PT. i. Astronomy and Geology compared. 9 



Euclid ; it is quite sufficient for him to have con- 

 sulted the diagram and to have mastered the 

 demonstration in order to convince him that, under 

 all possible circumstances, and in every quarter of 

 the Universe wherever an isosceles triangle is found, 

 the angles at its base are equal. The demonstrations 

 upon which rest the truth of Newton's ' Principia,' 

 which may be regarded as the most refined examples 

 from geometrical proofs, are as certain and as fully 

 demonstrative as Euclid's fifth proposition can be ; 

 they are equally independent of the evidence of 

 fact, and facts when in accordance with them in the 

 planetary system must of necessity be bound by 

 them. The same reasoning applies to all the methods 

 of Algebraical analysis up to the Integral Calculus, 

 and the great distinguishing superiority of this mode 

 of reasoning follows throughout, that it is indepen- 

 dent of the evidence of facts, but facts must obey 

 its laws wherever the conditions are in conformity 

 with them. 



The second method of proof is by establishing an 

 invariable and continuous connection of Cause and 

 Effect, by showing that certain events invariably 

 follow from certain antecedents, thereby establishing 

 a necessary connection between them. By this 



