46 DISSERTATION SECOND. [parti. 



balance one another ; and also, that a cylinder, or parallelo- 

 piped of homogeneous matter, will be balanced about its 

 centre of magnitude. These, however, are not inferences 

 from experience ; they are, properly speaking, conclusions 

 deduced from the principle of the sufficient reason. 



The same great geometer gave a beginning to the science 

 of Hvdrostaticks, and discovered the law which determines 

 the loss of weight sustained by a body on being immersed 

 in water, or in any other fluid. His demonstration rests on 

 a principle, which he lays down as a postulatum, that, in 

 water, the parts which are less pressed are always ready to 

 yield in any direction to those that are more pressed, and 

 from this, by the application of mathematical reasoning, the 

 whole theory of floating bodies is derived. The above is 

 the same principle on which the modern writers on hvdros- 

 taticks proceed ; they give it not as a postulatum, but as 

 constituting the definition of a fluid. 



Archimedes, therefore, is the person who first made the 

 application of mathematicks to natural philosophy. No in- 

 dividual, perhaps, ever laid the foundation of more great 

 discoveries than that geometer, of whom Wallis has said 

 with so much truth, " Vir stupendae sagacitatis, qui pri- 

 ma fundamenta posuit inventionum fere omnium in quibus 

 promovendis aelas nostra gloriatur." 



The mechanical inquiries, begun by the geometer of Sy- 

 racuse, were extended by Ctesibius and Hero ; by Anthe- 

 mius of Tralles ; and, lastly, by Pappus Alexandrinus. — 

 Ctesibius and Hero were the first who analyzed mechanical 

 engines, reducing them all to combinations of five simple 

 mechanical contrivances, to which they gave the name of 

 Avntftus, or Powers, the same which they retain at the pre- 

 sent moment. 



Even in mechanicks, however, the success of these in- 

 vestigations was limited ; and failed in those cases where 



