ARCHIMEDES 3 



and thus developed the important subject of machines. 

 The lever and set of pulleys became available for the multi- 

 plication of power to almost any desired extent, and in a 

 predictable manner, and striking instances of the successful 

 applications of these principles, as, for example, to the 

 raising of heavy ships, are related. The Archimedean screw 

 is still named after him to-day. 



He also developed our knowledge of the centre of gravity, 

 which allows us to understand and predict how the weight of 

 a heavy body acts when it is supported in a given manner. 

 He is also the founder of the theory of the equilibrium of 

 liquid bodies (hydrostatics); the Archimedean principle of 

 the upward force on bodies immersed in liquids, which also 

 determines the equilibrium of floating bodies, constantly 

 finds application. His work 'On Floating Bodies' presents us 

 with a mass of finely thought out details; the idea of specific 

 gravity, or density, is already fully worked out. 



He also greatly advanced geometry and mathematics. 

 He discovered how to calculate the circumference of a circle, 

 by means of inscribing and circumscribing polygons, starting 

 with the hexagon, and repeatedly doubling the number of 

 sides. This method is one which gives the number later 

 designated by the Greek letter tt to any required degree of 

 accuracy. He also developed the theory of conic sections, 

 which later became so important for astronomy, and likewise 

 the calculation of the surface of ellipses and parabolas, and 

 the calculation of the volume of a sphere and of other solids. 

 He is also known by his investigation of the Archimedean 

 spiral named after him. His profundity is shown in the fact 

 that he was the first to actually grasp the concept of infinity, 

 as opposed merely to the very great, a fact clearly shown by 

 his essay known as the 'Sand-reckoner.' 



