ADVANCEMENT OF LEARNING 171 



have a knowledge of what has already been done. This 

 inventory will be the more artificial and useful, if it also 

 contain things of every kind, which, according to common 

 opinion, are impossible; as likewise such as seemed next 

 to impossible, yet have been effected, the one to whet the 

 human invention, and the other to direct it, so that from 

 these optatives and potentials actives may the more readily 

 be deduced. 



The second thing is, that a calendar be made of such 

 experiments as are most extensively useful, and that lead 

 to the discovery of others. For example, the experiment 

 of artificial freezing, by means of ice and bay salt, is of 

 infinite extent, and discovers a secret method of condensa 

 tion of great service to mankind; fire is ready at hand for 

 rarefaction, but the means of condensation are wanted. And 

 it would greatly shorten the way to discoveries, to have 

 a particular catalogue of these leading experiments. 



CHAPTEE VI 



The Great Appendix of Natural Philosophy both Speculative and Practical. 

 Mathematics. Its Proper Position not among the Substantial Sciences, 

 but in their Appendix. Mathematics divided into Pure and Mixed 



IT WAS well observed by Aristotle, that physics and 

 mathematics produce practice, or mechanics; 1 there- 

 fore as we have treated both the speculative and 

 practical part of the doctrine of nature we should also 

 consider mathematics as an auxiliary science to both, which 

 being revived into philosophy, comes in as a third part after 

 physics and metaphysics. But upon due recollection, if we 

 designed it as a substantial and principal science, it were 

 more agreeable to method and the nature of the thing to 

 make it a part of metaphysics. For quantity, the subject 

 of mathematics applied to matter, is as the dose of nature, 



1 Metaphysics, i. and xi. 



