SIMSON. 143 



every reason to consider the restored work as greatly 

 superior to the lost original. 



The history of this excellent treatise shows in a 

 striking manner the cautious and modest nature of its 

 author. He had completed it in 1738; but, unsatisfied 

 with it, he kept it by him for eight years. He could 

 not bring himself to think that he had given the 

 "ipsissimae propositiones of Apollonius in the very 

 order and spirit of the original work." He was then 

 persuaded to let the book appear, and it was pub- 

 lished in 1746. His former scruples and alarms re- 

 curred; he stopped the publication; he bought up the 

 copies that had been sold ; he kept them three years 

 longer by him; and it was only in 1749 that the work 

 really appeared. Thus had a geometrician complied 

 with the rule prescribed by Horace for those who 

 have no standard by which to estimate with exactness 

 the merit of their writings. 



In the meantime he had extended his researches 

 into other parts of the subject. Among the rest he 

 had restored and greatly extended the work on Deter- 

 minate Section, or the various propositions respecting 

 the properties of the squares and rectangles of seg- 

 ments of lines passing through given points. There 

 is no doubt that the prolixity, however elegant, with 

 which the ancients treated this subject, is somewhat 

 out of proportion to its importance ; and as it is pecu- 

 liarly adapted to the algebraical method, presenting, 

 indeed, little difficulty to the analyst, the loss of the 

 Pergaean treatise is the less to be deplored, and its re- 

 storation was the less to be desired. Apollonius had 

 even thought it expedient to give a double set of solu- 

 tions ; one by straight lines, the other by semicircles. 

 Dr. Simson's restoration is most full, certainly, and 

 contains many and large additions of his own. It fills 

 above three hundred quarto pages. His predecessors 

 had been Snellius, whose attempt, published in 1608, 

 was universally allowed to be a failure ; and Anderson, 



