REMAINING LAWS OF NATURE. 173 



pictures of objects as effectually as from the objects 

 themselves. The other is, the demonstrative cha- 

 racter of geometrical truths ; which was at one time 

 supposed to constitute a radical distinction between 

 them and physical truths, the latter, as resting on 

 merely probable evidence, being deemed essentially 

 uncertain and unprecise. The advance of knowledge 

 has, however, made it manifest that physical science, 

 in its better understood branches, is quite as demon- 

 strative as geometry ; the task of deducing its details 

 from a few comparatively simple principles being 

 found to be anything but the impossibility it was once 

 supposed to be ; and the notion of the superior cer- 

 tainty of geometry being an illusion arising from the 

 ancient prejudice which in that science mistakes the 

 ideal data from which we reason, for a peculiar class 

 of realities, while the corresponding ideal data of any 

 deductive physical science are recognised as what they 

 really are, mere hypotheses. 



Every theorem in geometry is a law of external 

 nature, and might have been ascertained by gene- 

 ralizing from observation and experiment, which in 

 this case resolve themselves into comparison and mea- 

 surement. But it was found practicable, and .being 

 practicable, was desirable, to deduce these truths by 

 ratiocination from a small number of general laws of 

 nature, the certainty and universality of which was 

 obvious to the most careless observer, and which com- 

 pose the first principles and ultimate premisses of the 

 science. Among these general laws must be included 

 the same two which we have noticed as ultimate prin- 

 ciples of the Science of Number also, and which are 

 applicable to every description of quantity ; viz., the 

 sums of equals are equal, and things which are equal 

 to the same thing are equal to one another ; the latter 



