Length and Space. 71 



terms, space, room, kxtent, surface, superficies. The 

 meaning of these terms is usually explained to children, 

 by showing that the room in which they are, contains more 

 space than the table, the table more than the paper on 

 which they write, the paper more than one's hand, and 

 the hand more than the blade of a knife. It is no solid 

 objection to this account, that the ideas thus furnished are 

 inaccurate, and that we afterwards discover, by mathemat- 

 ical contemplation, that there are no material objects 

 without breadth. This correction of our ideas is long 

 posterior to the origin of them, and pre-supposes much 

 experience in thinking and reasoning. We learn, then, 

 after all this aid to think of those creatures of imagination 

 called MNEs, that is length without breadth or thickness, 

 and inquire into their properties. We thus also acquire 

 correct ideas of surface, and learn the art of measuring it. 

 Neither let it be objected that, if nature did not give us the 

 idea of a mathematical line, no effort of imagination could. 

 This may probably be true. Children, and very ignorant 

 persons, have nearly the same, probably the very same 

 conception of a hair, a thread, a fibre, and other long thin 

 substances, that a matiieniatician has of a line. Experience 

 and reflection afterwards discover, that no body can be felt 

 which has not sensible breadth and thickness ; and the 

 Hjathematician transfers to the creatures of his imagination, 

 the properties which he had formerly, but erroneously, 

 attributed to certain material objects. That is, he thinks 

 certain things, namely lines, to be long and not broad ; 

 which is exactly the distinction made by inexperienced 

 persoiif, between Bubstances that have surface or breadth, 

 and those that arc thought to have none. 'I'he distinction 

 between burfuccs and solids, is rudely introduced, and 



