96 PHYSICAL SCIENCES IX AXCIEXT GREECE. 



CHAPTER I. 



EARLIEST STAGES or MECHANICS AND HYDROSTATICS. 



Sect. 1. Mechanics. 



A STRONOMY is a science so ancient that we can hardly ascend to 

 *. a period when it did not exist ; Mechanics, on the other hand, is 

 a science which did not begin to be till after the time of Aristotle ; for 

 Archimedes must be looked upon as the author of the first sound 

 knowledge on this subject. What is still more curious, and shows re- 

 markably how little the continued progress of science follows inevitably 

 from the nature of man, this department of knowledge, after the right 

 road had been fairly entered upon, remained absolutely stationary for 

 nearly two thousand years ; no single step was made, in addition to the 

 propositions established by Archimedes, till the time of Galileo and 

 Stevinus. This extraordinary halt will be a subject of attention here- 

 after ; at present we must consider the original advance. 



The great step made by Archimedes in Mechanics was the establish- 

 ing, upon true grounds, the general proposition concerning a straight 

 lever, loaded with two heavy bodies, and resting upon a fulcrum. The 

 proposition is, that two bodies so circumstanced will balance each 

 other, when the distance of the smaller body from the fulcrum is 

 greater than the distance of the other, in exactly the same proportion 

 in which the weight of the body is less. 



This proposition is proved by Archimedes in a work which is still 

 extant, and the proof holds its place in our treatises to this day, as the 

 simplest which can be given. The demonstration is made to rest on 

 assumptions which amount in effect to such Definitions and Axioms 

 as these : That those bodies are of equal weight which balance each 

 other at equal arms of a straight lever ; and that in every heavy body 

 there is a definite point called a Centre of Gravity, in which point we 

 may suppose the weight of the body collected. 



The principle, which is really the foundation of the validity of the 

 demonstration thus given, and which is the condition of all experiment- 

 al knowledge on the subject, is this : that when two equal weights are 

 supported on a lever, they act on the fulcrum of the lever with the 



