g38 LECTURE XX. 



ments both in mathematics and in mechanics, and in particular that he dis- 

 covered the well known relation between the hypotenuse and the sides of a 

 right angled triangle, and demonstrated that the square of the hypotenuse is 

 always equal to the sum of the squares of the sides. This theorem is more 

 essential to the perfection of geometry than any other proposition that can be 

 named: and if we may judge by the story of his having sacrificed a hecatomb 

 to the Muses, on occasion of the discovery, beseems to have had a foresight of 

 the magnificence of the edifice, that was in subsequent times to be built on this 

 foundation. 



Democritus of Abdera lived about a century after Pythagoras, whose works 

 he studied, and whose principles he adopted. He appears to have been possess- 

 ed of very extensive knowledge and profound learning; but little remains of 

 his works, excepting their titles. Some have attributed to him the invention 

 of the method of arranging stones so as to form an arch. Seneca thinks that 

 so simple an invention must have been practised in earlier ages: but Mr. King 

 has endeavoured to show that its general introduction in building was of much 

 later date. Architecture, and other mechanical arts had however been con- 

 siderably advanced some time before this period, if it is true that Ctesiphon 

 or Chersiphron, who built the temple of Ephesus, was cotemporary with 

 Croesus and Thales. It is uncertain at what time bridges of stone were first 

 built; and it is doubtful whether the art of building bridges of wood was very 

 well understood in those ages : for according to Herodotus, it was commonly 

 believed, that Thales avoided the necessity of procuring a passage over the 

 Halys for the army of Croesus, by encamping them on its banks, and cutting 

 a channel for the river in their rear, although the historian himself is of opi- 

 nion, that they passed over bridges which already existed. Curtius speaks of a 

 bridge of stone over the F.uphrates at Babylon, which appears to have been 

 built long before the time of Alexander, whose expedition he relates; and it 

 is scarcely probable that a stone bridge could have withstood the impulse of 

 so rapid a river, if it had been supported by columns only, without arches. 

 We are informed by Pliny that Ctesiphon lowered his large blocks of stone by 

 placing them on ])eaps of sand bags, and letting out the sand by degrees; it 

 does not appear how he raised them, but the inclined plane seems to afford 

 the simplest and most obvious method. 



