APPENDIX AA. 



DEFINITIONS OF THE SCIENCES. 



Mathematics (Greek, /m^^ara, from pavdaveiv, to know). This 

 science is that of magnitudes (or of quantities) whether in time 

 or in space ; it bears upon rigorous truths which reason is capable 

 of discovering without the aid of experiments, but which, neverthe- 

 less, experiments can confirm. It is a deductive science so that 

 it is wrong to believe that deductive reasoning should be discarded ; 

 the fact being that both deductive and inductive reasoning must be 

 used in science both are equal in power. 



Mathematics is an exact science par excellence. It is divided 

 into two chief branches : arithmetic (of which algebra is an offshoot), 

 or the science of numbers, and geometry and its offshoots (trigono- 

 metry, conic sections, mechanics, etc.), or the science of space 

 or extent. (A fuller subdivision is given at page 197.) 



This science was cultivated from the earliest antiquity, in 

 Chaldaea, Egypt, India, and even China. It passed from Egypt into 

 Greece, where its limits were extended. It was reserved to modern 

 times to make mathematical discoveries and applications which may 

 be called sublime. 



The practical importance of this science has been pointed out at 

 page 198. 



Mechanics (/^x aI/7 7> a machine), that branch of mathematics 

 which considers the nature and laws of moving powers with their 

 effect in machines, and the nature, generation, and communication 

 of motion ; in other words, the science which treats of the laws 

 of equilibrium and motion, or which demonstrates the laws of 

 motion and mechanical combinations. 



