«ict. ii.] DISSERTATION SECOND. 93 



science, to a great extent, was carried on by reasoning from 

 those laws, in the same manner that the geometer makes his 

 discoveries by reasoning on the definitions, by help of a 

 few axioms, or self-evident propositions. The only differ- 

 ence is, that, in the one case, the definitions and axioms are 

 supplied solely from the mind itself, while, in the other, all 

 the definitions and axioms, which are not those of pure 

 geometry, are furnished by experience. 1 



Bacon certainly was not fully aware of the advantages 

 that were thus to accrue to the physical sciences. He was 

 not ignorant, that the introduction of mathematical reason- 

 ing into those sciences is not only possible, but that, under 

 certain conditions, it may be attended with the greatest ad- 

 vantage. He knew also in what manner this application had 

 been abused by the Platonists, who had attempted, by 

 means of geometry, to establish the first principles of phy- 

 sicks, or had used them, in axiomalis constituendis, which 

 is exactly the province belonging exclusively to experience. 

 At the same time, he pointed out, with great precision, the 

 place which the mathematicks may legitimately occupy, as 

 serving to measure and compare the objects of physical in- 

 quiry. He did not, however, perceive beforehand, nor was 

 it possible that he should, the vast extent to which the ap- 

 plication of that science was capable of being carried. In 

 the book, De Augmentis, he has made many excellent re- 

 marks on this subject, full of the sagacity which penetrated 

 so far into futurity, but, nevertheless, could only perceive 

 a small part of the scene which the genius of Newton was 

 afterwards to unfold. 



1 The part of mechanieks which involves only statical considera- 

 tions, or the equilibrium of forces, is capable of being treated by 

 reasoning a priori entirely, without any appeal to experience. 

 This will appear, when the subject of Mechanieks is more parti- 

 cularly treated of. 



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