282 REASONING. 



2nd, that surface parabolic; 3rd, those rays parallel to 

 each other and to the axis of the surface. It is to be 

 proved that the concourse of these three circumstances 

 is a mark that the reflected rays will pass through the 

 focus of the parabolic surface. Now each of the 

 three circumstances is singly a mark of something 

 material to the case. Rays of light impinging on a 

 reflecting surface, are a mark that those rays will be 

 reflected at an angle equal to the angle of incidence. 

 The parabolic form of the surface is a mark that, from 

 any point of it, a line drawn to the focus and a line 

 parallel to the axis will make equal angles with the 

 surface. And finally, the parallelism of the rays to the 

 axis is a mark that their angle of incidence coincides 

 with one of these equal angles. The three marks 

 taken together are therefore a mark of all these three 

 things united. But the three united are evidently a 

 mark that the angle of reflexion must coincide with 

 the other of the two equal angles, that formed by a 

 line drawn to the focus ; and this again, by the funda- 

 mental axiom concerning straight lines, is a mark 

 that the reflected rays pass through the focus. Most 

 chains of physical deduction are of this more com- 

 plicated type ; and even in mathematics such are 

 abundant, as in all propositions where the hypothesis 

 includes numerous conditions : " If a circle be taken, 

 and if within that circle a point be taken, not the 

 centre, and if straight lines be drawn from that point 

 to the circumference, then," &c. 



4. The considerations now stated remove a 

 serious difficulty from the view we have taken of 

 reasoning ; which view might otherwise have seemed 

 not easily reconcilable with the fact that there are 

 Deductive or Ratiocinative Sciences. It might seem 



