GEOMETRICAL INSTRUMENTS AND 

 MODELS. 



NEXT to the science of number, the science of space is that which 

 is at once the most abstract, and admits of the most universal 

 application to the study of natural phenomena. Everything that 

 takes place takes place in space ; and thus Geometry, or the science 

 of space, necessarily intervenes in all exact observation of events. 



When we begin to think about space at all, the properties of it 

 which first impress the mind are its continuity, and its apparently 

 indefinite extent, our imaginations being perhaps unable to con- 

 ceive the absence of either of these two properties. Probably we 

 next notice the existence of three dimensions of space (as seen in the 

 length, breadth, and height of any object), and we cannot conceive 

 it to possess more or fewer. We further observe, (i) that at any 

 two different points space is exactly similar to itself, and (2) that 

 in all the directions which exist at any one point it has identical 

 properties. 



These general assertions, if not really of themselves evident, are 

 at least readily admitted as being in accordance with universal 

 experience. They are all assumed in, and may be said to form 

 the basis of, that analytical representation of space which we owe 

 to Descartes, and which justly entitles him to be regarded as the 

 founder of modem geometry. In accordance with this represen- 

 tation we regard space as a complex (if we may use this word as 

 a translation of the German maimigfattigkdf) of three indetermi- 

 nate quantities corresponding to its three dimensions ; the surfaces, 



