346 



GREEK SCIENCE. 



Archimedes. 

 B.C. 289. 



Centre of 

 gravity. 



is nearly impossible to distinguish the one from the other. We learn 

 at once from the writings of Aristotle, what the state of mechanical 

 theory was in his time : for we find him maintaining, that if one body 

 have ten times the density of another, it will move with ten times the 

 velocity, and that both being let fall from the same height, the one 

 will fall through ten times the space that the other will in the same 

 time ; that the velocity of the same body, in different mediums, is 

 reciprocally as their densities ; and other equally absurd and incon- 

 sistent notions : and the difficulty which Galileo experienced in eradi- 

 cating these false hypotheses, is a proof that, in the long interval 

 between his time and that of the Stagirite, no theory of motion of a 

 more intelligible and satisfactory description had appeared ; although 

 the doctrine of equilibrium had already begun to assume a scientific 

 form in the hands of Archimedes and Pappus. 



In the writings of Archimedes that are still extant, we find the 

 earliest attempt to reduce the laws of equilibrium to order and con- 

 sistency. His work ' De jEquiponderantibus ' first unites and assimi- 

 lates them with the pure principles of geometry. With this view, he 

 began by considering the case of a lever or balance, supported on a 

 fulcrum, and loaded with a weight at each extremity ; then assuming 

 it as an axiom, that when the two arms of the balance are equal, the 

 two weights supposed in equilibrio are also necessarily equal, he de- 

 monstrated that if one of the arms of this lever be augmented in 

 length, the weight applied to it in order to preserve the equilibrium, 

 must be reduced in the same ratio : and hence he concluded, that 

 generally, when two weights suspended from the unequal arms of a 

 lever are in equilibrio, these weights ought to be reciprocally propor- 

 tional to the distance of their respective points of application from the 

 centre of motion. He also observed, that each of these two weights 

 produced the same pressure on the fulcrum or point of support as it 

 would do if it were immediately applied at that point ; he next pro- 

 ceeded to make this substitution mentally, and to combine the sum of 

 the two weights with a third ; thus attaining the same conclusion for 

 an assemblage of the three weights as for the first two ; and so on 

 for any greater number. Hence he demonstrated, step by step, that 

 there exists in every system of bodies, as well as in every single body, 

 regarded as a system, a general centre, which we denominate the 

 centre of gravity. He then applied this theory to certain examples, 

 and determined the centres of gravity in the parallelogram, the tri- 

 angle, the trapezium, the area of the parabola, &c. &c. 



This deduction, as we have above observed, was the first step 

 towards establishing a rational theory of mechanics ; and the surprise 

 expressed by Hiero at the famous assertion of our philosopher, " Give 

 me a place to stand on, and I will move the earth," shows at once 

 the novelty of the doctrine, and the wretched state of mechanical 

 knowledge prior to this discovery. To the same author has also been 

 attributed the theory of the inclined plane, the pulley, and the screw ; 



