468 SIMSON. 



cannot with any correctness be affirmed; both are 

 equally strict ; indeed if each be mathematical in its 

 nature, and consist of a series of identical propositions 

 arising one out of another, neither can be less perfect 

 than the other, for of certainty there can be no de- 

 grees. Nevertheless it must be a matter of regret 

 and here the great master and author of modern mathe- 

 matics has joined in expressing it that so much less 

 attention is now paid to the Ancient Geometry than its 

 beauty and clearness deserve ; and if he could justly 

 make this complaint a century and a half ago, 

 when the old method had but recently, and only in 

 part, fallen into neglect and disuse, how much more 

 are such regrets natural in our day, when the very 

 name of the Ancient Analysis has almost ceased to be 

 known, and the beauties of the Greek Geometry are 

 entirely veiled from the mathematician's eyes ! It be- 

 comes, for this reason, necessary that the life of Sim- 

 son, the great restorer of that geometry, should be 

 prefaced by some remarks upon the nature of the sci- 

 ence, in order that, in giving an account of his works, 

 we may say his discoveries, it may not appear that we 

 are recording the services of a great man to some sci- 

 ence different from the mathematical. 



The analysis of the Greek geometers was a method 

 of investigation of peculiar elegance, and of no incon- 

 siderable power. It consisted in supposing the thing 

 as already done, the problem solved, or the truth of 

 the theorem established ; and from thence it reasoned 

 until something was found, some point reached, by 

 pursuing steps each one of which led to the next, and 

 by only assuming things which were already known 



