PHILOSOPHY OF INDUCTIVE INFERENCE. 267 



Sir George Airy has also recorded a curious case, in 

 which he accidentally fell by trial on a new geometrical 

 property of the sphere.* 1 Many of the most important and 

 now trivial propositions in geometry, were probably thus 

 discovered by the ancient Greek geometers ; and we have 

 pretty clear evidence of this in the Commentaries of 

 Proclus/ But discovery in such cases means nothing 

 more than suggestion, and it is always by pure deduction 

 that the general law is really established. As Proclus 

 puts it, we must pass from sense to consideration. 



Given, for instance, the series of figures in the accom- 

 panying diagram, a little examination and measurement 

 will show that the curv- 

 ed lines approximate to 

 semicircles, and the rec- 

 tilineal figures to right- 

 angled triangles. These 

 figures may seem to sug- 

 gest to the mind the gen- 

 eral law that angles in- 

 scribed in semicircles are right angles ; but no number of 

 instances, and no possible accuracy of measurement would 

 really establish the truth of that general law. Availing 

 ourselves of the suggestion furnished by the figures, we 

 can only investigate deductively the consequences which 

 flow from the definition of a circle, until we discover 

 among them the property of containing right angles. 

 Many persons, after much labour, have thought that they 

 had discovered a method of trisecting angles by plane 

 geometrical construction, because a certain complex ar- 

 rangement of lines and circles had appeared to trisect an 

 angle in every case tried by them, and they inferred, by a 



<i 'Philosophical Transactions/ [1866] vol. 146, p. 334. 

 r Bk. ii. chap. iv. 



