24 MOVEMENT 



show how the successive positions of a straight line 

 can produce cylinders, cones, conoids, and hyperboloids 

 by revolution. There is a particularly rich collection 

 of such diagrams at the Academy of Arts and Crafts 

 — very useful as a means of popularizing the study 

 of solid geometry. 



Now, if the geometry of to-day has become purely 

 a speculative science, there is no doubt that, like all 

 other sciences, it had an experimental origin. It is 

 not likely that the conception of a straight line was 

 evolved from man's brain as a purely abstract ex- 

 pression, but rather that it entered therein, on seeing 

 a stretched thread, for instance, or some other recti- 

 linear object. 



In the same way the conception of a plane or a 

 circle found its origin from noticing a flat surface or 

 an object of circular form. 



There are, so to speak, traces of these concrete 

 origins of geometrical figures in the definitions given 

 to solid figures or to those of three dimensions. 



Such objects are said to be " engendered " by straight 

 lines or curves, which undergo various displacements. 

 Thus a regular cylindrical surface is engendered by 

 a straight line which moves parallel to another, straight 

 line, and yet remains at the same distance from it. 

 The straight line which moves is the " generator " of 

 the cylinder ; that which remains fixed is its axis. 



Under such circumstances, let us suppose that the 

 straight line, as it moves in space, leaves a record of 

 its track at every point which it successively passes. 

 Now, this purely imaginary supposition may become 

 an accomplished fact, thanks to photography. Indeed, 

 supposing we take a series of instantaneous views of 

 an illuminated thread as it moves in front of a dark 

 screen, figures are produced which exactly resemble 

 the stereoscopic forms obtained by stretching a series 



