KISE AND PEOGKESS OF MECHANICAL PHILOSOPHY. 415 



The foundations of Hydrostatical Science were also laid by the 

 same great geometer. His work de humido imidentibiis is derived 

 from the principle of the equality of fluid pressure a principle 

 still adopted as the basis of this science. In this work he has 

 shown that a heavy body, when immersed in a liquid, loses a 

 portion of its weight equal to that of the liquid displaced. It is 

 by the aid of this theorem a theorem on which the present mode 

 of determining the specific gravities of bodies is made to depend 

 that the philosopher of Syracuse is supposed to have solved the 

 famous problem of the crown, proposed by King Hiero, and to 

 have detected the fraud of his workman. 



A long period of darkness followed the discoveries of Archi- 

 medes. The philosophers of Alexandria, Ctesibius, and Hero, 

 Pappus Alexandrinus and others, pursued the inquiries which he 

 had begun, and by their inventions added much to practical 

 mechanics. To the two first of these authors we owe the analysis 

 of the various classes of machines, and their reduction to five 

 simple ones ; and the name of $vvajj.ttc, or powers, which they 

 affixed to these elementary machines, is still retained. But yet 

 the theory remained nearly as it had been left by Archimedes, 

 and the doctrine of equilibrium was destined to receive no addition 

 until the close of the 16th century. 



Hitherto the theory of the Mechanic Powers was understood 

 only so far as it could be derived from the principle of the lever ; 

 and no method was known of determining the conditions of equili- 

 brium of forces whose directions were inclined. It was at this 

 point that the progress of the ancients in Mechanical Philosophy 

 was arrested, and it is here that we are to look for the first im- 

 portant extension of this science. The problem was attempted, 

 but unsuccessfully, by Ghiido "Ubaldi, a mathematician of Italy, 

 in the 16th century ; and was finally solved by Stevinus, a cele- 

 brated engineer of the Low Countries, who demonstrated the 

 principle of equilibrium on the Inclined Plane. In this remarkable 

 demonstration, he supposes a chain of uniform thickness to encom- 

 pass the plane entirely round : part of this will rest on the plane, 

 along its hypothenusal side, part will hang vertically beside its 

 altitude, and the remainder will form a loop below the base. 

 Now the whole is in equilibria, for if not, a perpetual motion must 

 ensue in the direction of the greater force ; and as the part which 

 hangs below the plane draws equally in both directions, its effect 



