I N A U G U R A T I O N O F P H I L O S O P H Y C O U R S E S 9 7 1 between real figures and geometry. In this example we see the meaning of the consider- ations made about this science in the preceding paragraph. It is entertaining to work with the shadows projected from these bodies onto a plane tan- gent to that spherical surface by a point source of light located at the point antipodal to the tangency. Those shadows will grow longer the closer those bodies move toward the source of light. If we imagine that these shadows are new bodies and that they are the exclusive inhabitants of that plane, how would they learn of the increase in size they experience as they move away from the point at which their world touches the] sphere? Something quite different would occur if other, rigid bodies were present right there, a ruler, for example: with it they could prove that fact. The examples we have mentioned, he said, illustrate the real meaning of geometry. He then extended the preceding considerations to three-dimensional space.