148 ADVANCEMENT OP LEAllNmC. [BOOK Itl. 



physics. It is a strange fatality, that mathematics and 

 logic, which ought to be but handmaids to physics, should 

 boast their certainty before it, and even exercise dominion 

 against it. But the place and dignity of this science is a 

 sccondaiy consideration with regard to the thing itself 



Mathematics is either pure or mixed. To the pure belong 

 the sciences employed about quantity, wholly abstracted 

 from matter and physical axioms. This has two parts, — 

 geometry and arithmetic ; the one regarding continued, and 

 the other discrete quantity. These two sciences have been 

 cultivated with very great subtilty and application ; but in 

 plain geometry there has nothing considerable been added 

 to the labours of Euclid, thougli he lived many ages since. 

 The doctrine of solids has not been prosecuted and extended 

 equal to its use and excellency, neither by the ancients nor 

 the moderns ; and in arithmetic there is still wanting a suffi- 

 cient variety of short and commodious methods of calcula- 

 tion, especially with regard to progressic^ns, whose use in 

 physics is very considerable.^ Neither i? algebra brought to 



^ In nature no two beings exist perfectly equal, and the same being 

 cannot retain its qualities unchanged for an instant ot time together. 

 In the universe everything moves in a constant progression and series, 

 and it probably was the presentiment of this truth that led the greatest 

 mathematicians after Bacon's time to turn nearly all their attention to 

 this department of mathematics. Beyond the analogy, however, there 

 is nothing in these phenomena which has any relation with the reality 

 of things ; nor have any philosophers since Flud's day ever dealt with 

 them except as pure conditional verities. With data sufficiently deter- 

 minate, we may approach the solution of any question to which they 

 refer; but if these facts are not given, the problem must remain unre- 

 solved. The mathematician may draw consequences ; but it is not 

 allowed him to form principles, and if he attempt to apply figures to 

 any hypothesis not warranted by facts, he must be content with the 

 fate of the Samian who constructed the world out of arithmetic, and 

 tas been rewarded by the derision of ages for his pains. 



No part of learning has perhaps been more cultivated since this 

 author wrote than mathematics, as every other science, or the body of 

 Ijhilosophy itself, seems rendered mathematical. The doctrine of solids 

 •"ias been improved by several ; the shorter ways of calculation here 

 •jioted as deficient are in a great measure su.pplied by the invention 

 MI logarithms. Algebra has been so far improved and applied as to 

 Bival, or almost prejudice, the ancient geometry; add to this the new 

 '^j*scoverie8 of the Method of Fluxions, the Method of Tangents, the 

 Doctrine of Infinites, the Squaring of Curves, &c. For the general 

 n^fttem of mathematical learning, see *' Wolfii Elementa Matheseos Uni- 



