

 \ it is hard to say. They certainly had become acquainted with the plan- 



> ets ; but whether the Egyptians had discovered, as Macrobius assures 

 us, that Mercury and Venus revolve round the sun, is not so clear. 

 Their notions respecting the length of the solar year, and the mean 

 length of the lunation, must have been a near approximation to the truth. 

 This is evident from the famous Chaldean period called Saros. It con- 



! sisted of two hundred and twenty-three lunar months, at the end of 



> which the sun and moon were in the same situation with respect to each 

 J other as when the period began. This period includes a certain num- 



ber of eclipses of each luminary, which are repeated every saros in the 

 same order. 



The Chaldeans appear to have divided the day into twelve hours, and 

 to have constructed sun-dials for pointing out the hour. The sun-dial 

 of Ahaz is mentioned in the Old Testament, on the occasion of the re- 

 covery of Hezekiah ; but nothing is said about its construction. Un- 

 doubtedly, however, such sun-dials would require a certain knowledge 

 of gnomonics which, therefore, the Chaldeans must have possessed. 



That the Egyptians had made some progress in mathematics admits 

 of no doubt, as the Greeks inform us that they derived their first knowl- 

 edge of that branch of science from the Egyptian priests. But that the 

 mathematical knowledge of the people could not have been very exten- 

 sive, is evident from the ecstasy into which Pythagoras was thrown 

 when he discovered that the square of the hypotenuse of a right-angled 

 triangle is equal to the square of the two sides : for ignorance of this 

 very elementary, but important proposition, necessarily implies very 

 little knowledge even of the most elementary parts of mathematics. 



It was in Greece that pure mathematics first made decided progress. 

 P 

 1 The works of three Greek mathematicians still remain, from which we 



I have obtained information of all or almost all the mathematical knowl- 



> ed^e attained by the Greeks. These are Euclid, Appolonius, and 

 [ Archimedes. 



Euclid lived in Alexandria during the reign of the first Ptolemy. 

 Nothing whatever is known respecting the place of his nativity ; though 

 it is certain he lived in Greece, and that he died in Egypt, after the 



